Zhang Anqi, Piao Daqing, Bunting Charles F, Pogue Brian W
School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA.
J Opt Soc Am A Opt Image Sci Vis. 2010 Mar 1;27(3):648-62. doi: 10.1364/JOSAA.27.000648.
This work presents an analytic treatment for photon diffusion in a homogeneous medium bounded externally or internally by an infinitely long circular cylindrical applicator. Focusing initially on the steady-state condition, the photon diffusion in these two geometries is solved in cylindrical coordinates by using modified Bessel functions and by applying the extrapolated boundary condition. For large cylinder diameter, the analytic solutions may be simplified to a format employing the physical source and its image source with respect to a semi-infinite geometry and a radius-dependent term to account for the shape and dimension of the cylinder. The analytic solutions and their approximations are evaluated numerically to demonstrate qualitatively the effect of the applicator curvature--either concave or convex--and the radius on the photon fluence rate as a function of the source-detector distance, in comparison with that in the semi-infinite geometry. This work is subjected to quantitative examination in a coming second part and possible extension to time-resolved analysis.
本文针对光子在由无限长圆柱形施照器外部或内部界定的均匀介质中的扩散问题，给出了一种解析处理方法。最初聚焦于稳态条件，通过使用修正贝塞尔函数并应用外推边界条件，在柱坐标系中求解这两种几何结构中的光子扩散问题。对于大圆柱直径，解析解可简化为一种形式，该形式采用相对于半无限几何结构的物理源及其镜像源，以及一个与半径相关的项来考虑圆柱的形状和尺寸。通过数值评估解析解及其近似值，以定性地展示施照器曲率（凹或凸）和半径对作为源 - 探测器距离函数的光子注量率的影响，并与半无限几何结构中的情况进行比较。本文工作将在后续的第二部分进行定量研究，并可能扩展到时间分辨分析。
