Bayesian photon counting with electron-multiplying charge coupled devices (EMCCDs)

¹ Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, 2100 Copenhagen Ø, Denmark
e-mail: harpsoe@nbi.ku.dk
² Centre for Star and Planet Formation, Natural History Museum of Denmark, University of Copenhagen, Øster Voldgade 5-7, 1350 Copenhagen K, Denmark

Received: 15 April 2011
Accepted: 18 October 2011

Abstract

Context. The EMCCD is a charge coupled devices (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.

Aims. 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.

Methods. 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.

Results. 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.