Optical photon transport in powdered-phosphor scintillators. Part II. Calculation of single-scattering transport parameters

Abstract

Purpose: Monte Carlo methods based on the Boltzmann transport equation (BTE) have previously been used to model light transport in powdered-phosphor scintillator screens. Physically motivated guesses or, alternatively, the complexities of Mie theory have been used by some authors to provide the necessary inputs of transport parameters. The purpose of Part II of this work is to: (i) validate predictions of modulation transform function (MTF) using the BTE and calculated values of transport parameters, against experimental data published for two Gd2O2S:Tb screens; (ii) investigate the impact of size-distribution and emission spectrum on Mie predictions of transport parameters; (iii) suggest simpler and novel geometrical optics-based models for these parameters and compare to the predictions of Mie theory. A computer code package called phsphr is made available that allows the MTF predictions for the screens modeled to be reproduced and novel screens to be simulated.

Methods: The transport parameters of interest are the scattering efficiency (Q sct), absorption efficiency (Q abs), and the scatter anisotropy (g). Calculations of these parameters are made using the analytic method of Mie theory, for spherical grains of radii 0.1-5.0 μm. The sensitivity of the transport parameters to emission wavelength is investigated using an emission spectrum representative of that of Gd2O2S:Tb. The impact of a grain-size distribution in the screen on the parameters is investigated using a Gaussian size-distribution (σ = 1%, 5%, or 10% of mean radius). Two simple and novel alternative models to Mie theory are suggested: a geometrical optics and diffraction model (GODM) and an extension of this (GODM+). Comparisons to measured MTF are made for two commercial screens: Lanex Fast Back and Lanex Fast Front (Eastman Kodak Company, Inc.).

Results: The Mie theory predictions of transport parameters were shown to be highly sensitive to both grain size and emission wavelength. For a phosphor screen structure with a distribution in grain sizes and a spectrum of emission, only the average trend of Mie theory is likely to be important. This average behavior is well predicted by the more sophisticated of the geometrical optics models (GODM+) and in approximate agreement for the simplest (GODM). The root-mean-square differences obtained between predicted MTF and experimental measurements, using all three models (GODM, GODM+, Mie), were within 0.03 for both Lanex screens in all cases. This is excellent agreement in view of the uncertainties in screen composition and optical properties.

Conclusions: If Mie theory is used for calculating transport parameters for light scattering and absorption in powdered-phosphor screens, care should be taken to average out the fine-structure in the parameter predictions. However, for visible emission wavelengths (λ < 1.0 μm) and grain radii (a > 0.5 μm), geometrical optics models for transport parameters are an alternative to Mie theory. These geometrical optics models are simpler and lead to no substantial loss in accuracy.