I was wondering how would Poisson statistics be used in a photodetectors to account for the number of events that I'm missing in my experiment. Say I have a material (scintillator, ...) that emits $n$ photons per particle and a Photomultiplier tube (PMT) or any other photodetector with quantum efficiency Q. If I have $N$ particles arriving to the detector, how would I use Poisson statistics to calculate the number of particles that I'm missing?
The convolution of a Poisson with a binomial is a Poisson - which makes life easy. $n$ will be Poisson, and $N$ will be Poisson with mean $nQ$.