A Uncertainties in Poisson processes

[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 N_photons 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 N_avg 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

 

[Simon Bridge]

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.

 

[marco1235]

Thank you so much! it helped a lot :)

 

[Andy Resnick]

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

 

[marco1235]

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..