pc5271AY2526wiki - User contributions [en]

Precision Measurement of Material and Optical Properties Using Interferometry

2026-04-21T17:44:14Z

Sanguk: /* Idea */

=Team Members=
Yang SangUk

Zhang ShunYang

Xu Zifang

=List of Apparatus=

Light source: 780nm laser diode (GH0781RA2C SHARP diode) with LT230-B collimation tube

Optics: optical isolator (Thorlabs IO-3D-780-VLP), beamsplitter, two 25.4mm broadband dielectric mirrors (BB1-E02-10)

Salt water of different concentrations in a transparent container (for determining the refractive index of solutions of different concentrations)

Analog powermeter

Oscilloscope (Rohde & Schwarz RTB2004, 100MHz bandwidth), power supply

Peltier, thermocouple (for heating the mirror and measuring its temperature)

=Idea=
We will be constructing an interferometer as a tool for precision measurement. One primary objective is to determine the refractive index of the solutions of different salt concentrations by analyzing the resulting shift in interference fringes. Additionally, the thermal expansion of the metal sample will be measured by monitoring changes in the optical path length as the temperature of the sample varies. The project will highlight the relationship between wave optics and measurable physical parameters and illustrate the advantages of high-precision experimental technique.

==Project Description==
This project aims to design, construct, and apply a Michelson interferometer as a precision optical instrument for experimental measurement. The interferometer is used to investigate how small physical changes in an optical system can be detected through shifts in interference fringes. A primary objective of the project is to determine the refractive index of salt solutions of different concentrations by analyzing the change in optical path length produced when the solution is placed in one arm of the interferometer. As the salt concentration changes, the refractive index of the medium varies, producing a corresponding phase shift in the interference signal. By measuring this fringe shift, the change in refractive index can be quantitatively evaluated.

A second objective of the project is to investigate the effect of thermal expansion on the interferometer output by heating a mirror and monitoring the resulting change in optical path difference. As the temperature of the mirror or its supporting structure changes, the physical expansion alters the effective path length of one interferometer arm, which in turn shifts the observed interference pattern. By tracking these fringe movements, the corresponding displacement can be determined with high sensitivity. In this way, the project uses interferometric measurements to connect optical phase change with mechanical expansion.

The project also emphasizes the experimental and analytical processes required for high-precision interferometry. These include interferometer construction and alignment, signal detection with a photodiode and oscilloscope, and systematic analysis of the measured data through fringe identification, signal processing, and phase-based interpretation. Through these investigations, the project demonstrates the relationship between wave optics and measurable physical parameters, while highlighting the advantages of interferometric techniques for detecting very small changes in refractive index and displacement.

=Theory=

===Michelson Interferometer===

An interferometer is a precision scientific instrument in which a light wave is split into multiple paths and later recombined. The resulting interference depends on the relative phase difference accumulated along the different paths. Because the phase is sensitive to path length and optical properties, interferometers are widely used for precision measurements. A common example is the '''Michelson interferometer''', which illustrates the basic principles of optical interference.

The basic version of the Michelson interferometer consists of a 50:50 beam splitter (BS) and two mirrors placed in separate arms of the interferometer. Assume that the input beam is a linearly polarized monochromatic source of wavelength <math>\lambda</math> and field amplitude <math>E_0</math>. The light is incident on the input port of the BS, where it is divided into two beams that propagate along the two arms toward the mirrors. Each beam is reflected by its respective mirror and recombined at BS, producing an interference pattern at the output port.

The output electric field can be described by summing the two contributions from the two arms. If the path lengths are <math>L_1</math> and <math>L_2</math>, the output field:

<math>
E_{out} = E_1 + E_2 = \frac{1}{2}E_0 e^{i2kL_1}(1+e^{i2k\Delta L})
</math>

where <math>\Delta L=L_2-L_1</math> and <math>k=2\pi/\lambda</math>. Field maxima occur whenever

<math>
\frac{4\pi\Delta L}{\lambda} = 2m\pi,
</math>

and minima when

<math>
\frac{4\pi\Delta L}{\lambda} = (2m+1)\pi,
</math>

where <math>m</math> is an integer.

Changes in the optical path length of either arm caused by displacement of a mirror, or variation of refractive index in a medium will change the relative phase difference, leading to a shift of the interference fringes. he high sensitivity of the interference pattern to such changes forms the basis for precision measurements using a Michelson interferometer.

For example, a transparent container of length <math>L</math> can be placed in one arm of the interferometer. The container is initially filled with air (refractive index approximately 1), and is then gradually filled with a solution of refractive index <math>n</math>. The presence of the solution changes the optical path length in that arm. The additional optical path difference introduced by the solution is

<math>
\Delta \text{OPL} = 2(n-1)L,
</math>

where the factor of 2 arises because the light passes through the container twice (forward and backward).

The corresponding phase change is

<math>
\Delta \phi = \frac{2\pi}{\lambda} \cdot 2(n-1)L.
</math>

As the concentration of the solution changes, the refractive index <math>n</math> varies, leading to a continuous shift of the interference fringes. By counting the fringe shifts at the output port, the change in optical path length can be determined, allowing us to measure the dependence of the refractive index <math>n</math> on the solution concentration.

===Measuring Salt Solution Concentration===

This part mainly focuses on how the Michelson interferometer can quantitatively relate fringe shifts to salt concentration in water, via refractive index and optical path length.

When a cup of solution is placed in one of the arms of the interferometer, the refractive index relative to air, pure water, and the container wall changes, altering the optical path length (OPL) and, ultimately, resulting in a measurable phase shift via a powermeter when interference occurs.

In summary, the measurement chain is:

Fringe Shift → Phase → OPL → Refractive Index → Salt Concentration

Beginning form the equation we introduced above:

<math>
\Delta \phi = \frac{2\pi}{\lambda} \cdot 2(n-1)L.
</math>

At room temperature, when the solution concentration is reasonably small, the relationship between the solution's refractive index and concentration can be approximated by a linear function, say

<math>
n = \alpha C + \beta T + n_0,
</math>

where C is concentration, T is temperature (with <math>\beta << \alpha</math> at least for salt and alchoho), and <math>n_0</math> is the refractive index of pure water.

Substituting the second equation into the first, we have

<math>
\Delta \phi = \frac{2\pi}{\lambda} \cdot 2(\alpha C + \beta T + n_0 - 1)L,
</math>

which leads to the conclusion that

<math>
C(\Delta\phi) = \frac{1}{\alpha}(\frac{\lambda}{4\pi L}\Delta \phi - \beta T - (n_0 - 1)).
</math>

In practice, we can assume the temperature effect is negligible due to the small <math>\beta</math> approximation. Also, we only measure the relative phase shift, so the constant terms are negligible. After that, the final function relating <math>C</math> and <math>\phi</math> is

<math>
C(\Delta\phi) = \frac{\lambda}{4\pi \alpha L}\Delta \phi.
</math>

For salt, the value of <math>\alpha</math> is approximately 0.002. Using this value for estimation, we only need about 1 milligram of salt per liter of water to see a significant phase shift, as long as the container shape is not eccentric. Instead of adding salt crystals directly to water, for the simplicity of experiment, we prefer adding a high-concentration salt solution to the measured solution to better control the final concentration.

===Thermal Expansion of the Mirror===

In a Michelson interferometer, a change in the position of a mirror leads to a variation in the optical path length of that arm, resulting in a phase shift between the two beams and a corresponding shift in the interference fringes.

For a temperature change <math>\Delta T</math>, the linear thermal expansion of a material is given by

<math>\Delta L = \alpha L \Delta T</math>,

where <math>\alpha</math> is the linear thermal expansion coefficient and <math>L</math> is the initial length.

In the interferometer, a displacement <math>\Delta L</math> of the mirror produces an optical path difference of

<math>\Delta \mathrm{OPL} = 2\Delta L</math>,

due to the round-trip propagation of light. Since one fringe shift corresponds to a path change of one wavelength <math>\lambda</math>, the number of fringes shifted is

<math>N = \frac{2\Delta L}{\lambda}</math>.

Combining the above expressions, the thermal expansion coefficient can be written as

<math>\alpha = \frac{N\lambda}{2L\Delta T}</math>.

=Experiment Procedures & Discussion=
==Constructing a Michelson Interferometer==

A basic Michelson interferometer will be constructed for the experiment.

===Interferometer alignment and stability===

[[Image: interferometer_setup.png|350px]]

Figure 1: Schematic of the Michelson interferometer used for measuring the refractive index of the solution. For the thermal expansion measurement, the solution cell is removed, and one of the mirrors is attached to a Peltier element mounted on the mirror holder. OI: optical isolator; M: mirror; BS: beam splitter; PM: powermeter

{| style="width:80%; text-align:center;"
| [[File:interferometer_photo.jpeg|400px]]
| [[File:interferometer_expan.jpeg|400px]]
|-
| ''(a) Setup for refractive index measurement''
| ''(b) Setup for thermal expansion measurement''
|}

Figure 2: Photo of the actual Michelson interferometer setup constructed according to the schematic.

After constructing the interferometer, the beams reflected from both mirrors were carefully aligned so that they recombined at the beam splitter. The resulting interference signal was monitored using an analog power meter.

During the early stage of the interferometer construction, several sources of fluctuations that could affect the stability of the interference signal were identified:

'''Optical feedback into the laser diode:''' Reflected light entering the laser cavity can cause intensity fluctuations and frequency instability. 
Counter: An optical isolator was added to suppress back reflections.

'''Mechanical vibrations:''' Vibrations from the environment (for example, people walking near the setup) could be observed as fluctuations in the signal on the oscilloscope. 
Counter: Sorbothane vibration-isolation feet (Thorlabs AV4) were placed under the aluminum breadboard to provide basic vibration and acoustic isolation.

'''Air currents:''' Air movement around the optical paths can change the optical path length through refractive index variations. 
Counter: The entire interferometer setup was enclosed inside a styrofoam box to reduce airflow and improve thermal stability.

===Interference fringes===

For simplicity, no active elements were included to stabilize or control the optical path length of the interferometer. The interferometer was allowed to free run, and the interference signal was recorded using the oscilloscope.

Two datasets are presented here: one at the maximum intensity and one at the minimum intensity of the interference signal. Each measurement corresponds to a 12-second-long trace.

[[File:24MAR-05 peak troughn.png|800px]]

Figure 3: Oscilloscope trace of the interference signal at minimum intensity.

This figure shows the trace corresponding to the minimum intensity that can be achieved. The average voltage is 1.66 V. The red region in the plot represents intentionally induced noise spikes that were excluded from the averaging process. These excluded points account for approximately 8.8% of the dataset.

[[File:24MAR-06 peak troughn.png|800px]]

Figure 4: Oscilloscope trace of the interference signal at maximum intensity.

This shows the trace corresponding to the maximum intensity of the interference signal. The average voltage measured in this case is 2.06 V.

'''Discussion on Fringe Visibility'''

The relatively low fringe visibility observed in this interferometer is primarily attributed to the poor spatial mode of the laser diode. The emitted beam is neither perfectly Gaussian nor symmetric, resulting in imperfect spatial overlap when the two beams recombine at the beam splitter. Consequently, only partial interference occurs, which reduces the observed visibility.

Another contribution may arise from imperfect power splitting at the beam splitter, leading to unequal intensities in the two arms and further degrading the interference contrast.

We also observe that the fringe visibility varies over time. Each time the setup is restarted and realigned, the measured visibility changes slightly. This behavior is likely due to the lack of a stabilized optical table, making the system sensitive to small mechanical perturbations and environmental disturbances that affect alignment.

Despite the relatively low and time-varying visibility, this does not significantly impact the objective of the experiment. Since the measurement relies on extracting phase information, it is sufficient to maintain a clear and distinguishable difference between the maximum and minimum signals. As long as the interference fringes can be reliably resolved using the powermeter, the phase variation can still be determined with sufficient accuracy.

==Refractive index of the solution==

Place the test solution in one arm of the interferometer. Gradually vary the solution concentration by adding either distilled water or a higher-concentration solution to the container, and observe the resulting changes in the interference pattern.

The analysis begins by reading each oscilloscope CSV as a time-voltage trace, with the detector voltage treated as a proxy for the Michelson output intensity. A separate calibration was used to establish the bright and dark interference levels. The calibration trace was low-pass filtered so that the bright and dark levels were estimated from the underlying fringe swing rather than from point-to-point fluctuation.

The interferometer output was modeled with the standard cosine response

<math>
V = V_{\mathrm{mid}} + A\cos(\Delta \phi)
</math>

where V is the measured detector voltage, <math>V_{\mathrm{mid}}</math> is the midpoint voltage between bright and dark fringe, A is half of the fringe swing, and Delta phi is the phase difference between the two interferometer arms. From the calibration trace, the midpoint and amplitude were defined as:

<math>
V_{\mathrm{mid}} = \frac{V_{\mathrm{bright}} + V_{\mathrm{dark}}}{2}
</math>

<math>
A = \frac{V_{\mathrm{bright}} - V_{\mathrm{dark}}}{2}
</math>

For the present dataset, those calibration values were:

Dark level = 1.074943 V

Bright level = 1.393521 V

Midpoint = 1.234232 V

Amplitude = 0.159289 V

Each salt solution dataset was then low-pass filtered and represented by its median filtered voltage, <math>V_{\mathrm{data}}</math>. This representative voltage was normalized according to:

<math>
x = \frac{V_{\mathrm{data}} - V_{\mathrm{mid}}}{A}
</math>

so that x corresponds to the cosine interference term and, in the ideal model, lies between -1 and +1. This step connects the raw oscilloscope voltage directly to the interferometric phase response.

===Phase Extraction and Refractive Index Conversion===

Once the normalized interference variable x has been obtained, the phase was extracted from the inverse cosine relation:

<math>
\phi = \cos^{-1}(x)
</math>

Because intensity-only detection measures the cosine of the phase rather than the signed phase itself, a second mathematically valid branch also exists:

<math>
\phi_{\mathrm{alt}} = 2\pi - \phi
</math>

The water only dataset was used as the phase reference. For each subsequent drop count, the smallest phase change consistent with the measured voltage was taken relative to that reference.

The phase shift was then converted into refractive-index change through the Michelson optical path relation. As the beam traverses the sample on the forward and return paths, the optical path change is:

<math>
\Delta \mathrm{OPL} = 2L\,\Delta n
</math>

and the corresponding phase shift is:

<math>
\Delta \phi = \frac{2\pi}{\lambda}\Delta \mathrm{OPL} = \frac{4\pi L}{\lambda}\Delta n
</math>

Rearranging gives the working equation used to calculate the refractive-index change from the measured phase shift:

<math>
\Delta n = \frac{\Delta \phi\lambda}{4\pi L}
</math>

With wavelength = 780nm and L = 55mm, one full fringe corresponds to a refractive index change of approximately:

<math>
\Delta n_{\mathrm{one\ fringe}} = \frac{\lambda}{2L} \approx 7.091e-06
</math>

[[File:Delta n vs drops upto6 linear fit 2.png|600px]]

Figure 5: Change in refractive index as a function of the number of added drops of salt solution.

<math>
|\Delta n| = \left(2.176 \times 10^{-7}\right) N_{\mathrm{drops}} - 1.997 \times 10^{-7}
</math>

===Discussions===

The main difficulty in this experiment lies in maintaining optical path length stability while varying the concentration of the solution. When drops are added to adjust the concentration, the solution requires time to become homogeneous. During this mixing process, refractive index gradients can exist within the liquid, leading to additional phase fluctuations in the interferometer signal.

At the same time, environmental perturbations such as mechanical vibrations and air currents introduce further phase noise. As a result, it becomes challenging to distinguish the phase shift caused by the change in concentration from fluctuations due to external disturbances. We suspect that the outliers observed in the results arise from excessive disturbance of the water during the addition of drops, which leads to transient and non-uniform refractive index changes and consequently inaccurate phase measurements.

Several improvements can be made to enhance the reliability of the measurement. First, a reference interferometer could be implemented to monitor and subtract environmental phase fluctuations, thereby isolating the contribution from the solution. Second, the method of introducing the solution can be improved by using a controlled delivery system to regulate the rate and volume of added liquid, reducing mechanical disturbances. Finally, allowing sufficient settling time after each adjustment, or introducing gentle mixing methods, can help ensure the solution reaches a homogeneous state before measurement.

With these improvements, the accuracy and repeatability of the concentration-dependent refractive index measurement can be significantly enhanced.

==Thermal expansion of the mirror==

In this part, a Peltier element is used to heat the mirror assembly. The hot side of the Peltier is placed in contact with the back of the mirror, while the cold side is attached to the mirror mount. In this configuration, both the mirror and parts of the mount are heated simultaneously.

As the temperature increases, the thermal expansion of the mirror assembly causes a displacement of the reflecting surface, leading to a shift in the interference fringes. The temperature is monitored using a thermocouple, and the fringe movement is recorded using the interferometer signal.

In practice, the measured expansion corresponds to an ''effective'' thermal expansion coefficient, as contributions may arise not only from the mirror substrate but also from the mount and the thermal interface between them.

===Collection of data & analysis===

During this experiment, a video recording was taken to simultaneously capture the oscilloscope trace and the temperature reading from the thermocouple. Due to the large file size, the full video is not included here but is available upon request. An example segment is presented below to illustrate the method used for counting fringe shifts.

[[File: 17APR-01 segment start to -160 shifted.png|800px]]

[[File: 17APR-01 segment start to -160 shifted fringe count.png |800px]]

Figure 6: Example of interference signal during mirror heating. The raw oscilloscope trace (gray) is overlaid with a low-pass filtered signal (blue) to highlight the fringe evolution. Successive maxima and minima are labeled and used to count fringe shifts (N), corresponding to changes in optical path length as the mirror expands with increasing temperature.

[[File:thermal_expansion.jpg|600px]]

Figure 7: Measured displacement as a function of temperature during mirror heating.

During the experiment, a time trace of the detector signal was recorded while the mirror was being heated. The recorded signal shows a slow but sustained drift in voltage, superimposed with oscillatory behavior. This reflects the gradual expansion of the mirror assembly, which changes the optical path length and causes the interference signal to cycle through successive bright and dark fringes.

The detector voltage is interpreted using the standard interferometric model:

<math>
V_{det}(t) = V_{mid} + A \cos(\Delta \phi(t)),
</math>

where <math>V_{mid}</math> is the midpoint voltage and <math>A</math> is the fringe amplitude. As the mirror expands, the phase difference <math>\Delta \phi</math> evolves continuously in time.

In a Michelson interferometer, a physical displacement <math>\Delta x</math> of the mirror produces an optical path change of <math>2\Delta x</math> due to the round-trip propagation of light. The corresponding phase shift is

<math>
\Delta \phi = \frac{4\pi}{\lambda} \Delta x.
</math>

Fringe counting provides a robust method to extract displacement from the measured signal. One complete fringe corresponds to a phase change of <math>2\pi</math>, which is equivalent to a mirror displacement of <math>\frac{\lambda}{2}.</math>

Thus, the total displacement can be determined from the number of counted fringes <math>\Delta N</math>:

<math>
\Delta x = \Delta N \frac{\lambda}{2}.
</math>

For the laser wavelength used in this experiment (<math>\lambda = 780\ \mathrm{nm}</math>), each fringe corresponds to a displacement of 390 nm.

The displacement as a function of temperature is then obtained by accumulating the fringe count over time. The thermal expansion relation is given by

<math>
\Delta x = \alpha L_{\mathrm{eff}} \Delta T,
</math>

where <math>\alpha</math> is the linear thermal expansion coefficient and <math>L_{\mathrm{eff}}</math> is the effective length of the heated structure. Taking the derivative with respect to temperature gives

<math>
\alpha = \frac{1}{L_{\mathrm{eff}}} \frac{d(\Delta x)}{dT}.
</math>

From the linear fit of the displacement–temperature data, the slope is estimated to be

<math>
\frac{d(\Delta x)}{dT} \approx 501.43\ \mathrm{nm/^\circ C}.
</math>

Assuming an effective length of (from Thorlabs)

<math>
L_{\mathrm{eff}} \approx 6\ \mathrm{mm},
</math>

the thermal expansion coefficient is calculated as

<math>
\alpha \approx \frac{501.43 \times 10^{-9}}{6 \times 10^{-3}} = 8.36 \times 10^{-5}\ \mathrm{^\circ C^{-1}}.
</math>

===Discussion===

Several factors may influence the measured thermal expansion coefficient:

'''Mirror mount and composite structure:'''
The measured thermal expansion coefficient is significantly larger than that of silica (by approximately two orders of magnitude), indicating that the expansion is dominated by the mirror mount and surrounding structure rather than the mirror substrate alone. The measured displacement therefore includes contributions from the mirror, mount, and thermal interfaces. Since these components typically have larger expansion coefficients (e.g., aluminum), the extracted value represents an ''effective'' expansion of the entire assembly rather than that of the mirror alone.

'''Thermal gradients:'''
Thermal gradients across the mirror assembly can lead to non-uniform expansion. The Peltier element heats the mirror from one side, so different parts of the structure may be at different temperatures. As a result, the measured displacement may not correspond to a single well-defined temperature, introducing systematic error.

'''Thermocouple response and placement:'''
There can be a time lag and spatial offset between the thermocouple reading and the actual temperature of the reflecting surface, especially during continuous heating. While the linear fit reduces random fluctuations, it does not fully eliminate this systematic mismatch.

'''Mechanical drift and environmental perturbations:'''
Similar to the previous experiment, mechanical drift and residual environmental perturbations (e.g., vibrations or air currents) can introduce slow phase shifts that are not related to thermal expansion. These effects may contribute to deviations from perfect linearity in the displacement–temperature relation.

Despite these limitations, the approximately linear trend observed in the data suggests that thermal expansion is the dominant effect. The extracted coefficient therefore provides a reasonable estimate of the effective expansion of the mirror assembly.

=Conclusion=
The project successfully demonstrated that a Michelson interferometer can be built and used as an effective tool for precision measurement. After alignment and testing of the optical system, clear interference signals were obtained and analyzed using a photodiode and oscilloscope. The interferometer proved sufficiently sensitive to detect small physical changes in the system, both in the case of salt-solution concentration changes and in the case of thermal effects associated with mirror heating. This confirmed the suitability of interferometry as a practical method for translating minute optical path changes into experimentally observable signals.

For the salt-solution investigation, the interferometer was used to monitor changes in the optical path length caused by the addition of concentrated salt solution to water in a 55 mm container. By analyzing the resulting fringe and phase shifts, the change in refractive index was estimated as the salt concentration increased. The data showed that the refractive index generally increased with the number of drops added, and over the initial concentration range a near-linear relationship was observed, with the measured change being on the order of <math>10^{-7}</math>per drop. Although the measured value was smaller than the theoretical estimate, the experiment still demonstrated the expected physical trend and verified that interferometric phase measurements can be used to detect concentration-dependent refractive-index changes. The difference between measured and theoretical values also highlighted the importance of practical experimental factors such as alignment, calibration, mixing uniformity, effective optical path length, and environmental stability.

For the thermal-expansion investigation, heating of the mirror produced a measurable shift in the interference condition, showing that the interferometer was able to detect displacement caused by thermal expansion. By counting fringe shifts and relating them to mirror displacement through the Michelson interferometer relation, the change in optical path length was quantified as the temperature increased. This part of the study showed that thermal expansion of the mirror or its supporting structure directly affects the received interference output, and that such changes can be tracked with high sensitivity through fringe motion. Under the simplifying assumption that the observed displacement arose from expansion of the 6 mm mirror alone, an effective expansion coefficient was estimated from the manually counted data. Although this assumption is idealized and the actual displacement may include contributions from the mount or other mechanically coupled components, the result still demonstrated how interferometric measurements can be used to infer thermally induced dimensional changes.

Overall, the project established a clear link between interference fringe motion and underlying physical parameters. The constructed Michelson interferometer was shown to be capable of measuring refractive-index variation in salt solutions and displacement caused by thermal expansion, thereby illustrating both the theoretical principles of wave optics and the experimental power of interferometric methods. In this way, the project achieved its main objective of showing how precise optical interference measurements can be used to investigate small but physically meaningful changes in material and geometric properties.

=References=
M. Fox, "Quantum Optics: An Introduction", (Oxford University Press, 2006) Chap. 2.

Shang, J., Ping, L., Ling, Y. et al. A instrument for measuring solution concentration. Opt Rev 30, 310–321 (2023).

Precision Measurement of Material and Optical Properties Using Interferometry

2026-04-21T17:39:10Z

Sanguk:

=Team Members=
Yang SangUk

Zhang ShunYang

Xu Zifang

=List of Apparatus=

Light source: 780nm laser diode (GH0781RA2C SHARP diode) with LT230-B collimation tube

Optics: optical isolator (Thorlabs IO-3D-780-VLP), beamsplitter, two 25.4mm broadband dielectric mirrors (BB1-E02-10)

Salt water of different concentrations in a transparent container (for determining the refractive index of solutions of different concentrations)

Analog powermeter

Oscilloscope (Rohde & Schwarz RTB2004, 100MHz bandwidth), power supply

Peltier, thermocouple (for heating the mirror and measuring its temperature)

=Idea=
We will be constructing an interferometer as a tool for precision measurement. One primary objective is to determine the refractive index of the solutions of different salt concentrations by analyzing the resulting shift in interference fringes. Additionally, the thermal expansion of the metal sample will be measured by monitoring changes in the optical path length as the temperature of the sample varies. The project will highlight the relationship between wave optics and measurable physical parameters and illustrate the advantages of high-precision experimental technique.

=Theory=

===Michelson Interferometer===

An interferometer is a precision scientific instrument in which a light wave is split into multiple paths and later recombined. The resulting interference depends on the relative phase difference accumulated along the different paths. Because the phase is sensitive to path length and optical properties, interferometers are widely used for precision measurements. A common example is the '''Michelson interferometer''', which illustrates the basic principles of optical interference.

The basic version of the Michelson interferometer consists of a 50:50 beam splitter (BS) and two mirrors placed in separate arms of the interferometer. Assume that the input beam is a linearly polarized monochromatic source of wavelength <math>\lambda</math> and field amplitude <math>E_0</math>. The light is incident on the input port of the BS, where it is divided into two beams that propagate along the two arms toward the mirrors. Each beam is reflected by its respective mirror and recombined at BS, producing an interference pattern at the output port.

The output electric field can be described by summing the two contributions from the two arms. If the path lengths are <math>L_1</math> and <math>L_2</math>, the output field:

<math>
E_{out} = E_1 + E_2 = \frac{1}{2}E_0 e^{i2kL_1}(1+e^{i2k\Delta L})
</math>

where <math>\Delta L=L_2-L_1</math> and <math>k=2\pi/\lambda</math>. Field maxima occur whenever

<math>
\frac{4\pi\Delta L}{\lambda} = 2m\pi,
</math>

and minima when

<math>
\frac{4\pi\Delta L}{\lambda} = (2m+1)\pi,
</math>

where <math>m</math> is an integer.

Changes in the optical path length of either arm caused by displacement of a mirror, or variation of refractive index in a medium will change the relative phase difference, leading to a shift of the interference fringes. he high sensitivity of the interference pattern to such changes forms the basis for precision measurements using a Michelson interferometer.

For example, a transparent container of length <math>L</math> can be placed in one arm of the interferometer. The container is initially filled with air (refractive index approximately 1), and is then gradually filled with a solution of refractive index <math>n</math>. The presence of the solution changes the optical path length in that arm. The additional optical path difference introduced by the solution is

<math>
\Delta \text{OPL} = 2(n-1)L,
</math>

where the factor of 2 arises because the light passes through the container twice (forward and backward).

The corresponding phase change is

<math>
\Delta \phi = \frac{2\pi}{\lambda} \cdot 2(n-1)L.
</math>

As the concentration of the solution changes, the refractive index <math>n</math> varies, leading to a continuous shift of the interference fringes. By counting the fringe shifts at the output port, the change in optical path length can be determined, allowing us to measure the dependence of the refractive index <math>n</math> on the solution concentration.

===Measuring Salt Solution Concentration===

This part mainly focuses on how the Michelson interferometer can quantitatively relate fringe shifts to salt concentration in water, via refractive index and optical path length.

When a cup of solution is placed in one of the arms of the interferometer, the refractive index relative to air, pure water, and the container wall changes, altering the optical path length (OPL) and, ultimately, resulting in a measurable phase shift via a powermeter when interference occurs.

In summary, the measurement chain is:

Fringe Shift → Phase → OPL → Refractive Index → Salt Concentration

Beginning form the equation we introduced above:

<math>
\Delta \phi = \frac{2\pi}{\lambda} \cdot 2(n-1)L.
</math>

At room temperature, when the solution concentration is reasonably small, the relationship between the solution's refractive index and concentration can be approximated by a linear function, say

<math>
n = \alpha C + \beta T + n_0,
</math>

where C is concentration, T is temperature (with <math>\beta << \alpha</math> at least for salt and alchoho), and <math>n_0</math> is the refractive index of pure water.

Substituting the second equation into the first, we have

<math>
\Delta \phi = \frac{2\pi}{\lambda} \cdot 2(\alpha C + \beta T + n_0 - 1)L,
</math>

which leads to the conclusion that

<math>
C(\Delta\phi) = \frac{1}{\alpha}(\frac{\lambda}{4\pi L}\Delta \phi - \beta T - (n_0 - 1)).
</math>

In practice, we can assume the temperature effect is negligible due to the small <math>\beta</math> approximation. Also, we only measure the relative phase shift, so the constant terms are negligible. After that, the final function relating <math>C</math> and <math>\phi</math> is

<math>
C(\Delta\phi) = \frac{\lambda}{4\pi \alpha L}\Delta \phi.
</math>

For salt, the value of <math>\alpha</math> is approximately 0.002. Using this value for estimation, we only need about 1 milligram of salt per liter of water to see a significant phase shift, as long as the container shape is not eccentric. Instead of adding salt crystals directly to water, for the simplicity of experiment, we prefer adding a high-concentration salt solution to the measured solution to better control the final concentration.

===Thermal Expansion of the Mirror===

In a Michelson interferometer, a change in the position of a mirror leads to a variation in the optical path length of that arm, resulting in a phase shift between the two beams and a corresponding shift in the interference fringes.

For a temperature change <math>\Delta T</math>, the linear thermal expansion of a material is given by

<math>\Delta L = \alpha L \Delta T</math>,

where <math>\alpha</math> is the linear thermal expansion coefficient and <math>L</math> is the initial length.

In the interferometer, a displacement <math>\Delta L</math> of the mirror produces an optical path difference of

<math>\Delta \mathrm{OPL} = 2\Delta L</math>,

due to the round-trip propagation of light. Since one fringe shift corresponds to a path change of one wavelength <math>\lambda</math>, the number of fringes shifted is

<math>N = \frac{2\Delta L}{\lambda}</math>.

Combining the above expressions, the thermal expansion coefficient can be written as

<math>\alpha = \frac{N\lambda}{2L\Delta T}</math>.

=Experiment Procedures & Discussion=
==Constructing a Michelson Interferometer==

A basic Michelson interferometer will be constructed for the experiment.

===Interferometer alignment and stability===

[[Image: interferometer_setup.png|350px]]

Figure 1: Schematic of the Michelson interferometer used for measuring the refractive index of the solution. For the thermal expansion measurement, the solution cell is removed, and one of the mirrors is attached to a Peltier element mounted on the mirror holder. OI: optical isolator; M: mirror; BS: beam splitter; PM: powermeter

{| style="width:80%; text-align:center;"
| [[File:interferometer_photo.jpeg|400px]]
| [[File:interferometer_expan.jpeg|400px]]
|-
| ''(a) Setup for refractive index measurement''
| ''(b) Setup for thermal expansion measurement''
|}

Figure 2: Photo of the actual Michelson interferometer setup constructed according to the schematic.

After constructing the interferometer, the beams reflected from both mirrors were carefully aligned so that they recombined at the beam splitter. The resulting interference signal was monitored using an analog power meter.

During the early stage of the interferometer construction, several sources of fluctuations that could affect the stability of the interference signal were identified:

'''Optical feedback into the laser diode:''' Reflected light entering the laser cavity can cause intensity fluctuations and frequency instability. 
Counter: An optical isolator was added to suppress back reflections.

'''Mechanical vibrations:''' Vibrations from the environment (for example, people walking near the setup) could be observed as fluctuations in the signal on the oscilloscope. 
Counter: Sorbothane vibration-isolation feet (Thorlabs AV4) were placed under the aluminum breadboard to provide basic vibration and acoustic isolation.

'''Air currents:''' Air movement around the optical paths can change the optical path length through refractive index variations. 
Counter: The entire interferometer setup was enclosed inside a styrofoam box to reduce airflow and improve thermal stability.

===Interference fringes===

For simplicity, no active elements were included to stabilize or control the optical path length of the interferometer. The interferometer was allowed to free run, and the interference signal was recorded using the oscilloscope.

Two datasets are presented here: one at the maximum intensity and one at the minimum intensity of the interference signal. Each measurement corresponds to a 12-second-long trace.

[[File:24MAR-05 peak troughn.png|800px]]

Figure 3: Oscilloscope trace of the interference signal at minimum intensity.

This figure shows the trace corresponding to the minimum intensity that can be achieved. The average voltage is 1.66 V. The red region in the plot represents intentionally induced noise spikes that were excluded from the averaging process. These excluded points account for approximately 8.8% of the dataset.

[[File:24MAR-06 peak troughn.png|800px]]

Figure 4: Oscilloscope trace of the interference signal at maximum intensity.

This shows the trace corresponding to the maximum intensity of the interference signal. The average voltage measured in this case is 2.06 V.

'''Discussion on Fringe Visibility'''

The relatively low fringe visibility observed in this interferometer is primarily attributed to the poor spatial mode of the laser diode. The emitted beam is neither perfectly Gaussian nor symmetric, resulting in imperfect spatial overlap when the two beams recombine at the beam splitter. Consequently, only partial interference occurs, which reduces the observed visibility.

Another contribution may arise from imperfect power splitting at the beam splitter, leading to unequal intensities in the two arms and further degrading the interference contrast.

We also observe that the fringe visibility varies over time. Each time the setup is restarted and realigned, the measured visibility changes slightly. This behavior is likely due to the lack of a stabilized optical table, making the system sensitive to small mechanical perturbations and environmental disturbances that affect alignment.

Despite the relatively low and time-varying visibility, this does not significantly impact the objective of the experiment. Since the measurement relies on extracting phase information, it is sufficient to maintain a clear and distinguishable difference between the maximum and minimum signals. As long as the interference fringes can be reliably resolved using the powermeter, the phase variation can still be determined with sufficient accuracy.

==Refractive index of the solution==

Place the test solution in one arm of the interferometer. Gradually vary the solution concentration by adding either distilled water or a higher-concentration solution to the container, and observe the resulting changes in the interference pattern.

The analysis begins by reading each oscilloscope CSV as a time-voltage trace, with the detector voltage treated as a proxy for the Michelson output intensity. A separate calibration was used to establish the bright and dark interference levels. The calibration trace was low-pass filtered so that the bright and dark levels were estimated from the underlying fringe swing rather than from point-to-point fluctuation.

The interferometer output was modeled with the standard cosine response

<math>
V = V_{\mathrm{mid}} + A\cos(\Delta \phi)
</math>

where V is the measured detector voltage, <math>V_{\mathrm{mid}}</math> is the midpoint voltage between bright and dark fringe, A is half of the fringe swing, and Delta phi is the phase difference between the two interferometer arms. From the calibration trace, the midpoint and amplitude were defined as:

<math>
V_{\mathrm{mid}} = \frac{V_{\mathrm{bright}} + V_{\mathrm{dark}}}{2}
</math>

<math>
A = \frac{V_{\mathrm{bright}} - V_{\mathrm{dark}}}{2}
</math>

For the present dataset, those calibration values were:

Dark level = 1.074943 V

Bright level = 1.393521 V

Midpoint = 1.234232 V

Amplitude = 0.159289 V

Each salt solution dataset was then low-pass filtered and represented by its median filtered voltage, <math>V_{\mathrm{data}}</math>. This representative voltage was normalized according to:

<math>
x = \frac{V_{\mathrm{data}} - V_{\mathrm{mid}}}{A}
</math>

so that x corresponds to the cosine interference term and, in the ideal model, lies between -1 and +1. This step connects the raw oscilloscope voltage directly to the interferometric phase response.

===Phase Extraction and Refractive Index Conversion===

Once the normalized interference variable x has been obtained, the phase was extracted from the inverse cosine relation:

<math>
\phi = \cos^{-1}(x)
</math>

Because intensity-only detection measures the cosine of the phase rather than the signed phase itself, a second mathematically valid branch also exists:

<math>
\phi_{\mathrm{alt}} = 2\pi - \phi
</math>

The water only dataset was used as the phase reference. For each subsequent drop count, the smallest phase change consistent with the measured voltage was taken relative to that reference.

The phase shift was then converted into refractive-index change through the Michelson optical path relation. As the beam traverses the sample on the forward and return paths, the optical path change is:

<math>
\Delta \mathrm{OPL} = 2L\,\Delta n
</math>

and the corresponding phase shift is:

<math>
\Delta \phi = \frac{2\pi}{\lambda}\Delta \mathrm{OPL} = \frac{4\pi L}{\lambda}\Delta n
</math>

Rearranging gives the working equation used to calculate the refractive-index change from the measured phase shift:

<math>
\Delta n = \frac{\Delta \phi\lambda}{4\pi L}
</math>

With wavelength = 780nm and L = 55mm, one full fringe corresponds to a refractive index change of approximately:

<math>
\Delta n_{\mathrm{one\ fringe}} = \frac{\lambda}{2L} \approx 7.091e-06
</math>

[[File:Delta n vs drops upto6 linear fit 2.png|600px]]

Figure 5: Change in refractive index as a function of the number of added drops of salt solution.

<math>
|\Delta n| = \left(2.176 \times 10^{-7}\right) N_{\mathrm{drops}} - 1.997 \times 10^{-7}
</math>

===Discussions===

The main difficulty in this experiment lies in maintaining optical path length stability while varying the concentration of the solution. When drops are added to adjust the concentration, the solution requires time to become homogeneous. During this mixing process, refractive index gradients can exist within the liquid, leading to additional phase fluctuations in the interferometer signal.

At the same time, environmental perturbations such as mechanical vibrations and air currents introduce further phase noise. As a result, it becomes challenging to distinguish the phase shift caused by the change in concentration from fluctuations due to external disturbances. We suspect that the outliers observed in the results arise from excessive disturbance of the water during the addition of drops, which leads to transient and non-uniform refractive index changes and consequently inaccurate phase measurements.

Several improvements can be made to enhance the reliability of the measurement. First, a reference interferometer could be implemented to monitor and subtract environmental phase fluctuations, thereby isolating the contribution from the solution. Second, the method of introducing the solution can be improved by using a controlled delivery system to regulate the rate and volume of added liquid, reducing mechanical disturbances. Finally, allowing sufficient settling time after each adjustment, or introducing gentle mixing methods, can help ensure the solution reaches a homogeneous state before measurement.

With these improvements, the accuracy and repeatability of the concentration-dependent refractive index measurement can be significantly enhanced.

==Thermal expansion of the mirror==

In this part, a Peltier element is used to heat the mirror assembly. The hot side of the Peltier is placed in contact with the back of the mirror, while the cold side is attached to the mirror mount. In this configuration, both the mirror and parts of the mount are heated simultaneously.

As the temperature increases, the thermal expansion of the mirror assembly causes a displacement of the reflecting surface, leading to a shift in the interference fringes. The temperature is monitored using a thermocouple, and the fringe movement is recorded using the interferometer signal.

In practice, the measured expansion corresponds to an ''effective'' thermal expansion coefficient, as contributions may arise not only from the mirror substrate but also from the mount and the thermal interface between them.

===Collection of data & analysis===

During this experiment, a video recording was taken to simultaneously capture the oscilloscope trace and the temperature reading from the thermocouple. Due to the large file size, the full video is not included here but is available upon request. An example segment is presented below to illustrate the method used for counting fringe shifts.

[[File: 17APR-01 segment start to -160 shifted.png|800px]]

[[File: 17APR-01 segment start to -160 shifted fringe count.png |800px]]

Figure 6: Example of interference signal during mirror heating. The raw oscilloscope trace (gray) is overlaid with a low-pass filtered signal (blue) to highlight the fringe evolution. Successive maxima and minima are labeled and used to count fringe shifts (N), corresponding to changes in optical path length as the mirror expands with increasing temperature.

[[File:thermal_expansion.jpg|600px]]

Figure 7: Measured displacement as a function of temperature during mirror heating.

During the experiment, a time trace of the detector signal was recorded while the mirror was being heated. The recorded signal shows a slow but sustained drift in voltage, superimposed with oscillatory behavior. This reflects the gradual expansion of the mirror assembly, which changes the optical path length and causes the interference signal to cycle through successive bright and dark fringes.

The detector voltage is interpreted using the standard interferometric model:

<math>
V_{det}(t) = V_{mid} + A \cos(\Delta \phi(t)),
</math>

where <math>V_{mid}</math> is the midpoint voltage and <math>A</math> is the fringe amplitude. As the mirror expands, the phase difference <math>\Delta \phi</math> evolves continuously in time.

In a Michelson interferometer, a physical displacement <math>\Delta x</math> of the mirror produces an optical path change of <math>2\Delta x</math> due to the round-trip propagation of light. The corresponding phase shift is

<math>
\Delta \phi = \frac{4\pi}{\lambda} \Delta x.
</math>

Fringe counting provides a robust method to extract displacement from the measured signal. One complete fringe corresponds to a phase change of <math>2\pi</math>, which is equivalent to a mirror displacement of <math>\frac{\lambda}{2}.</math>

Thus, the total displacement can be determined from the number of counted fringes <math>\Delta N</math>:

<math>
\Delta x = \Delta N \frac{\lambda}{2}.
</math>

For the laser wavelength used in this experiment (<math>\lambda = 780\ \mathrm{nm}</math>), each fringe corresponds to a displacement of 390 nm.

The displacement as a function of temperature is then obtained by accumulating the fringe count over time. The thermal expansion relation is given by

<math>
\Delta x = \alpha L_{\mathrm{eff}} \Delta T,
</math>

where <math>\alpha</math> is the linear thermal expansion coefficient and <math>L_{\mathrm{eff}}</math> is the effective length of the heated structure. Taking the derivative with respect to temperature gives

<math>
\alpha = \frac{1}{L_{\mathrm{eff}}} \frac{d(\Delta x)}{dT}.
</math>

From the linear fit of the displacement–temperature data, the slope is estimated to be

<math>
\frac{d(\Delta x)}{dT} \approx 501.43\ \mathrm{nm/^\circ C}.
</math>

Assuming an effective length of (from Thorlabs)

<math>
L_{\mathrm{eff}} \approx 6\ \mathrm{mm},
</math>

the thermal expansion coefficient is calculated as

<math>
\alpha \approx \frac{501.43 \times 10^{-9}}{6 \times 10^{-3}} = 8.36 \times 10^{-5}\ \mathrm{^\circ C^{-1}}.
</math>

===Discussion===

Several factors may influence the measured thermal expansion coefficient:

'''Mirror mount and composite structure:'''
The measured thermal expansion coefficient is significantly larger than that of silica (by approximately two orders of magnitude), indicating that the expansion is dominated by the mirror mount and surrounding structure rather than the mirror substrate alone. The measured displacement therefore includes contributions from the mirror, mount, and thermal interfaces. Since these components typically have larger expansion coefficients (e.g., aluminum), the extracted value represents an ''effective'' expansion of the entire assembly rather than that of the mirror alone.

'''Thermal gradients:'''
Thermal gradients across the mirror assembly can lead to non-uniform expansion. The Peltier element heats the mirror from one side, so different parts of the structure may be at different temperatures. As a result, the measured displacement may not correspond to a single well-defined temperature, introducing systematic error.

'''Thermocouple response and placement:'''
There can be a time lag and spatial offset between the thermocouple reading and the actual temperature of the reflecting surface, especially during continuous heating. While the linear fit reduces random fluctuations, it does not fully eliminate this systematic mismatch.

'''Mechanical drift and environmental perturbations:'''
Similar to the previous experiment, mechanical drift and residual environmental perturbations (e.g., vibrations or air currents) can introduce slow phase shifts that are not related to thermal expansion. These effects may contribute to deviations from perfect linearity in the displacement–temperature relation.

Despite these limitations, the approximately linear trend observed in the data suggests that thermal expansion is the dominant effect. The extracted coefficient therefore provides a reasonable estimate of the effective expansion of the mirror assembly.

=Conclusion=
The project successfully demonstrated that a Michelson interferometer can be built and used as an effective tool for precision measurement. After alignment and testing of the optical system, clear interference signals were obtained and analyzed using a photodiode and oscilloscope. The interferometer proved sufficiently sensitive to detect small physical changes in the system, both in the case of salt-solution concentration changes and in the case of thermal effects associated with mirror heating. This confirmed the suitability of interferometry as a practical method for translating minute optical path changes into experimentally observable signals.

For the salt-solution investigation, the interferometer was used to monitor changes in the optical path length caused by the addition of concentrated salt solution to water in a 55 mm container. By analyzing the resulting fringe and phase shifts, the change in refractive index was estimated as the salt concentration increased. The data showed that the refractive index generally increased with the number of drops added, and over the initial concentration range a near-linear relationship was observed, with the measured change being on the order of <math>10^{-7}</math>per drop. Although the measured value was smaller than the theoretical estimate, the experiment still demonstrated the expected physical trend and verified that interferometric phase measurements can be used to detect concentration-dependent refractive-index changes. The difference between measured and theoretical values also highlighted the importance of practical experimental factors such as alignment, calibration, mixing uniformity, effective optical path length, and environmental stability.

For the thermal-expansion investigation, heating of the mirror produced a measurable shift in the interference condition, showing that the interferometer was able to detect displacement caused by thermal expansion. By counting fringe shifts and relating them to mirror displacement through the Michelson interferometer relation, the change in optical path length was quantified as the temperature increased. This part of the study showed that thermal expansion of the mirror or its supporting structure directly affects the received interference output, and that such changes can be tracked with high sensitivity through fringe motion. Under the simplifying assumption that the observed displacement arose from expansion of the 6 mm mirror alone, an effective expansion coefficient was estimated from the manually counted data. Although this assumption is idealized and the actual displacement may include contributions from the mount or other mechanically coupled components, the result still demonstrated how interferometric measurements can be used to infer thermally induced dimensional changes.

Overall, the project established a clear link between interference fringe motion and underlying physical parameters. The constructed Michelson interferometer was shown to be capable of measuring refractive-index variation in salt solutions and displacement caused by thermal expansion, thereby illustrating both the theoretical principles of wave optics and the experimental power of interferometric methods. In this way, the project achieved its main objective of showing how precise optical interference measurements can be used to investigate small but physically meaningful changes in material and geometric properties.

=References=
M. Fox, "Quantum Optics: An Introduction", (Oxford University Press, 2006) Chap. 2.

Shang, J., Ping, L., Ling, Y. et al. A instrument for measuring solution concentration. Opt Rev 30, 310–321 (2023).

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Main Page

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'''Welcome to the wiki page for the course PC5271: Physics of Sensors "(in AY25/26 Sem 2)!'''

This is the repository where projects are documented. You will need to create an account for editing/creating pages. If you need an account, please contact Christian.

'''Logistics''':
Our '''location is S11-02-04''', time slots for "classes" are '''Tue and Fri 10:00am-12:00noon'''.

==Projects==

===[[Fluorescence Sensor for Carbon Quantum Dots: Synthesis, Characterization, and Quality Control]]===

Group menber: Zhang yiteng, Li Xiaoyue, Peng Jianxi

This project aims to develop a low-cost, repeatable optical sensing system to quantify the quality of Carbon Quantum Dots (CQDs). We synthesize CQDs using a microwave-assisted method with citric acid and urea, and characterize their fluorescence properties using a custom-built setup comprising a UV LED excitation source and a fiber-optic spectrometer. By analyzing spectral metrics such as peak wavelength, intensity, and FWHM, we establish a robust quality control protocol for nanomaterial production.

===[[Inductive Sensors of Ultra-high Sensitivity Based on Nonlinear Exceptional Point]]===
Team members: Yuan Siyu; Zhu Ziyang; Wang Peikun; Li Xunyu

We are building two coupled oscillating circuits: one that naturally loses energy (lossy) and one that gains energy (active) using a specific amplifier that saturates at high amplitudes. When tuning these two circuits to a nonlinear Exceptional Point (NEP), the system becomes extremely sensitive to small perturbations in inductance, following a steep cubic-root response curve, while remaining resistant to noise.

'''CK:''' We likely have all the parts for this, but let us know the frequency so we can find the proper amplifier and circuit board.

'''SY:''' Thanks for your confirmation. The operating frequency is around 70-80 kHz.

'''CK:''' Have!

===[[EA Spectroscopy as a series of sensors: Investigating the Impact of Film-Processing Temperature on Mobility in Organic Diodes]]===
Team members: Li Jinhan; Liu Chenyang

We will use EA spectroscopy, which will include optical sensors, electrical sensors, and lock-in amplifiers, among other components as a highly sensitive, non-destructive optical sensing platform to measure the internal electric field modulation response of organic diodes under operating conditions, and to quantitatively extract carrier mobility based on this measurement. By systematically controlling the thin film preparation temperature and comparing the EA response characteristics of different samples, the project aims to reveal the influence of film preparation temperature on device mobility and its potential physical origins.

===[[Optical Sensor of Magnetic Dynamics: A Balanced-Detection MOKE Magnetometer]]===
Team members: LI Junxiang; Patricia Breanne Tan Sy

We will use a laser-based magneto-optical Kerr effect setup featuring a high-sensitivity differential photodiode array to measure the Kerr rotation angle induced by surface magnetism. This system serves as a versatile optical platform to investigate how external perturbations such as magnetic fields or radiation source alter the magnetic ordering of materials, allowing for the quantitative extraction of the magneto-optical coupling coefficients of various thin films.

===[[Precision Measurement of Material and Optical Properties Using Interferometry]]===
Team members: Yang SangUk; Zhang ShunYang; Xu Zifang

We will be constructing an interferometer and use it as a tool for precision measurement. One primary objective is determination of the refractive index of solution of different salt concentration by analyzing the resulting shift interference fringes.

===[[Precision Thermocouple Based Temperature Measurement System]]===
Team members: Sree Ranjani Krishnan; Nisha Ganesh ; Burra Srikari

We will design, build, and validate a precision thermocouple-based temperature measurement system using the Seebeck effect. The system will convert the extremely small thermoelectric voltage generated by a thermocouple into accurate, real-time temperature data. Since the output voltage is really small we will be using an instrumentation amplifier to amplify the output voltage and use an Arduino to digitalize the results.
Materials needed: K-type thermocouple/Thermophile;Arduino

===[[Surface EMG Sensor for Muscle Activity Measurement: AFE Design and Signal Processing]]===
Team members: Liu Chenxi; Wang Jingyi; Zhong Baoqi; Hong Jialuo; Zhang Lishang;

Electromyography (EMG) measures the electrical activity generated by skeletal muscles and is widely used in biomedical sensing, rehabilitation, and human–machine interfaces. The electrical signals produced by muscle fibers are typically in the microvolt to millivolt range and are easily corrupted by noise and motion artifacts, making proper signal conditioning essential. In this project, we design and implement an analog front-end (AFE) for surface EMG acquisition, including an instrumentation amplifier, band-pass filtering, and a 50 Hz notch filter to suppress power-line interference. The conditioned signal is then observed and recorded using an oscilloscope for further analysis of muscle activity in both the time and frequency domains.

===[[Humidity Detector Based on Quartz Crystal Oscillator]]===

Group menber: Ma Xiangyi; Li Xukuan; Zhang Yixuan; Zhu Rongqi

This project aims to develop a humidity sensor based on a quartz crystal oscillator. The group will first construct the oscillator circuit on a breadboard. They will then fabricate the sensing device by depositing water-absorbing materials onto the quartz crystal. Humidity detection will be achieved by measuring the frequency change of the circuit caused by the mass variation on the crystal surface.

'''To Prof.''' Several materials are available for use as the water-absorbing layer, such as PVA, polyimide, graphene oxide, and silica gel. We are currently unsure which material would be the most suitable for our device. Could you provide us with some suggestions?

==Resources==
===Books and links===
* A good textbook on the Physics of Sensors is Jacob Fraden: Handbook of Mondern Sensors, Springer, ISBN 978-3-319-19302-1 or [https://link.springer.com/book/10.1007/978-3-319-19303-8 doi:10.1007/978-3-319-19303-8]. There shoud be an e-book available through the NUS library at https://linc.nus.edu.sg/record=b3554643
* Another good textbook: John B.Bentley: Principles of Measurement Systems, 4th Edition, Pearson, ISBN: 0-13-043028-5 or https://linc.nus.edu.sg/record=b2458243 in our library.

===Software===
* Various Python extensions. [https://www.python.org Python] is a very powerful free programming language that runs on just about any computer platform. It is open source and completely free.
* [https://www.gnuplot.info Gnuplot]: A free and very mature data display tool that works on just about any platform used that produces excellent publication-grade eps and pdf figures. Can be also used in scripts. Open source and completely free.
* Matlab: Very common, good toolset also for formal mathematics, good graphics. Expensive. We may have a site license, but I am not sure how painful it is for us to get a license for this course. Ask if interested.
* Mathematica: More common among theroetical physicists, very good in formal maths, now with better numerics. Graphs are ok but can be a pain to make looking good. As with Matlab, we do have a campus license. Ask if interested.

===Apps===
Common mobile phones these days are equipped with an amazing toolchest of sensors. There are a few apps that allow you to access them directly, and turn your phone into a powerful sensor. Here some suggestions:

* Physics Toolbox sensor suite on [https://play.google.com/store/apps/details?id=com.chrystianvieyra.physicstoolboxsuite&hl=en_SG Google play store] or [https://apps.apple.com/us/app/physics-toolbox-sensor-suite/id1128914250 Apple App store].

===Data sheets===
A number of components might be useful for several groups. Some common data sheets are here:
* Photodiodes:
** Generic Silicon pin Photodiode type [[Media:Bpw34.pdf|BPW34]]
** Fast photodiodes (Silicon PIN, small area): [[Media:S5971_etc_kpin1025e.pdf|S5971/S5972/S5973]]
* Photogates:
** reflective, with mounting holes: [[Media:TTElectronics-OPB704WZ.pdf|OPB704.WZ]]
** transmissive, no mounting holes: [[Media:Vishay_TCST1103.pdf|TCST1103]]
* PT 100 Temperature sensors based on platinum wire: [[Media:PT100_TABLA_R_T.pdf|Calibration table]]
* Thermistor type [[Media:Thermistor B57861S.pdf|B57861S]] (R0=10kΩ, B=3988Kelvin). Search for [https://en.wikipedia.org/wiki/Steinhart-Hart_equation Steinhart-Hart equation]. See [[Thermistor]] page here as well.
* Humidity sensor
** Sensirion device the reference unit: [[media:Sensirion SHT30-DIS.pdf|SHT30/31]]
* Thermopile detectors:
** [[Media:Thermopile_G-TPCO-035 TS418-1N426.pdf|G-TPCO-035 / TS418-1N426]]: Thermopile detector with a built-in optical bandpass filter for light around 4μm wavelength for CO2 absorption
** [[Media:Thermopile_TS305_TCPO-033.pdf|TPCO-033 / TS305]]: Thermopile detector with wideband sensitivity 5um-25um
** [[Media:Thermopile_G-TPCO-019_TS105-10L5.5MM.pdf|G-TPCO-019 /TS105-10L5.5MM]]: Thermopile detector with wideband sensitivity 5um-25um and silicon lens (field of view: 10 degree)
* Resistor color codes are explained [https://en.wikipedia.org/wiki/Electronic_color_code here]

* Magnetic field sensors:
** Fluxgate magnetometer [[media:Data-sheet FLC-100.pdf|FCL100]]
** Hall switch 1 (SOT-23 casing): [[media:INFineon_TLE49681KXTSA1.pdf|TLE49681]]
** Hall switch 2 (TO-92 casing): [[media:DiodesInc_AH9246-P-8.pdf|AH9246]]
** Linear Hall sensor (to come)
* Lasers
** Red laser diode [[media:HL6501MG.pdf|HL6501MG]]
* Generic amplifiers
** Instrumentation amplifiers: [[media:Ad8221.pdf|AD8221]] or [[media:AD8226.pdf|AD8226]]
** Conventional operational amplifiers: Precision: [[media:OP27.pdf | OP27]], General purpose: [[media:OP07.pdf | OP07]]
** JFET op-amp, reasonably fast: [https://www.ti.com/document-viewer/tl071/datasheet TL071]
** Transimpedance amplifiers for photodetectors: [[media:AD8015.pdf | AD8015]]

==Some wiki reference materials==
* [https://www.mediawiki.org/wiki/Special:MyLanguage/Manual:FAQ MediaWiki FAQ]
* [[Writing mathematical expressions]]
* [[Uploading images and files]]

==Old wikis==
You can find entries to the wiki from [https://pc5271.org/PC5271_AY2425S2 AY2024/25 Sem 2] and [https://pc5271.org/PC5271_AY2324S2 AY2023/24 Sem 2].

Precision Measurement of Material and Optical Properties Using Interferometry

2026-03-13T02:48:55Z

Sanguk: /* Idea */

=Team Members=
Yang SangUk

Zhang ShunYang

Xu Zifang

=List of Apparatus=

Light source: laser diode (GH0781RA2C SHARP diode) with LT230-B collimation tube

Optics: beamsplitter, 2 mirrors

Salt water of different concentrations in a transparent container

Powermeter

=Introduction=
==Idea==
We will be constructing an interferometer as a tool for precision measurement. One primary objective is to determine the refractive index of the solutions of different salt concentration by analyzing the resulting shift in interference fringes. Additionally, the thermal expansion of the metal sample will be measured by monitoring changes in the optical path length as the temperature of the sample varies. The project will highlight the relationship between wave optics and measurable physical parameters and illustrates the advantages of high-precision experimental technique.

==Background==

=References=

Precision Measurement of Material and Optical Properties Using Interferometry

2026-03-06T01:00:17Z

Sanguk: /* List of Apparatus/tools required */

=Team Members=
Yang SangUk

Zhang ShunYang

Xu Zifang

=List of Apparatus/tools required=

Laser Diode

Beam Splitter

Mirrors

Heater

=Introduction=
==Idea==
We will be constructing an interferometer as a tool for precision measurement. One primary objective is to determine the refractive index of the various gases by analyzing the resulting shift in interference fringes. Additionally, the thermal expansion of the metal sample will be measured by monitoring changes in the optical path length as the temperature of the sample varies. The project will highlight the relationship between wave optics and measurable physical parameters and illustrates the advantages of high-precision experimental technique.
==Background==

=References=

Precision Measurement of Material and Optical Properties Using Interferometry

2026-02-19T06:19:43Z

Sanguk:

=Team Members=
Yang SangUk

Zhang ShunYang

Xu Zifang

=List of Apparatus/tools required=

Laser Diode [Red]

Beam Splitter

Gas cells (Multiple cells of different gases required [Vacuum Pump])

Mirrors (One will be heated [5-10K Aluminum mirror])

Heater (Used to heat the mirror for thermal expansion [Cap heater])

=Introduction=
==Idea==
We will be constructing an interferometer as a tool for precision measurement. One primary objective is to determine the refractive index of the various gases by analyzing the resulting shift in interference fringes. Additionally, the thermal expansion of the metal sample will be measured by monitoring changes in the optical path length as the temperature of the sample varies. The project will highlight the relationship between wave optics and measurable physical parameters and illustrates the advantages of high-precision experimental technique.
==Background==

=References=

Precision Measurement of Material and Optical Properties Using Interferometry

2026-02-13T09:59:21Z

Sanguk: /* List of Apparatus/tools required (Incomplete - Details will be added) */

=Team Members=
Yang SangUk

Zhang ShunYang

Xu Zifang

=List of Apparatus/tools required (Incomplete - Details will be added)=

Laser Diode [Red]

Beam Splitter

Gas cells (Multiple cells of different gases required [Vacuum Pump])

Mirrors (One will be heated [5-10K Aluminum mirror])

Heater (Used to heat the mirror for thermal expansion [Cap heater])

=Introduction=
==Idea==
We will be constructing an interferometer as a tool for precision measurement. One primary objective is to determine the refractive index of the various gases by analyzing the resulting shift in interference fringes. Additionally, the thermal expansion of the metal sample will be measured by monitoring changes in the optical path length as the temperature of the sample varies. The project will highlight the relationship between wave optics and measurable physical parameters and illustrates the advantages of high-precision experimental technique.
==Background==

=References=