Spatial Pileup Considerations for Pixellated Gamma -ray Detectors.

High-spatial-resolution solid-state detectors being developed for gamma-ray applications benefit from having pixel dimensions substantially smaller than detector slab thickness. This leads to an enhanced possibility of charge partially spreading to neighboring pixels as a result of diffusion (and secondary photon emission) transverse to the drift direction. An undesirable consequence is the effective magnification of the event "size" and the spatial overlap issues which result when two photons are absorbed in close proximity within the integration time of the detector/readout system. In this work, we develop the general statistics of spatial pileup in imaging systems and apply the results to detectors we are developing based on pixellated cadmium zinc telluride (CdZnTe) and a multiplexing application-specific integrated circuit (ASIC) readout. We consider the limitations imposed on total count rate capacity and explore in detail the consequences for the LISTMODE data-acquisition strategy. Algorithms are proposed for identifying and, where possible, resolving overlapping events by maximum-likelihood estimation. The efficacy and noise tolerance of these algorithms will be tested with a combination of simulated and experimental data in future work.