PC5271 wiki - User contributions [en]

Laser Distance Measurer

2025-04-29T11:54:56Z

Jonathan: /* Results */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5 and the accopmanying circuit diagram.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that (when the function output is on) visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode on the linear translation stage and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens. (Note: the LED--and the detector below--should be mounted on the translation stage via postholders so that their heights are adjustable.)

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position on the translation stage such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Recording the Time Delay vs. Distance Mapping====
Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. With the light from LED hitting the photodetector, observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve.

With the apparatus in place, the following procedure outlines how to measure the time delay and the corresponding distance:

# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–3 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–3''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:reference.png|700px]]
|-
| '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 ns, which, when calculated, gives about 6-9 m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80 cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410 cm. This would lead to an additional delay of 13.7 ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10 cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5 cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:47:02Z

Jonathan: /* Results */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5 and the accopmanying circuit diagram.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that (when the function output is on) visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode on the linear translation stage and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens. (Note: the LED--and the detector below--should be mounted on the translation stage via postholders so that their heights are adjustable.)

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position on the translation stage such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Recording the Time Delay vs. Distance Mapping====
Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. With the light from LED hitting the photodetector, observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve.

With the apparatus in place, the following procedure outlines how to measure the time delay and the corresponding distance:

# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–3 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–3''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:reference.png|700px]]
|-
| '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 ns, which, when calculated, gives about 6-9 m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80 cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410 cm. This would lead to an additional delay of 13.7 ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:46:46Z

Jonathan: /* Results */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5 and the accopmanying circuit diagram.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that (when the function output is on) visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode on the linear translation stage and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens. (Note: the LED--and the detector below--should be mounted on the translation stage via postholders so that their heights are adjustable.)

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position on the translation stage such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Recording the Time Delay vs. Distance Mapping====
Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. With the light from LED hitting the photodetector, observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve.

With the apparatus in place, the following procedure outlines how to measure the time delay and the corresponding distance:

# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–3 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–3''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:reference.png|700px]]
|-
| '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 ns, which, when calculated, gives about 6-9 m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80 cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7 ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:45:46Z

Jonathan: /* Experiment Setup */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5 and the accopmanying circuit diagram.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that (when the function output is on) visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode on the linear translation stage and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens. (Note: the LED--and the detector below--should be mounted on the translation stage via postholders so that their heights are adjustable.)

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position on the translation stage such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Recording the Time Delay vs. Distance Mapping====
Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. With the light from LED hitting the photodetector, observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve.

With the apparatus in place, the following procedure outlines how to measure the time delay and the corresponding distance:

# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–3 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–3''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:reference.png|700px]]
|-
| '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:45:14Z

Jonathan: /* Results */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that (when the function output is on) visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode on the linear translation stage and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens. (Note: the LED--and the detector below--should be mounted on the translation stage via postholders so that their heights are adjustable.)

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position on the translation stage such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Recording the Time Delay vs. Distance Mapping====
Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. With the light from LED hitting the photodetector, observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve.

With the apparatus in place, the following procedure outlines how to measure the time delay and the corresponding distance:

# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–3 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–3''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:reference.png|700px]]
|-
| '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:44:24Z

Jonathan: /* Recording the Time Delay vs. Distance Mapping */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that (when the function output is on) visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode on the linear translation stage and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens. (Note: the LED--and the detector below--should be mounted on the translation stage via postholders so that their heights are adjustable.)

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position on the translation stage such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Recording the Time Delay vs. Distance Mapping====
Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. With the light from LED hitting the photodetector, observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve.

With the apparatus in place, the following procedure outlines how to measure the time delay and the corresponding distance:

# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–3 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–3''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:43:12Z

Jonathan: /* Experiment Setup */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that (when the function output is on) visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode on the linear translation stage and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens. (Note: the LED--and the detector below--should be mounted on the translation stage via postholders so that their heights are adjustable.)

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position on the translation stage such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Recording the Time Delay vs. Distance Mapping====
Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. With the light from LED hitting the photodetector, observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following procedure outlines how to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:42:26Z

Jonathan: /* Experiment Setup */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that (when the function output is on) visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode on the linear translation stage and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position on the translation stage such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Recording the Time Delay vs. Distance Mapping====
(Note: the detector and LED should be mounted on the translation stage via postholders so that their heights are adjustable.)
Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. With the light from LED hitting the photodetector, observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following procedure outlines how to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:32:45Z

Jonathan: /* Equipment List */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Linear translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring that the beam returning to the detector at all positions is aligned along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:32:24Z

Jonathan: /* Equipment List */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetectorwith an amplifier
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring that the beam returning to the detector at all positions is aligned along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:32:07Z

Jonathan: /* Detection and Amplification Circuit Configuration */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, mount the Hamamatsu S5971 silicon photodiode to a position such that it can detect the light signal. To amplify the signal linearly without saturation, the detector output is connected to a high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the detector/amplifier combination to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring that the beam returning to the detector at all positions is aligned along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:29:59Z

Jonathan: /* Experimental Work */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experiment Setup==
For a visual of the completed setup, please refer to figure 5.

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring that the beam returning to the detector at all positions is aligned along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T11:27:38Z

Jonathan: /* Laser Modulation and System Initialisation */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 1 to 3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring that the beam returning to the detector at all positions is aligned along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:data1.png|600px]]
| [[File:data2.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

We can calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples. This will be the <math>\delta t_i</math>.

Then to calculate uncertainty for difference in delay: <math>\delta t = \sqrt{(\delta t_1)^2 + (\delta t_2)^2}</math>

Finally, the uncertainty of calculated difference distance from delay time: <math>\delta d = d \times \sqrt{\bigl(\frac{\delta t}{t_1 - t_2}\bigr)^2}</math>

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:final1.png|600px]]
| [[File:final2.png|600px]]
|-
| '''Table 5.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Table 6.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. Furthermore, the values obtained go beyond the calculated uncertainties in Table 5 and 6. This shows that the main source of error was experimental, likely due to the challenges mentioned such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T10:09:02Z

Jonathan: /* Time Delay vs. Distance Mapping */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring that the beam returning to the detector at all positions is aligned along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. If we calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples.

This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T10:03:02Z

Jonathan: /* Detection and Amplification Circuit Configuration */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; compare it to the reference signal from the function generator (Channel 1) as the modulation phase reference; the two signals should be out of phase.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. If we calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples.

This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T10:02:26Z

Jonathan: /* Laser Modulation and System Initialisation */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Use a T-section to connect the oscilloscope (same port used by the function generator) to the laser LED, and verify that visible light is emitted from the laser. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. If we calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples.

This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T10:00:44Z

Jonathan: /* Laser Modulation and System Initialisation */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the function generator to the oscilloscope and verify that the signal output from the function generator can be observed on the oscilloscope. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode, and connect the photodiode to another channel the oscilloscope.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. If we calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples.

This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T09:59:11Z

Jonathan: /* Laser Modulation and System Initialisation */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Connect the DC power supply set to constant voltage (5.0 V in this setup) to the photodiode.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. If we calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples.

This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T09:57:30Z

Jonathan: /* Optical Alignment */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use the aspheric lens to collimate and focus the beam onto the reflective target surface. The lens should be placed in a cage plate and mounted in a position such that the distance between the lens and the LED is the focal length of the lens.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. If we calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples.

This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T09:56:14Z

Jonathan: /* Equipment List */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens (model used: Thorlabs F220FC-B, f = 10.99 mm)
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. If we calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples.

This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T09:49:56Z

Jonathan: /* Equipment List */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

For our experiment, using an oscilloscope, you can measure the phase delay between generated wave and reflected wave. This makes the task of finding the distance based on phase delay much simpler. <math>\text{Calculated Distance from phase delay} = \delta t \times c</math> where c is the speed of light.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Aspheric lens to mount on the LED and collimate the light beam
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# '''Repeat steps 1–4 for different distances''' on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and '''repeat steps 1–4''' for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. The length of the BNC cables was 410cm. This would lead to an additional delay of 13.7ns. We hypothesise that the rest of the delay is due to the internal wiring functions of the oscilloscope.

To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path. The beam spot on the detector is shown in Figure 9.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
# There might have also been a possibility of saturating our photodetector, as our beam was incident directly on it. We tried to reduce the input voltage to the LED, but reducing the voltage below 3V led to no signal appearing on the oscilloscope.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}

Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. The uncertainty of the meter ruler was <math>\pm 0.1cm</math> and the uncertainty of the oscilloscope was <math>\pm 0.001ns</math>. If we calculate the uncertainty using the standard error which is <math>\frac{\sigma}{\sqrt{n}}</math> where <math>\sigma</math> is the standard deviation of the raw data and n is the number of samples.

This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T08:05:34Z

Jonathan: /* References */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

Laser Distance Measurer

2025-04-29T08:05:06Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

[4] Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]

[5] Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]

[6] Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]

Laser Distance Measurer

2025-04-29T08:00:06Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Note: Advantages of Phase-delay measurement ===

The phase-shift measurement method is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required[4]. Because this technique extracts distance from the phase of a continuous waveform rather than from absolute travel time or geometry, it can achieve high precision with modest electronic bandwidths.
The use of a continuous waveform allows the transmitter to run at lower power and simpler circuitry, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms[5], and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling[6].

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

[4] Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]

[5] Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]

[6] Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]

Laser Distance Measurer

2025-04-29T07:53:58Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) measurement[1]. Here we will construct an apparatus according to the third approach.

=== Mathematical Background on Phase-Shift Distance Measurement ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Note: Advantages of Phase-delay measurement ===

The phase-shift measurement method is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required[4].
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms[5], and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling[6].

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

[4] Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]

[5] Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]

[6] Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]

Laser Distance Measurer

2025-04-29T07:39:21Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based distance measurement is a technique to measure distances remotely when on-site measurement becomes inconvenient. This has many applications such as autonomous driving, radar, and precision manufacturing. The working principle of using lasers to measure such distances can generally be categorised into one of three approaches: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging[1]. Here we will construct an apparatus according to the third approach.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required[4].
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms[5], and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling[6].

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of '''10cm''' was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of '''46.5cm'''was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

[4] Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]

[5] Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]

[6] Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]

Laser Distance Measurer

2025-04-29T07:18:24Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing. Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging[1].
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required[4].
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms[5], and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling[6].

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|650px]]
| [[File:finalwithmirror.png|650px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

[4] Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]

[5] Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]

[6] Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]

Laser Distance Measurer

2025-04-29T07:17:56Z

Jonathan: /* References */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing. Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging[1].
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required[4].
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms[5], and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling[6].

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|650px]]
| [[File:finalwithmirror.png|650px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]

[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]

[4] Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]

[5] Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]

[6] Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]

Laser Distance Measurer

2025-04-29T07:17:38Z

Jonathan: /* Reference */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing. Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging[1].
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required[4].
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms[5], and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling[6].

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|650px]]
| [[File:finalwithmirror.png|650px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]
[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]
[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]
[4] Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]
[5] Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]
[6] Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]

Laser Distance Measurer

2025-04-29T07:17:18Z

Jonathan: /* References */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing. Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging[1].
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required[4].
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms[5], and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling[6].

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==
[1]Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

Laser Distance Measurer

2025-04-29T07:16:49Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing. Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging[1].
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light[2].
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math>[3]

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required[4].
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms[5], and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling[6].

== References ==
[1] Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]
[2] Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]
[3] Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]
[4] Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]
[5] Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]
[6] Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:finalwithoutmirror.png|600px]]
| [[File:finalwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==
[1]Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

Laser Distance Measurer

2025-04-29T07:16:30Z

Jonathan: /* References */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref name="Blais2004" />
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref name="PaschottaRP" />
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref name="Wu2022" />
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref name="Li2023" />

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref name="Park2018" />
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms,<ref name="Liu2024" />
and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.<ref name="Ho1998" />

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==
[1]Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

Laser Distance Measurer

2025-04-29T07:11:49Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref name="Blais2004" />
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref name="PaschottaRP" />
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref name="Wu2022" />
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref name="Li2023" />

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref name="Park2018" />
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms,<ref name="Liu2024" />
and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.<ref name="Ho1998" />

== References ==
<references>
<ref name="Blais2004">Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524 DOI]</ref>
<ref name="PaschottaRP">Paschotta, R. ''Phase Shift Method for Distance Measurements,'' RP Photonics Encyclopedia. [https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html]</ref>
<ref name="Wu2022">Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]</ref>
<ref name="Li2023">Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]</ref>
<ref name="Park2018">Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]</ref>
<ref name="Liu2024">Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]</ref>
<ref name="Ho1998">Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]</ref>
</references>

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==
[1]Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

Laser Distance Measurer

2025-04-29T07:09:00Z

Jonathan: /* Reference */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref>
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref>Paschotta, R. ''Phase Shift Method for Distance Measurements,'' RP Photonics Encyclopedia. [https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html]</ref>
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref>Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]</ref>
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref>Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]</ref>

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref>Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]</ref>
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms,<ref>Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]</ref>
and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.<ref>Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]</ref>

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==
[1]Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]

Laser Distance Measurer

2025-04-29T07:08:36Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref>
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref>Paschotta, R. ''Phase Shift Method for Distance Measurements,'' RP Photonics Encyclopedia. [https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html]</ref>
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref>Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]</ref>
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref>Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]</ref>

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref>Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]</ref>
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms,<ref>Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]</ref>
and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.<ref>Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]</ref>

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T07:08:05Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref></ref>
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref>Paschotta, R. ''Phase Shift Method for Distance Measurements,'' RP Photonics Encyclopedia. [https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html]</ref>
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref>Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]</ref>
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref>Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]</ref>

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref>Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]</ref>
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms,<ref>Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]</ref>
and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.<ref>Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]</ref>

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T07:07:31Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref>Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]</ref>
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref>Paschotta, R. ''Phase Shift Method for Distance Measurements,'' RP Photonics Encyclopedia. [https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html]</ref>
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref>Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]</ref>
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref>Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]</ref>

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref>Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]</ref>
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms,<ref>Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]</ref>
and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.<ref>Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]</ref>

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T07:07:07Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref></ref>
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref>Paschotta, R. ''Phase Shift Method for Distance Measurements,'' RP Photonics Encyclopedia. [https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html]</ref>
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref>Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]</ref>
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref>Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]</ref>

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref>Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]</ref>
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms,<ref>Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]</ref>
and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.<ref>Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]</ref>

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T07:06:14Z

Jonathan: /* References */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref>Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524]</ref>
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref>Paschotta, R. ''Phase Shift Method for Distance Measurements,'' RP Photonics Encyclopedia. [https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html]</ref>
The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref>Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]</ref>
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref>Li, Y. (2023). ''Phase-Modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]</ref>

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref>Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]</ref>
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms,<ref>Liu, M. (2024). ''Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR.'' Sensors, 24(5), 1617. [https://www.mdpi.com/1424-8220/24/5/1617]</ref>
and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.<ref>Ho, T. (1998). ''Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal.'' Sensors and Actuators A, 66(1–3), 110–115. [https://doi.org/10.1016/S0924-4247(97)01716-3]</ref>

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T07:05:59Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== References ==
<references />

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T06:58:18Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== Background and Theory ==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref>Blais, F. (2004). ''Review of 20 Years of Range Sensor Development.'' Journal of Laser Applications, 17(4), 208–220. [https://doi.org/10.2351/1.1848524 DOI]</ref> Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref>Paschotta, R. ''Phase Shift Method for Distance Measurements,'' RP Photonics Encyclopedia. [https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html]</ref> The present work adopts the third approach. Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

=== Phase-Shift Ranging Theory ===
When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi = \frac{4\pi d}{\lambda_m}, \qquad \lambda_m = \frac{c}{f_m}</math>,

where ''d'' is the one-way distance and ''c'' is the speed of light.<ref>Wu, D. (2022). ''Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation.'' Photonics, 9(9), 603. [https://www.mdpi.com/2304-6732/9/9/603]</ref>
Solving for ''d'' gives

<math>d = \frac{\lambda_m \Delta\phi}{4\pi} = \frac{c\Delta\phi}{4\pi f_m}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_\text{max} = \frac{c}{2f_m}.</math><ref>Li, Y. (2023). ''Phase-modulated Continuous-Wave Coherent Ranging Method for High-Precision Measurement.'' Optics Express, 31(4), 6514–6524. [https://doi.org/10.1364/OE.474931]</ref>

For <math>f_m = 10~\text{MHz}</math>, <math>d_\text{max} \approx 15~\text{m}</math>, adequate for laboratory-scale demonstrations.

=== Phase-delay measurement offers clear advantages for distance determination ===
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref>Park, J. (2018). ''Multi-tone Modulated Continuous-Wave LiDAR,'' Proceedings of SPIE. [https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf]</ref>
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

== References ==
<references />

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T06:18:49Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T06:17:48Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.<ref name="Blais2004">{{cite journal |last=Blais |first=F. |title=Review of 20 Years of Range Sensor Development |journal=Journal of Laser Applications |year=2004 |volume=17 |issue=4 |pages=208–220 |doi=10.2351/1.1848524}}</ref>

Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.<ref name="Paschotta">{{cite web |last=Paschotta |first=R. |title=Phase Shift Method for Distance Measurements |url=https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html |website=RP-Photonics Encyclopedia |access-date=2025-04-29}}</ref>

When a CW laser is intensity-modulated at frequency <math>f_m</math>, round-trip propagation to a target introduces a phase delay … (formula)。<ref name="Wu2022">{{cite journal |last=Wu |first=D. |title=Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation |journal=Photonics |year=2022 |volume=9 |issue=9 |pages=603 |doi=10.3390/photonics9090603}}</ref><ref name="Ho1998">{{cite journal |last=Ho |first=T. |title=Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal |journal=Sensors and Actuators A |year=1998 |volume=66 |issue=1-3 |pages=110–115 |doi=10.1016/S0924-4247(97)01716-3}}</ref>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is … (formula)。<ref name="Li2023">{{cite journal |last=Li |first=Y. |title=Phase-modulated Continuous-Wave Coherent Ranging for High-Precision Measurement |journal=Optics Express |year=2023 |volume=31 |issue=4 |pages=6514–6524 |doi=10.1364/OE.474931}}</ref>

Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.<ref name="Park2018">{{cite conference |last=Park |first=J. |title=Multi-Tone Modulated Continuous-Wave LiDAR |book-title=Proceedings of SPIE |year=2018 |url=https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf}}</ref><ref name="Liu2024">{{cite journal |last=Liu |first=M. |title=Deep Neural Network-Based Phase-Modulated CW LiDAR |journal=Sensors |year=2024 |volume=24 |issue=5 |pages=1617 |doi=10.3390/s24051617}}</ref>

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-29T06:12:07Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based distance measurement is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our '''reference distance'''. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as '''distance difference'''. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an '''absolute''' delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the project's concept was fairly straightforward, the yielded results were not precise within the instruments' uncertainty. This points to experimental errors, such as the lack of a focusing mirror, which caused fluctuations in the delay. The data obtained from calculating the distance difference is ~20-30cm higher than the manually measured distance, which makes it quite inaccurate. To reduce the inaccuracies, the measured distance difference can be larger, in the order of meters. This would mean that the changes in the delay would be in the order of a few nanoseconds rather than a few tenths of a nanosecond, reducing the error from the fluctuation. However, aligning the LED onto the detector would be even more difficult and might cause more fluctuations on the delay if there is no focusing lens.

==Improvements and Future Work==
# Install a focusing lens for the photodetector to reduce the fluctuation of the time delay on the oscilloscope.
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.
# Longer translating stage for longer distance measurement

==Reference==

Laser Distance Measurer

2025-04-28T16:08:28Z

Jonathan: /* Reference */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

====Methodological Outline====
1.Modulation：Tektronix AFG1022 supplies a 10 MHz, 0–3.1 Vpp square wave to drive a 650 nm diode laser.

2.Beam delivery：The beam is collimated (''f'' = 20 mm lens), reflected from a mirror on a precision translation stage, and returned through a 650 nm ± 5 nm band-pass filter.

3.Detection：A Hamamatsu S5971 photodiode converts the echo to an electrical signal; a >100 MHz, 40 dB pre-amplifier conditions the signal.

4.Synchronous sampling：Oscilloscope channel 2 (echo) is compared with channel 1 (reference) to obtain the temporal delay <math>\Delta t</math>; phase delay follows as <math>\Delta\phi = 2\pi f_{m}\Delta t</math>.

5.Calibration & scanning:Static points (0–80 cm, 10 cm steps) yield a delay-distance curve; continuous stage motion tests linearity and temporal resolution.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our "reference" distance. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as "distance difference". We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an "absolute" delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the concept of the project was fairly straightforward, the yielded results were not precise within the uncertainty. This points to experimental errors such as the lack of a focusing mirror which caused fluctuations in the delay.

==Improvements and Future Work==
# Install a focusing lens for the photodetector
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.

==Reference==

Laser Distance Measurer

2025-04-28T16:07:49Z

Jonathan:

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

====Methodological Outline====
1.Modulation：Tektronix AFG1022 supplies a 10 MHz, 0–3.1 Vpp square wave to drive a 650 nm diode laser.

2.Beam delivery：The beam is collimated (''f'' = 20 mm lens), reflected from a mirror on a precision translation stage, and returned through a 650 nm ± 5 nm band-pass filter.

3.Detection：A Hamamatsu S5971 photodiode converts the echo to an electrical signal; a >100 MHz, 40 dB pre-amplifier conditions the signal.

4.Synchronous sampling：Oscilloscope channel 2 (echo) is compared with channel 1 (reference) to obtain the temporal delay <math>\Delta t</math>; phase delay follows as <math>\Delta\phi = 2\pi f_{m}\Delta t</math>.

5.Calibration & scanning:Static points (0–80 cm, 10 cm steps) yield a delay-distance curve; continuous stage motion tests linearity and temporal resolution.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our "reference" distance. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can refer to this as "distance difference". We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an "absolute" delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average Distance Difference from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of Calculated Average Distance Difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the concept of the project was fairly straightforward, the yielded results were not precise within the uncertainty. This points to experimental errors such as the lack of a focusing mirror which caused fluctuations in the delay.

==Improvements and Future Work==
# Install a focusing lens for the photodetector
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.

==Reference==
<references>
{{cite journal
|last1 = Wu
|first1 = D.
|title = Phase-Shift Laser Ranging Technology Based on Multi-Frequency Modulation
|journal = Photonics
|year = 2022
|volume = 9
|issue = 9
|pages = 603
|doi = 10.3390/photonics9090603
}} 

{{cite journal
|last1 = Guo
|first1 = X.
|title = Frequency-modulated continuous-wave laser ranging using low-duty-cycle LFM signals
|journal = Optics Letters
|year = 2021
|volume = 46
|issue = 2
|pages = 258–261
}} 

{{cite journal
|last1 = Li
|first1 = Y.
|title = Phase-modulated continuous-wave coherent ranging method for high-precision measurement
|journal = Optics Express
|year = 2023
|volume = 31
|issue = 4
|pages = 6514–6524
}} 

{{cite web
|url = https://www.rp-photonics.com/phase_shift_method_for_distance_measurements.html
|title = Phase Shift Method for Distance Measurements
|last = Paschotta
|first = R.
|website = RP Photonics Encyclopedia
|access-date = 29 April 2025
}} 

{{cite journal
|last1 = Zhen
|first1 = D.
|last2 = Chen
|first2 = W.
|title = A laser ranging method with high precision and large range in high speed based on phase measurement
|journal = Journal of Optoelectronics & Laser
|year = 2015
|volume = 26
|pages = 303–308
}} 

{{cite conference
|last1 = Park
|first1 = J.
|title = Multi-tone Modulated Continuous-Wave LiDAR
|book-title = Proceedings of SPIE
|year = 2018
|url = https://apdsl.eng.uci.edu/RecentConferences/Multi-tone%20modulated%20continuous-wave%20lidar.pdf
}} 

{{cite journal
|last1 = Ho
|first1 = T.
|title = Error Analysis of Phase-Shift Laser Rangefinder with High-Level Signal
|journal = Sensors and Actuators A
|year = 1998
|volume = 66
|issue = 1–3
|pages = 110–115
}} 

{{cite journal
|last1 = Liu
|first1 = M.
|title = Deep Neural Network-Based Phase-Modulated Continuous-Wave LiDAR
|journal = Sensors
|year = 2024
|volume = 24
|issue = 5
|pages = 1617
|doi = 10.3390/s24051617
}} 
</references>

Laser Distance Measurer

2025-04-28T13:07:52Z

Jonathan: /* Methodological Outline */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

====Methodological Outline====
1.Modulation：Tektronix AFG1022 supplies a 10 MHz, 0–3.1 Vpp square wave to drive a 650 nm diode laser.

2.Beam delivery：The beam is collimated (''f'' = 20 mm lens), reflected from a mirror on a precision translation stage, and returned through a 650 nm ± 5 nm band-pass filter.

3.Detection：A Hamamatsu S5971 photodiode converts the echo to an electrical signal; a >100 MHz, 40 dB pre-amplifier conditions the signal.

4.Synchronous sampling：Oscilloscope channel 2 (echo) is compared with channel 1 (reference) to obtain the temporal delay <math>\Delta t</math>; phase delay follows as <math>\Delta\phi = 2\pi f_{m}\Delta t</math>.

5.Calibration & scanning:Static points (0–80 cm, 10 cm steps) yield a delay-distance curve; continuous stage motion tests linearity and temporal resolution.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our "reference" distance. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an "absolute" delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average distance from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average distance from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of calculated distance difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of calculated distance difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the concept of the project was fairly straightforward, the yielded results were not precise within the uncertainty. This points to experimental errors such as the lack of a focusing mirror which caused fluctuations in the delay.

==Improvements and Future Work==
# Install a focusing lens for the photodetector
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.

Laser Distance Measurer

2025-04-28T13:07:23Z

Jonathan: /* Phase-delay measurement offers clear advantages for distance determination */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

====Methodological Outline====
1.Modulation：Tektronix AFG1022 supplies a 10 MHz, 0–3.1 Vpp square wave to drive a 650 nm diode laser.
2.Beam delivery：The beam is collimated (''f'' = 20 mm lens), reflected from a mirror on a precision translation stage, and returned through a 650 nm ± 5 nm band-pass filter.
3.Detection：A Hamamatsu S5971 photodiode converts the echo to an electrical signal; a >100 MHz, 40 dB pre-amplifier conditions the signal.
4.Synchronous sampling：Oscilloscope channel 2 (echo) is compared with channel 1 (reference) to obtain the temporal delay <math>\Delta t</math>; phase delay follows as <math>\Delta\phi = 2\pi f_{m}\Delta t</math>.
5.Calibration & scanning:Static points (0–80 cm, 10 cm steps) yield a delay-distance curve; continuous stage motion tests linearity and temporal resolution.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our "reference" distance. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an "absolute" delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average distance from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average distance from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of calculated distance difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of calculated distance difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the concept of the project was fairly straightforward, the yielded results were not precise within the uncertainty. This points to experimental errors such as the lack of a focusing mirror which caused fluctuations in the delay.

==Improvements and Future Work==
# Install a focusing lens for the photodetector
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.

Laser Distance Measurer

2025-04-28T13:06:14Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: pulsed time-of-flight (ToF), optical triangulation and phase-shift continuous-wave (CW) ranging.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

These merits justify a bottom-up exploration that reveals how modulation linearity, detector bandwidth and amplifier noise ultimately limit accuracy.

====Methodological Outline====
1.Modulation：Tektronix AFG1022 supplies a 10 MHz, 0–3.1 Vpp square wave to drive a 650 nm diode laser.
2.Beam delivery：The beam is collimated (''f'' = 20 mm lens), reflected from a mirror on a precision translation stage, and returned through a 650 nm ± 5 nm band-pass filter.
3.Detection：A Hamamatsu S5971 photodiode converts the echo to an electrical signal; a >100 MHz, 40 dB pre-amplifier conditions the signal.
4.Synchronous sampling：Oscilloscope channel 2 (echo) is compared with channel 1 (reference) to obtain the temporal delay <math>\Delta t</math>; phase delay follows as <math>\Delta\phi = 2\pi f_{m}\Delta t</math>.
5.Calibration & scanning:Static points (0–80 cm, 10 cm steps) yield a delay-distance curve; continuous stage motion tests linearity and temporal resolution.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our "reference" distance. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an "absolute" delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average distance from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average distance from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of calculated distance difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of calculated distance difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the concept of the project was fairly straightforward, the yielded results were not precise within the uncertainty. This points to experimental errors such as the lack of a focusing mirror which caused fluctuations in the delay.

==Improvements and Future Work==
# Install a focusing lens for the photodetector
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.

Laser Distance Measurer

2025-04-28T13:05:49Z

Jonathan: /* Background and Theory */

{{Short description|Laser distance measurement using time‐of‐flight}}
==Group Members==
Arya Chowdhury, Liu Sijin, Jonathan Wong

==Background and Theory==

Laser-based ranging is an indispensable branch of modern optical metrology, underpinning industrial inspection, robotic navigation, 3-D scene reconstruction, autonomous-vehicle perception and precision manufacturing.
Three mainstream principles are generally distinguished: **pulsed time-of-flight (ToF)**, **optical triangulation** and **phase-shift continuous-wave (CW) ranging**.
The present work adopts the third approach.
Although commercial phase-shift rangers exist, rebuilding the technique from first principles clarifies its physical foundations, intrinsic error sources and ultimate performance limits, thereby guiding application-specific optimisation.

====Phase-Shift Ranging Theory====
When a CW laser is intensity-modulated at frequency <math>f_{m}</math>, round-trip propagation to a target introduces a phase delay

<math>\Delta\phi \;=\; \frac{4\pi d}{\lambda_{m}}, \qquad
\lambda_{m} \;=\; \frac{c}{f_{m}},</math>

where ''d'' is the one-way distance and ''c'' is the speed of light.
Solving for ''d'' gives

<math>d \;=\; \frac{\lambda_{m}\,\Delta\phi}{4\pi}
\;=\; \frac{c\,\Delta\phi}{4\pi f_{m}}.</math>

Because phase is measured modulo <math>2\pi</math>, the maximum unambiguous range is

<math>d_{\text{max}} \;=\; \frac{c}{2f_{m}}.</math>

For <math>f_{m}=10\;\text{MHz}</math>, <math>d_{\text{max}}\approx 15\;\text{m}</math>, adequate for laboratory-scale demonstrations.

====Phase-delay measurement offers clear advantages for distance determination====
Phase-shift ranging is preferred over pulsed ToF and optical triangulation whenever sub-millimetre accuracy, compact hardware and real-time operation are simultaneously required.
Because the technique extracts distance from the phase of a continuous, MHz-rate modulation rather than from absolute travel time or geometric baselines, it can achieve high precision with modest electronic bandwidths and without bulky optical assemblies.
The use of continuous-wave illumination allows the transmitter to run at low peak power, simplifying driver circuitry and easing eye-safety constraints, while the reliance on differential phase makes the measurement intrinsically insensitive to slow amplitude drifts, laser-power fluctuations or partial signal obscuration.
These attributes enable lightweight, low-cost sensor heads that are well suited to embedded or mobile platforms, and they motivate a bottom-up investigation of how modulation linearity, detector bandwidth and amplifier noise ultimately set the achievable accuracy ceiling.

These merits justify a bottom-up exploration that reveals how modulation linearity, detector bandwidth and amplifier noise ultimately limit accuracy.

====Methodological Outline====
1.Modulation：Tektronix AFG1022 supplies a 10 MHz, 0–3.1 Vpp square wave to drive a 650 nm diode laser.
2.Beam delivery：The beam is collimated (''f'' = 20 mm lens), reflected from a mirror on a precision translation stage, and returned through a 650 nm ± 5 nm band-pass filter.
3.Detection：A Hamamatsu S5971 photodiode converts the echo to an electrical signal; a >100 MHz, 40 dB pre-amplifier conditions the signal.
4.Synchronous sampling：Oscilloscope channel 2 (echo) is compared with channel 1 (reference) to obtain the temporal delay <math>\Delta t</math>; phase delay follows as <math>\Delta\phi = 2\pi f_{m}\Delta t</math>.
5.Calibration & scanning:Static points (0–80 cm, 10 cm steps) yield a delay-distance curve; continuous stage motion tests linearity and temporal resolution.

==Equipment List==
# Oscilloscope
# Function generator that can output square wave signal (model used: Tektronix AFG1022)
# DC power supply for photodetector (model used: Keithley 2231A-30-3)
# Hamamatsu S5971 silicon photodetector
# 650 nm (red) LED
# Collimating lens to mount on the LED
# Mirror
# Translation stage
# Optical breadboard, postholders and screws
# Ruler or measuring tape
# BNC cables

==Experimental Work==

====Laser Modulation and System Initialisation====
Configure the function generator to output a 10 MHz square wave with an amplitude of 0–3.1 V (High level: 3.1 V, Low level: 1.0 V, output impedance: 50 Ω) to modulate the laser diode. Use the DC power supply to provide 5.0 V to the laser driver circuit, with a current limit of 30 mA. Verify the laser beam stability to avoid multimode noise or thermal drift that could distort the modulation waveform.

====Optical Alignment====
Mount the 650 nm laser diode and use an aspheric lens to collimate and focus the beam onto the reflective target surface.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserwithlens1.jpeg|300px|alt=Laser with lens 1]]
| [[File:laserwithlens2.jpeg|300px|alt=Laser with lens 2]]
|-
| '''Figure 1.''' Front view of collimating lens for laser diode
| '''Figure 2.''' Side view of collimating lens for laser diode
|}

====Detection and Amplification Circuit Configuration====
For the photodetector, use the Hamamatsu S5971 silicon photodiode to detect the reflected light signal. To amplify the signal linearly without saturation, connect the detector output to a matched high-speed preamplifier (bandwidth >100 MHz, gain ∼10³–10⁵). Connect the amplifier output to Channel 2 of a digital oscilloscope; connect the reference signal from the function generator to Channel 1 as the modulation phase reference.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:laserdiode.jpeg|300px|alt=Laser diode and detector]]
|-
| '''Figure 3.''' Hamamatsu S5971 silicon photodiode with amplifier
|}

====Time Delay vs. Distance Mapping====
Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable. Turn on the LED and ensure that the beam is collimated by adjusting the distance of the lens to the LED. Incident the LED onto the photodetector and observe the function generated on the oscilloscope. Use the oscilloscope’s cursor measurement function to determine the relative time delay Δt between the modulation reference signal (Channel 1) and the return signal (Channel 2). Correlate the measured delay values with corresponding distances to establish the system’s delay–distance response curve. The following are the steps carried out to measure the time delay and the corresponding distance:

# Fix the LED source and the photodetector on a linear translation stage, ensuring proper alignment for the beam return to the detector at all positions along the translation stage; the detector and the laser diode were mounted on a postholder so that the height of the detectors was adjustable.
# Use a meter ruler to mark the distance along the translation stage.
# Move the LED source to the marked positions (e.g. 30 cm from detector) and adjust the beam until it is centralised on the photodetector.
# Measure the time delay on the oscilloscope. Record the minimum, maximum and mean time delay—take three readings per distance and average them.
# Repeat steps 1–4 for different distances on the translation stage.
# Insert a mirror in the setup to act as the “object we are trying to measure the distance of”, so that the beam path is reflected off the mirror to the photodetector.
# Measure the total path length manually and repeat steps 1–4 for each mirror position.

[[File:Laser_Diode_Experiment_setup_final.png|500px|thumb|centre|Schematic of experiment setup (without mirror). If the photodiode is in line with and can receive light from the LED, two waveforms (one from the source LED and one from the photodiode) will be shown on the oscilloscope.]]

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:nomirror.jpeg|500px|alt=Setup without mirror]]
|-
| '''Figure 4.''' Measurement experimental setup without mirror: LED and photodetector on translation stage.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:withmirror.jpeg|700px|alt=Setup with mirror]]
|-
| '''Figure 5.''' Measurement experimental setup with mirror acting as the “object.”
|}

==Results==
{| style="border:none; margin:auto; text-align:center;"
|+ '''Figure 6.''' Delay between the function generator and the received signal by the photodetector on the oscilloscope. Green graph represents the function generated by the function generator and the yellow graph represents the function produced from received the laser beam by the detector.
|-
| [[File:reference.png|700px]]
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Distance_of_LED_to_Detector_vs_Measured_Delay_TIme_on_Oscilloscope_WITHOUT_Mirror.jpeg|500px]]
| [[File:delaytimewithmirror.jpeg|500px]]
|-
| '''Table 1.''' Measured delay time vs manually measured distance between LED and photodetector
| '''Table 2.''' Measured delay time vs manually measured distance with mirror acting as the “object.”
|}

The measured delay time is in the order of 20-30 nanoseconds, which, when calculated, gives about 6-9m of distance. However, our incremental changes in the distance between the LED and the photodetector were in the order of 10-80cm. Hence, it was evident that this additional delay time was occurring due to all the cables attached to the oscilloscope and function generation and the distance between the laser and the detector. To account for this, we took the shortest distance as our "reference" distance. The difference between the successive measured distances and the shortest distance gives us the "absolute" distance. We can do this for the measured delay time as well. Take the delay time for the shortest manually measured distance and subtract it from the successive delay times to get an "absolute" delay time. Another method we thought of was simply plotting a linear plot of manually measured distance vs the delay time and obtaining the y-intercept, which would be the additional delay time due to the system and the cables. One could then subtract this additional delay time from the system from each measured delay time. However, when we measured the gradient of this linear plot on multiple days, the gradient was slightly different each time the measurements were carried out. Hence, we decided to adopt the former approach.

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:calculatedwithoutmirror.jpeg|600px]]
| [[File:calculatedwithmirror.jpeg|700px]]
|-
| '''Table 3.''' Calculated Average distance from delay time vs Manually measured distance between LED and photodetector. Separation distance of 10cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
| '''Table 4.''' Calculated Average distance from delay time vs Manually measured distance between LED and photodetector with the mirror acting as the "object". Separation distance of 46.5cm was taken as the "reference" distance and the successive distances were subtracted from it to give "absolute" values.
|}

{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:Graphwithoutmirror.png|600px]]
| [[File:Graphwithmirror.png|600px]]
|-
| '''Figure 7.''' Graph of calculated distance difference from delay time vs manually measured distance difference between LED and photodetector without mirror.
| '''Figure 8.''' Graph of calculated distance difference from delay time vs manually measured distance difference between LED and photodetector with a mirror acting as the "object"
|}

==Challenges and Conclusion==
# One of the challenges we faced was centring the beam onto the photodetector. Due to the lack of a focusing beam on the photodetector, the laser beam spot size was much larger than the surface area of the photodetector. What this led to was a constant fluctuation of the delay time on the oscilloscope as the brightest part of the beam was not always centred on the photodetector despite optimising stabilisation of the beam path.
# To have accurate distance measurements in the centimetre regime, the delay time we required was ~0.3ns for every 10cm. However, the fluctuation of the delay time on the oscilloscope was causing the 1st decimal place to fluctuate constantly.
{| style="border:none; margin:auto; text-align:center;"
|-
| [[File:spotondetector.jpeg|300px]]
|-
| '''Figure 9.''' Beam spot on photodetector
|}
Though the concept of the project was fairly straightforward, the yielded results were not precise within the uncertainty. This points to experimental errors such as the lack of a focusing mirror which caused fluctuations in the delay.

==Improvements and Future Work==
# Install a focusing lens for the photodetector
# Use a bandpass filter at 650 nm laser to filter out other frequencies to get less fluctuations in the delay time reading on the oscilloscope.