A photon counting detector model based on increment matrices to simulate statistically correct detector signals

We present a novel increment matrix concept to simulate the correlations in an energy-selective photon counting detector. Correlations between the energy bins of neighboring detector pixels are introduced by scattered and fluorescence photons, together with the broadening of the induced charge clouds as they travel towards the electrodes, leading to charge sharing. It is important to generate statistically correct detector signals for the different energy bins to be able to realistically assess the detector's performance in various tasks, e.g. material decomposition. Our increment matrix concept describes the counter increases in neighboring pixels on a single event level. Advantages of our model are the fact that much less random numbers are required than simulating single photons and that the increment matrices together with their probabilities have to be generated only once and can be stored for later use. The different occurring increment matrix sets and the corresponding probabilities are simulated using an analytic model of the photon-matter-interactions based on the photoelectric effect and Compton scattering, and the charge cloud drift, featuring thermal diffusion and Coulomb expansion of the charge cloud. The results obtained with this model are evaluated in terms of the spectral response for different detector geometries and the resulting energy bin sensitivity. Comparisons to published measured data and a parameterized detector model show both a good qualitative and quantitative agreement. We also studied the resulting covariance of reconstructed energy bin images.