  The EMCCD is a CCD type that delivers fast readout and negligible detector
noise, making it an ideal detector for high frame rate applications. Because of
the very low detector noise, this detector can potentially count single
photons. Considering that an EMCCD has a limited dynamical range and negligible
detector noise, one would typically apply an EMCCD in such a way that multiple
images of the same object are available, for instance, in so called lucky
imaging. The problem of counting photons can then conveniently be viewed as
statistical inference of flux or photon rates, based on a stack of images. A
simple probabilistic model for the output of an EMCCD is developed. Based on
this model and the prior knowledge that photons are Poisson distributed, we
derive two methods for estimating the most probable flux per pixel, one based
on thresholding, and another based on full Bayesian inference. We find that it
is indeed possible to derive such expressions, and tests of these methods show
that estimating fluxes with only shot noise is possible, up to fluxes of about
one photon per pixel per readout.
