Uncertainties in Poisson processes

In summary, the conversation discusses the issue of characterizing optical detectors in terms of quantum efficiency and other similar things. The main question is how to account for the uncertainty associated with repeated measurements, with two options being to compute the standard deviation or use a squared-root function for Poisson processes. The response suggests that for large counts, option 2 is preferred. However, there may be other noise sources present in the measurement and the use of Single Photon Avalanche Diodes may eliminate the need for gain steps. Hamamatsu has resources available on this topic.
  • #1
marco1235
Good morning PF,

I'm feeling a bit doubtful about this issue. I'm working with optical detectors and I have to characterize them in terms of quantum efficiency and other similar things. Now suppose my detector is, ideally, a single large pixel, which I illuminate for a specific time. Then I store the recorded Nphotons and repeat the procedure for 10k times! At each iteration, due to the randomness of the process I can get 100 counts in the first step, 102 at the second, 95, 87, 101, 106, ... an so on.
I want to make an average of such 10k values, and that's fine. But how about the uncertainty associated with this repeated measure? I have two ways:
1) computing the standard deviation using std-like function (Matlab)
2) putting Navg as argument of the squared-root like in Poisson processes

I'm really stucked in this situation.
Hope someone could help me!
Have a nice day
 
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  • #2
n data points from a poisson distribution are approximately normal for large n (standard deviation ##\sqrt{n}##.
If you have small numbers, then the distributon is strongly skewed and you'll need median and quartiles or some other way to account for skewdness.
So - if you have sufficiently large counts, you want option 2... though either should work.
 
  • #3
Thank you so much! it helped a lot :)
 
  • #4
marco1235 said:
But how about the uncertainty associated with this repeated measure?

It's not clear what you are really asking or trying to characterize- Simon Bridge's response refers only to the noise associated with incoherent photons (thermal light or 'shot noise'), but you have other noise sources: dark current, amplifier noise... Your measurement contains all of these noise sources, which are hopefully independent from each other. Hamamatsu has some very read-able references on this issue:

http://www.hamamatsu.com/jp/en/community/optical_sensors/all_sensors/guide_to_detector_selection/index.html
http://www.hamamatsu.com/jp/en/community/optical_sensors/sipm/measuring_mppc/index.html
http://www.hamamatsu.com/jp/en/community/optical_sensors/all_sensors/index.html
http://www.hamamatsu.com/resources/pdf/ssd/e05_handbook_image_sensors.pdf
 
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  • #5
Dear Andy,

thank you for your answer. You're right, probably I went a bit faster.. in case of an ideal detector (so only shot noise-limited) and photons coming out from a fluorescent specimen, is Simon's reply still valid? In real life my detector is a camera based on Single Photon Avalanche Diodes, and the designers told me that the sensor is only shot noise-limited, since SPADs are able to produce mA range currents upon photo-detection, and thus there's not the need of gain steps like in other optical sensor..
 

1. What is a Poisson process?

A Poisson process is a mathematical model used to describe the occurrence of rare events over a period of time. It is based on the assumption that the events occur independently of each other and at a constant rate.

2. How is uncertainty measured in Poisson processes?

Uncertainty in Poisson processes is typically measured using the standard deviation or variance of the number of events that occur within a given period of time. These measures reflect the randomness and variability in the process.

3. What are the sources of uncertainty in a Poisson process?

The main sources of uncertainty in a Poisson process include the randomness of the events, the variability in the rate of event occurrence, and the finite sample size. Other factors such as measurement errors and external influences can also contribute to uncertainty.

4. How can uncertainties in Poisson processes be reduced?

One way to reduce uncertainty in Poisson processes is to increase the sample size, which can lead to more precise estimates of the event rate. Additionally, identifying and controlling for external factors that may affect the process can also help reduce uncertainty.

5. What are some applications of Poisson processes in science?

Poisson processes have a wide range of applications in science, including in the study of radioactive decay, enzyme kinetics, and population dynamics. They are also commonly used in fields such as epidemiology, finance, and telecommunications to model the occurrence of rare events.

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