Joint Department of Physics, Division of Radiotherapy and Imaging, Institute of Cancer Research and Royal Marsden NHS Foundation Trust, Downs Road, Sutton, Surrey SM2 5PT, United Kingdom.
Med Phys. 2013 Apr;40(4):041904. doi: 10.1118/1.4794483.
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.
在这项两部分工作的第一部分中，基于三种不同的方法，对粉末磷光体屏幕中的光传输进行了预测。将基于屏幕结构的显式微观模型 (EMM) 的几何光学射线追踪预测与基于玻尔兹曼输运方程 (BTE) 和 Swank 扩散方程解的蒙特卡罗程序进行了比较。目的是：(I) 突出 BTE 蒙特卡罗方法和 Swank 模型（两者以前都在文献中使用过）相对于 EMM 方法的附加假设；(II) 证明在明确定义的条件下，这些方法是等效的；(III) 确定模型之间任何差异的开始和严重程度。提供了一套计算机代码（称为 phsphr），可用于重现本文中呈现的 BTE 蒙特卡罗结果。
为假设的荧光粉颗粒在结合剂中的微观结构实施 EMM 几何光学射线追踪模型。BTE 模型作为一个蒙特卡罗程序实现，其传输参数由输入的几何光学推导得出。Swank 对扩散方程的解析解与 EMM 和 BTE 预测进行了比较。针对一系列结合剂与荧光粉的相对折射率（n = 1.1-5.0）、屏幕厚度（t = 50-200 μm）和堆积填充因子（pf = 0.04-0.54）计算了吸收分数和调制传递函数（MTF）。
随着 n 和 pf 的增加，BTE 方法与 EMM 方法之间的差异也越来越大。对于最大的相对折射率（n = 5）和最高的堆积填充因子（pf = 0.5），BTE 模型低估了吸收分数和 MTF50，分别高达 40%和 20%。然而，对于实际磷光体屏幕（n≤2）的典型相对折射率，如 Gd2O2S:Tb，BTE 和 EMM 预测在所有模拟的堆积密度下都非常吻合。此外，当屏幕足够厚可以被视为混浊时，Swank 模型与 BTE 预测非常吻合。
尽管 BTE 的某些假设在实际的粉末磷光体屏幕中被违反，但这些假设在典型的磷光体和结合剂折射率的光传输建模中似乎没有产生显著影响。因此，使用基于 BTE 的蒙特卡罗代码来处理这个问题是合理的。此外，如果满足此处提出的浊度条件，则 Swank 的扩散方程解是一个合适的近似。
