PC5271 wiki - User contributions [en]

LED based avalanched photodetector

2025-04-24T09:24:30Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie Email:e1184418@u.nus.edu'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

<div style="text-align:center;">
[[File:pulse number.png|400px|frameless|alt=Fig.1]]
''Figure 1: Pulse number distribution vs Poisson distribution''
</div>

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

<div style="text-align:center;">
[[File:pulse hight.png|400px|frameless|alt=Fig.2]]
''Figure 2: Pulse height vs voltage of power supply''
</div>

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

<div style="text-align:center;">
[[File:Poisson distribution data.png|600px|frameless|alt=Fig.3]]
''Figure 3: Pulse number distribution compared to Poisson distribution''
</div>

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

LED based avalanched photodetector

2025-04-24T09:20:07Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

<div style="text-align:center;">
[[File:pulse number.png|400px|frameless|alt=Fig.1]]
''Figure 1: Pulse number distribution vs Poisson distribution''
</div>

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

<div style="text-align:center;">
[[File:pulse hight.png|400px|frameless|alt=Fig.2]]
''Figure 2: Pulse height vs voltage of power supply''
</div>

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

<div style="text-align:center;">
[[File:Poisson distribution data.png|600px|frameless|alt=Fig.3]]
''Figure 3: Pulse number distribution compared to Poisson distribution''
</div>

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

LED based avalanched photodetector

2025-04-24T09:17:55Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

<div style="text-align:center;">
[[File:pulse number.png|400px|thumb|Fig.1 Pulse number distribution vs Poisson distribution]]
</div>

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

<div style="text-align:center;">
[[File:pulse hight.png|400px|thumb|Fig.2 Pulse number distribution vs Poisson distribution]]
</div>

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

<div style="text-align:center;">
[[File:Poisson distribution data.png|600px|thumb|Fig.3 Pulse number distribution vs Poisson distribution]]
</div>

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

File:Pulse hight.png

2025-04-24T09:17:17Z

Shijie:

LED based avalanched photodetector

2025-04-24T09:16:58Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

<div style="text-align:center;">
[[File:pulse number.png|600px|thumb|Fig.1 Pulse number distribution vs Poisson distribution]]
</div>

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

<div style="text-align:center;">
[[File:pulse hight.png|600px|thumb|Fig.2 Pulse number distribution vs Poisson distribution]]
</div>

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

<div style="text-align:center;">
[[File:Poisson distribution data.png|600px|thumb|Pulse number distribution vs Poisson distribution]]
</div>

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

LED based avalanched photodetector

2025-04-24T09:16:00Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

<div style="text-align:center;">
[[File:pulse number.png|600px|thumb|Pulse number distribution vs Poisson distribution]]
</div>

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

[[File:2.png|thumb|Average photon current pulse height vs voltage of power supply]]

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

<div style="text-align:center;">
[[File:Poisson distribution data.png|600px|thumb|Pulse number distribution vs Poisson distribution]]
</div>

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

File:Pulse number.png

2025-04-24T09:15:12Z

Shijie:

LED based avalanched photodetector

2025-04-24T09:14:02Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

[[File:1.png|thumb|Average photon current pulse number vs voltage of power supply]]

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

[[File:2.png|thumb|Average photon current pulse height vs voltage of power supply]]

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

<div style="text-align:center;">
[[File:Poisson distribution data.png|600px|thumb|Pulse number distribution vs Poisson distribution]]
</div>

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

LED based avalanched photodetector

2025-04-24T09:12:56Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

[[File:1.png|thumb|Average photon current pulse number vs voltage of power supply]]

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

[[File:2.png|thumb|Average photon current pulse height vs voltage of power supply]]

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

<div style="text-align:center;">
[[File:Poisson distribution data.png|thumb|Pulse number distribution vs Poisson distribution]]
</div>

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

LED based avalanched photodetector

2025-04-24T09:12:12Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

[[File:1.png|thumb|Average photon current pulse number vs voltage of power supply]]

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

[[File:2.png|thumb|Average photon current pulse height vs voltage of power supply]]

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

[[File:Poisson distribution data.png|thumb|Pulse number distribution vs Poisson distribution]]

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

File:Poisson distribution data.png

2025-04-24T09:11:33Z

Shijie:

LED based avalanched photodetector

2025-04-24T09:10:53Z

Shijie: /* Code Listings */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

[[File:1.png|thumb|Average photon current pulse number vs voltage of power supply]]

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

[[File:2.png|thumb|Average photon current pulse height vs voltage of power supply]]

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

[[File:3.png|thumb|Pulse number distribution vs Poisson distribution]]

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

<div style="text-align:center;">
[[File:Arduino code.png|600px|thumb|center|Arduino code]]
</div>

LED based avalanched photodetector

2025-04-24T09:10:02Z

Shijie: /* Code Listings */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

[[File:1.png|thumb|Average photon current pulse number vs voltage of power supply]]

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

[[File:2.png|thumb|Average photon current pulse height vs voltage of power supply]]

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

[[File:3.png|thumb|Pulse number distribution vs Poisson distribution]]

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

[[File:Arduino code.png|thumb|Arduino code]]

File:Arduino code.png

2025-04-24T09:09:22Z

Shijie:

LED based avalanched photodetector

2025-04-24T09:08:22Z

Shijie: /* 3. Analysis and Result */

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

[[File:1.png|thumb|Average photon current pulse number vs voltage of power supply]]

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

[[File:2.png|thumb|Average photon current pulse height vs voltage of power supply]]

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

[[File:3.png|thumb|Pulse number distribution vs Poisson distribution]]

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

[[File:4.png|thumb|Arduino code]]

LED based avalanched photodetector

2025-04-24T09:06:23Z

Shijie: Analysis and Result

=== 3. Analysis and Result ===

'''Author: Cai Shijie'''
'''Date: April 2025'''

The avalanche effect can be observed with the power of the light source around 13 μW. This indicates that the detector is a sensitive APD capable of detecting low photon number densities.

[[File:1.pic.jpg|thumb|Average photon current pulse number vs voltage of power supply]]

Figure 1 measures the average pulse number per 50 ms versus the voltage of the power supply. The linear curve corresponds to the increasing photon number with higher voltage of the light source.

[[File:2.pic.jpg|thumb|Average photon current pulse height vs voltage of power supply]]

Figure 2 shows that the pulse height increases with the voltage of the power supply. For a single-photon avalanche photodiode (SAPD), the curve should be flat, meaning each pulse corresponds to one photon. However, when the power supply voltage is doubled, the pulse height increases by 14%, suggesting that each pulse corresponds to several photons.

By setting the photocurrent pulse number per 50 ms as one sample, 1000 or 10,000 samples are used for statistical analysis and compared with the theoretical Poisson distribution, resulting in Figure 3.

[[File:3.png|thumb|Pulse number distribution vs Poisson distribution]]

Several methods are used to analyze how closely the data match the theoretical model. The Kullback–Leibler (KL) divergence (result: 0.0061), Jensen–Shannon (JS) divergence (result: 0.0366), and Bhattacharyya distance (result: 0.0014) all qualitatively estimate the similarity between the real data and the theoretical Poisson distribution. All results are close to 0, indicating a high degree of similarity between the two distributions.

The Kolmogorov–Smirnov (KS) test is used to obtain a p-value, which is more sensitive than the previous methods. The p-value indicates the probability of observing the test statistic under the assumption that the data follow a Poisson distribution. The p-value obtained is 0.0264, which is smaller than 0.05, thus rejecting the Poisson distribution in this test.

Furthermore, the quantum efficiency (QE) is estimated by '''0.245%'''. The Python, Arduino code, and QE calculation are attached in the appendix.

'''In conclusion''', the LED-based APD cannot fully verify the Poisson distribution of the LED source, as it is not a true single-photon detector.

== Appendix ==

=== QE Estimation ===

'''Given Parameters'''
* Blue LED optical power: <math>P_\text{blue} = 1 \, \mu\text{W} = 1 \times 10^{-6} \, \text{W}</math>
* Wavelength of blue light: <math>\lambda_\text{blue} = 450 \, \text{nm}</math>
* Photon energy:
<math>
E_\text{ph} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \cdot 3.0 \times 10^8}{450 \times 10^{-9}} \approx 4.42 \times 10^{-19} \, \text{J}
</math>
* Photon emission rate:
<math>
N_\text{emit} = \frac{P_\text{blue}}{E_\text{ph}} = \frac{1 \times 10^{-6}}{4.42 \times 10^{-19}} \approx 2.26 \times 10^{12} \, \text{photons/s}
</math>
* Emission duration: <math>\Delta t = 50 \, \text{ms} = 0.05 \, \text{s}</math>
* Distance between LEDs: <math>d = 0.1 \, \text{m}</math>
* Red LED pn-junction radius: <math>r = 17 \, \mu\text{m} = 1.7 \times 10^{-5} \, \text{m}</math>
* Entrance area of the pn-junction:
<math>
A = \pi r^2 = \pi (1.7 \times 10^{-5})^2 \approx 9.08 \times 10^{-10} \, \text{m}^2
</math>
* Solid angle covered by receiving junction:
<math>
\Omega = \frac{A}{d^2} = \frac{9.08 \times 10^{-10}}{(0.1)^2} = 9.08 \times 10^{-8} \, \text{sr}
</math>
* Fraction of photons geometrically intercepted:
<math>
f = \frac{\Omega}{4\pi} = \frac{9.08 \times 10^{-8}}{4\pi} \approx 7.23 \times 10^{-9}
</math>
* Shell transmission rate at 450 nm (approximate): <math>T_\text{shell} = 0.2</math>
* Number of detected photo-pulses: <math>N_\text{detected} = 4</math>

'''Photons Reaching the pn-Junction in 50 ms:'''
<math>
N_\text{incident} = N_\text{emit} \cdot \Delta t \cdot f \cdot T_\text{shell} = 2.26 \times 10^{12} \cdot 0.05 \cdot 7.23 \times 10^{-9} \cdot 0.2 \approx 1.63 \times 10^3
</math>

<math>
\eta = \frac{N_\text{detected}}{N_\text{incident}} = \frac{4}{1.63 \times 10^3} \approx 2.45 \times 10^{-3} = 0.245\%
</math>

'''Conclusion:''' Using a realistic pn-junction area and accounting for geometric and spectral filtering factors, the estimated quantum efficiency of the red LED functioning as a photon detector is approximately '''0.245%'''. This aligns with expectations given that LEDs are not optimized for photodetection, especially under off-band excitation (blue light in a red LED).

=== Code Listings ===

[[File:4.png|thumb|Arduino code]]

Main Page

2025-04-24T08:53:42Z

Shijie: /* Single photon double-slit interference */

'''Welcome to the wiki page for the course PC5271: Physics of Sensors!'''

This is the repository where projects are documented. Creation of new accounts have now been blocked,and editing/creating pages is enabled. If you need an account, please contact Christian.

<span style="color: red">'''Deadline for report'''</span>

Deadline for finishing your report on this wiki will be <span style="color: red">'''29 April 2025 23:59:59</span>''' ;) Please be ensured you are happy with your project page at this point, as this will be the basis for our assessment.
Thanks!! Ramanathan Mahendrian and Christian Kurtsiefer

==Projects==
===[[Project 1 (Example)]]===
Keep a very brief description of a project or even a suggestion here, and perhaps the names of the team members, or who to contact if there is interest to join. Once the project has stabilized, keep stuff in the project page linked by the headline.

===[[Laser Gyroscope]]===
Team members: Darren Koh, Chiew Wen Xin

Build a laser interferometer to detect rotation.

===[[Laser Distance Measurer]]===
Team members: Arya Chowdhury, Liu Sijin, Jonathan Wong

This project aims to build a laser interferometer to measure distances.

(CK: We should have fast laser diodes and fast photodiodes, mounted in optics bench kits)

===[[Non-contact Alcohol Concentration Measurement Device At NIR Spectrum]]===
Team members: Lim Gin Joe,Sun Weijia, Yan Chengrui, Zhu Junyi
This project aims to build a sensor to measure the concentration of alcohol by optical method
(CK: you can check Optics Letters <b>47</b>, 5076-5079 (2022) https://doi.org/10.1364/OL.472890 for some info)

===[[Ultrasonic Acoustic Remote Sensing]]===
Team member(s): Chua Rui Ming

How well can we use sound waves to survey the environment?

(CK: we have some ultrasonic transducers around 40kHz, see datasheets below)

===[[Blood Oxygen Sensor]]===
Team members: He Lingzi, Zhao Lubo, Zhang Ruoxi, Xu Yintong

This project aims to build a sensor to detect the oxygen concentration in the blood.

(CK: We have LEDs at 940nm and 660nm peak wavelenth emission, plus some Si photodiodes)

===[[Terahertz Electromagnetic Wave Detection]]===
Team members: Shizhuo Luo, Bohan Zhang

This project aims to detect Terahertz waves, especially terahertz pulses (This is because they are intense and controllable). We may try different ways like electro-optical sampling and VO2 detectors.

===[[Optical measurement of atmospheric carbon dioxide]]===
Team member(s): Ta Na, Cao Yuan, Qi Kaiyi, Gao Yihan, Chen Yiming

This project aims to make use of the optical properties of carbon dioxide gas to create a portable and accurate measurement device of carbon dioxide.

===[[Photodetector with wavelength @ 780nm and 1560nm]]===
Team members: Sunke Lan

To design photodetector as power monitor with power within 10mW.

(CK: Standard problem, we have already the respective photodiodes)

===[[LED based avalanched photodetector]]===

Team members: Cai Shijie, Nie Huanxin, Yang Runzhi

1.Build a single photon detector using LED. The possible LED is gallium compounds based, emitting wavelength around 800nm(red light).

2. Other possible detector: photomultiplier or avalanche photon detector(do we have that?).

3.Do single double-slit interference experiment.

Other devices needed: use LED as single photon source (wavelength shorter than the emitting wavelength 800nm)

prove the detection is single photon: need optical fibre, counting module

===[[Motor Rotation Speed Measurement via the Hall Effect Sensor]]===

Team members: Mi Tianshuo

This project implements a Hall effect sensor to measure the rotation speed of a circuit board-controlled rotary plate.

===[[STM32-Based IMU Attitude Estimation]]===

Team members: Li Ding, Fan Xuting

This project utilizes an STM32 microcontroller and an MPU6050 IMU sensor to measure angular velocity and acceleration, enabling real-time attitude angle computation for motion tracking.

===[[Magnetic field sensing using a fluxgate magnetometer]]===
Team members: Ni Xueqi

This project uses the fluxgate magnetometer to quantify the magnitude of an external magnetic field generated through coils with varying currents and permanent magnets with varying distances.

===[[CO2 Concentration Detector]]===
Team members: Xie Zihan，Zhao Yun，Zhang Wenbo

Infrared absorption-based CO₂ gas sensors are developed based on the principle that different substances exhibit different absorption spectra. Because the chemical structures of different gas molecules vary, their degrees of absorption of infrared radiation at various wavelengths also differ. Consequently, when infrared radiation of different wavelengths is directed at the sample in turn, certain wavelengths are selectively absorbed and thus weakened by the sample, generating an infrared absorption spectrum.

Once the infrared absorption spectrum of a particular substance is known, its infrared absorption peaks can be identified. For the same substance, when the concentration changes, the absorption intensity at a given absorption peak also changes, and this intensity is directly proportional to the concentration. Therefore, by detecting how the gas alters the wavelength and intensity of the light, one can determine the gas concentration.

===[[Light Sensing System Based on the Photoelectric Effect]]===
Team members: Xu Ruizhe, Wei Heyi, Li Zerui, Ma Shunyu

This project utilizes the principle of the photoelectric effect to design a smart light sensing system. The system can detect ambient light intensity and process the data using Arduino or Raspberry Pi. When the light intensity changes beyond a predefined threshold, the system can trigger responses such as lighting up an LED, activating a buzzer, or automatically adjusting curtains.

===[[Temperature and humidity sensors]]===
Team members: Chen Andi, Chen Miaoge, Chen Yingnan, Fang Ye

This project aims to design and evaluate a real-time temperature and humidity monitoring system based on Arduino and the DHT11 sensor. The system is low-cost, easy to implement, and suitable for applications such as smart homes, agriculture, and storage environments. In addition to system development, the project compares the performance of the DHT11 and SHT31 sensors in various environments—indoor, outdoor, and rainy conditions—to assess their accuracy, stability, and response time. The results help guide practical sensor selection, especially in scenarios where cost and simplicity are prioritized over high precision.

===[[Ultrasonic Doppler Speedometer]]===
Team members: Yang Yuzhen, Liu Xueyi, Shao Shuai

Design and build an ultrasonic Doppler speedometer to measure the velocity of a moving object.

==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]]
* 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 CO<sub>2</sub> absorption
* Resistor color codes are explained [https://en.wikipedia.org/wiki/Electronic_color_code here]
* Ultrasonic detectors:
** plastic detctor, 40 kHz, -74dB: [[Media:MCUSD16P40B12RO.pdf|MCUSD16P40B12RO]]
** metal casing/waterproof, 48 kHz, -90dB, [[Media:MCUSD14A48S09RS-30C.pdf|MCUSD14A48S09RS-30C]]
** metal casing, 40 kHz, sensitivity unknown, [[Media:MCUST16A40S12RO.pdf|MCUST16A40S12RO]]
** metal casing/waterproof, 300kHz, may need high voltage: [[Media:MCUSD13A300B09RS.pdf|MCUSD13A300B09RS]]
* Magnetic field sensor
** Fluxgate magnetometer [[media:Data-sheet FLC-100.pdf|FCL100]]
* 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]]
** Transimpedance amplifiers for photodetectors: [[media:AD8015.pdf|AD8015]]

===Some code snippets===
* For the [[media:Generic FPGA board version 3 - Quantum Optics Wiki.pdf|pattern generator]], you need to send the following text file to it to generate ultrasonic pulses:

# This pattern is to generate a burst of 10..20 oscillations at 40 kHz
# every 100ms for a sonar test. Pulses are TTL level on the AUX output,
# I/O lane 0 bit 7 is a sync pulse (10ns long), I/O lane 0 bit 0 copies the
# aux line, bit 1 indicates the pause periode between bursts.
# Internal counter 0 is for burst counting, int counter 1 for pause cycles

# Set device to programming mode: reset table, reset RAM, program params
config 13
writew 0, 60571; # basic address is 0, input thres -0.5V (not used)
writew 0,0,0,0; # external counter preload (not used)
writew 9,999,0,0; # internal cnt preload only first one is relevant
# and determines the number of pulses (minus 1) and
# number minus 1 of multiples of 100us for pause
writew 0,0,0,0,0,0,0,0; # DAC preload - not used

config 4; # switch to RAM write

# This is the RAM sequence- starting with 40kHz burst
writew 0x80,0,0,0,0,0, 0,0x1010; # ad 0: sync pulse 10nsec, load cnt 0
writew 0x01 0,0,1,0,0,1248,0xc004; # ad 1: pulse on (12.49us), if done go ad4
writew 0x01 0,0,1,0,0, 0,0x1100; # ad 2: pulse on for 10ns, decr int cnt 0
writew 0x00,0,0,0,0,0,1249,0x0001; # ad 3: pulse off for 12.5us, then go 1

# Waiting time / pause
writew 0x02,0,0,0,0,0, 0,0x1020; # ad 4: preload internal cntr 1 (10ns)
writew 0x02,0,0,0,0,0,9998,0x1200; # ad 5: decr cnt1 (10ns)
writew 0x02,0,0,0,0,0, 0,0xd008; # ad 6: if count is down goto ad 8(10ns)
writew 0x02,0,0,0,0,0, 0,0x0005; # ad 7: goto ad 5(10ns)

writew 0x02,0,0,0,0,0, 0,0x0000; # ad 8: restart (goto ad 0; 10ns)

# start pattern and keep output level on AUX line to TTL level
config 0x400;

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

== Old Wiki ==
You can find entries to the wiki from [https://pc5271.org/PC5271_AY2324S2 AY2023/24 Sem 2]

Main Page

2025-03-04T02:22:29Z

Shijie: /* Single photon double-slit interference */

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2025-03-04T02:21:45Z

Shijie: /* Single photon double-slit interference */

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2025-03-04T02:08:21Z

Shijie: /* Single photon double-slit interference */

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2025-03-04T01:50:10Z

Shijie: /* Single photon double-slit interference */

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2025-02-20T07:28:03Z

Shijie: /* Single photon double-slit interference */

Main Page

2025-02-20T07:27:11Z

Shijie: /* Single photon double-slide interference */

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2025-02-20T07:26:36Z

Shijie: /* Single photon double-slide interference */

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2025-02-20T07:22:52Z

Shijie: /* Projects */

Main Page

2025-02-20T07:22:12Z

Shijie: /* Projects */