An analytical model of energy response function for CdTe-based photon counting detectors with inter-pixel communication for anti-coincidence corrections

In photon counting detectors (PCDs), the detected energy of an x-ray photon often deviates from its true energy due to a variety of reasons such as Compton scattering. For a given input x-ray energy or spectrum, the statistical distribution of the detected energy is referred to as the energy response function. Knowledge of the energy response function of a given PCD can greatly facilitate the evaluation of the spectral imaging performance and the optimization of PCD imaging systems. In this work, a physics-based analytical model of the energy response function of CdTe-based PCDs was developed. The model covers the whole diagnostic x-ray energy range and incorporates all relevant physical processes into consideration (e.g., K-fluorescence photon reabsorption or escape, Compton scattering). The model is applicable to PCDs operated under the anti-coincidence (i.e., anti-charge sharing) mode by modifying the parameters related to the severity of charge sharing. Those parameters can be experimentally calibrated to adapt the model to specific PCD systems. To validate the proposed model, experiments were performed using a CdTe-based PCD system. The results demonstrated that the model can accurately predict the PCD energy response functions of a variety of input x-ray spectra, under the anti-coincidence or the single pixel detection mode.