Modeling the impact of coincidence loss on count rate statistics and noise performance in counting detectors for imaging applications

Coincidence loss can have detrimental effects on the image quality provided by pixelated counting detectors, especially in dose-sensitive applications like cryoEM where the information extracted from the recorded signal needs to be maximized. In this work, we investigate the impact of coincidence loss phenomena on the recorded statistics in counting detectors producing sparse binary images. First, we derive exact analytical expressions for the mean and the variance of the recorded counts as a function of the incoming event rate. Second, we address the problem of the mean and variance of the recorded events (i.e., pixel clusters identified as individual incoming events), which also acts as a function of the incoming event rate. In this frame, we review previous studies from different disciplines on approximated two-dimensional models, and we critically reinterpret them in our context and evaluate the suitability of their adoption in the present case. The knowledge of the first two momenta of the recorded statistics allows inferring about the signal-to-noise ratio (SNR) and the detective quantum efficiency at zero frequency (DQE0). Analytical results are validated through comparison with numerical data obtained with a custom-made Monte Carlo code. We chose a realistic case study for cryoEM application consisting of a 25-µm-thick MAPS detector featuring a pixel size of 10 µm and illuminated with electrons of 300 keV energy over a wide range of incoming rate.