Analytic solution of the radiative transfer equation for the analysis of the efficiency and spatial resolution of a granular X-ray scintillator

In this study, we discussed the efficiency and spatial resolution of a granular X-ray scintillator using an analytic solution of the radiative transfer equation (RTE). A conventional X-ray scintillator employs a large high-density charge-coupled device (CCD) in direct contact with thin phosphor layers to remove imaging optics. To analyze the performance of the scintillator using the CCD, we derive the analytic solution of the RTE in order to calculate light propagation in a double-layer structure without imaging optics. The analytic solution calculates multiple light sources and scatterings in the phosphor layer as well as refraction in the dielectric-layer interface between the phosphor layer and the CCD. For the calculations, we introduced the scattering phase function, including the backward scattering due to micron-sized phosphor particles, and included the geometrical relations of the refraction at the interface. We analyzed the performance of the scintillator with respect to various scintillator design parameters, such as the size of phosphor particles, the thickness of the phosphor layer, and the thickness and refractive index of the dielectric interlayer. We confirmed the analytic calculation by comparing the results with those obtained using a Monte Carlo (MC) simulation tool. The results are in good agreement, with small differences of 1% and 3% on average for the total efficiency and spatial resolution of the scintillator, respectively.