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

TL;DR

This paper develops Bayesian methods for photon counting using EMCCDs, enabling flux estimation at the shot noise limit for high frame rate imaging with negligible detector noise.

Contribution

It introduces a probabilistic model and Bayesian inference techniques for photon counting with EMCCDs, a novel approach in this context.

Findings

Photon flux can be estimated up to about one photon per pixel per readout.

Bayesian inference outperforms simple thresholding in flux estimation.

Methods are validated through tests demonstrating shot noise-limited performance.

Abstract

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.