What is the standard deviation for this combination of functions

#1
I'm trying to compare the noise level of different cameras. I should be using identical exposures but I don't have them, so I have to average two images from one camera to approximate the exposure level of another camera.

Suppose camera A took an exposure of 1.5s
Camera B took exposures of 1s and 2s--so I would like to approximate the noise level of a 1.5s exposure by some combination of the 1s and 2s exposures.

The noise is Poisson / shot noise of the number of photons gathered. And the mean number of photons gathered is proportional to the time of the exposure. My goal is to make a blend of the 1s and 2s shot that would have the same SNR as a 1.5s shot.

I haven't touched statistics for years and my head is still spinning from trying to solve the problem--but maybe there's a simple solution here! :) Thanks :)
 

Mean Joe

TS Contributor
#2
Ok I don't know what an SNR is, but maybe there is a simple solution.

Fact 1: The sum of two independent Poisson random variables (with means m1 and m2) is a Poisson random variable (with mean m1+m2)

Fact 2: You say the mean number of photons gathered is proportional to the time of exposure

SO...I think you just need to average the 1s and 2s shots to get your info for a 1.5s shot.