Graphical thresholding procedure and optimal light level estimation for spatially resolved photon counting with EMCCDs

Thanks to the electron multiplying function that can effectively convert the weak incident photon signal to amplified electron output, electron multiplying charged-coupled devices (EMCCDs) are becoming useful and popular detectors in photon counting regimes necessitating also spatial resolution. A multi-imaging strategy has been already proposed and experimentally tested to improve the accuracy of photon counting with an EMCCD, by taking into account the random nature of its on-chip gain and the possibility of multiple photodetection events on 1 pixel. In this paper, referring to the thresholding procedure developed for photon counting, we present a clear graphical method for the threshold and the optimal light level estimations. Thanks to the graphical visualization of the probabilities involved in the detection errors on 1 pixel, we are able to derive in a straightforward way and for any EMCCD, the threshold level and thus the best mean level of illumination to be used in order to minimize the false detection probabilities that might ruin the image statistics, especially in cases where quantum spatial effects might be observed.