Compton coincidence in silicon photon-counting CT detectors

Compton interactions amount to a significant fraction of the registered counts in a silicon detector. In a Compton interaction, only a part of the photon energy is deposited and a single incident photon can result in multiple counts unless tungsten shielding is used. Silicon has proved to be a competitive material for photon-counting CT detectors but to improve the performance further, it is desirable to use coincidence techniques to identify Compton scattered photons and reconstruct their energies. In a detector with no tungsten shielding, incident photons can interact through a series of interactions. By using information about the position and energy of each interaction, probability-based methods can be used to estimate the incident photon energy. In this work we present a framework of likelihood functions that can be used to estimate the incident photon energy in a silicon detector. For a low count-rate case with one incident photon per time frame, we show that the proposed likelihood framework can estimate the incident photon energy with a mean error of -0.26 keV and an RMS error of 1.14 keV for an ideal case with a perfect detector. For a non-ideal case including spatial and energy resolution, the corresponding results were -0.08 keV and 0.66 keV, respectively. The fraction of correctly identified interaction chains, with respect to the interaction order, were 99.2% in the ideal case and 97.3% in the non-ideal case.