Optical photon transport in powdered-phosphor scintillators. Part 1. Multiple-scattering and validity of the Boltzmann transport equation

Abstract

In Part 1 of this two-part work, predictions for light transport in powdered-phosphor screens are made, based on three distinct approaches. Predictions of geometrical optics-based ray tracing through an explicit microscopic model (EMM) for screen structure are compared to a Monte Carlo program based on the Boltzmann transport equation (BTE) and Swank's diffusion equation solution. The purpose is to: (I) highlight the additional assumptions of the BTE Monte Carlo method and Swank's model (both previously used in the literature) with respect to the EMM approach; (II) demonstrate the equivalences of the approaches under well-defined conditions and; (III) identify the onset and severity of any discrepancies between the models. A package of computer code (called phsphr) is supplied which can be used to reproduce the BTE Monte Carlo results presented in this work. The EMM geometrical optics ray-tracing model is implemented for hypothesized microstructures of phosphor grains in a binder. The BTE model is implemented as a Monte Carlo program with transport parameters, derived from geometrical optics, as inputs. The analytical solution of Swank to the diffusion equation is compared to the EMM and BTE predictions. Absorbed fractions and MTFs are calculated for a range of binder-to-phosphor relative refractive indices (n = 1.1-5.0), screen thicknesses (t = 50-200 μm), and packing fill factors (pf = 0.04-0.54). Disagreement between the BTE and EMM approaches increased with n and pf. For the largest relative refractive index (n = 5) and highest packing fill (pf = 0.5), the BTE model underestimated the absorbed fraction and MTF50, by up to 40% and 20%, respectively. However, for relative refractive indices typical of real phosphor screens (n ≤ 2), such as Gd2O2S:Tb, the BTE and EMM predictions agreed well at all simulated packing densities. In addition, Swank's model agreed closely with the BTE predictions when the screen was thick enough to be considered turbid. Although some assumptions of the BTE are violated in realistic powdered-phosphor screens, these appear to lead to negligible effects in the modeling of optical transport for typical phosphor and binder refractive indices. Therefore it is reasonable to use Monte Carlo codes based on the BTE to treat this problem. Furthermore, Swank's diffusion equation solution is an adequate approximation if a turbidity condition, presented here, is satisfied.