A simple Monte Carlo model for the statistics of photon counting detectors

The statistics of photon counting detectors (PCDs) differ in several aspects from the statistics of energy integrating detectors (EIDs). Particularly, the effect of crosstalk in a PCD involves a 0/1 decision: a photon may be counted in a neighboring pixel or not whereas in an EID the neighboring pixel may just receive a fraction of the signal. Another interesting effect is that, especially for high counting thresholds, there exists a zone at the edge of the pixel where absorbed x-ray energy will not produce any signal. This may lead to a modulation transfer function (MTF) exceeding the theoretical limit given by the nominal pixel aperture. This fact has also been observed in measurements. Goal of this work is to present a simple but comprehensive description of PCD detectors in the low flux limit capable of including all relevant effects. The model presented is based on a Monte Carlo simulation of the x-ray energy deposition in the detector and a simple model of the charge cloud propagation. A reformulation of the probability generating function formalism allows calculating all relevant quantities like mean signal values or covariances between thresholds and/or neighboring pixels or the MTF and DQE as a function of input photon energy directly from the Monte Carlo simulation.