1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Uncertainties in Poisson processes

  1. Jul 3, 2016 #1
    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
  2. jcsd
  3. Jul 3, 2016 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    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.
  4. Jul 3, 2016 #3
    Thank you so much! it helped a lot :)
  5. Jul 5, 2016 #4

    Andy Resnick

    User Avatar
    Science Advisor
    Education Advisor

    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 [Broken]
    http://www.hamamatsu.com/jp/en/community/optical_sensors/sipm/measuring_mppc/index.html [Broken]
    http://www.hamamatsu.com/jp/en/community/optical_sensors/all_sensors/index.html [Broken]
    Last edited by a moderator: May 8, 2017
  6. Jul 9, 2016 #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..
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted