Zhang Anqi, Piao Daqing, Bunting Charles F
School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA.
J Opt Soc Am A Opt Image Sci Vis. 2012 Apr 1;29(4):545-58. doi: 10.1364/JOSAA.29.000545.
This is Part III of the work that examines photon diffusion in a scattering-dominant medium enclosed by a "concave" circular cylindrical applicator or enclosing a "convex" circular cylindrical applicator. In Part II of this work Zhang et al. [J. Opt. Soc. Am. A, 66 (2011)] predicted that, on the tissue-applicator interface of either "concave" or "convex" geometry, there exists a unique set of spiral paths, along which the steady-state photon fluence rate decays at a rate equal to that along a straight line on a planar semi-infinite interface, for the same line-of-sight source-detector distance. This phenomenon of steady-state photon diffusion is referred to as "straight-line-resembling-spiral paths" (abbreviated as "spiral paths"). This Part III study develops analytic approaches to the spiral paths associated with geometry of a large radial dimension and presents spiral paths found numerically for geometry of a small radial dimension. This Part III study also examines whether the spiral paths associated with a homogeneous medium are a good approximation for the medium containing heterogeneity. The heterogeneity is limited to an anomaly that is aligned azimuthally with the spiral paths and has either positive or negative contrast of the absorption or scattering coefficient over the background medium. For a weak-contrast anomaly the perturbation by it to the photon fluence rate along the spiral paths is found by applying a well-established perturbation analysis in cylindrical coordinates. For a strong-contrast anomaly the change by it to the photon fluence rate along the spiral paths is computed using the finite-element method. For the investigated heterogeneous-medium cases the photon fluence rate along the homogeneous-medium associated spiral paths is macroscopically indistinguishable from, and microscopically close to, that along a straight line on a planar semi-infinite interface.
这是一项研究的第三部分，该研究考察了光子在由“凹形”圆柱型施照器包围或包围“凸形”圆柱型施照器的散射主导介质中的扩散情况。在本研究的第二部分中，Zhang等人[《美国光学学会杂志A》，66 (2011)]预测，在“凹形”或“凸形”几何形状的组织 - 施照器界面上，存在一组独特的螺旋路径，对于相同的视线源 - 探测器距离，沿着这些螺旋路径的稳态光子注量率衰减速率与平面半无限界面上直线的衰减速率相等。这种稳态光子扩散现象被称为“类直线螺旋路径”（简称为“螺旋路径”）。本第三部分研究针对具有大径向尺寸几何形状的螺旋路径开发了解析方法，并给出了针对小径向尺寸几何形状通过数值方法找到的螺旋路径。本第三部分研究还考察了与均匀介质相关的螺旋路径对于包含非均匀性的介质是否是一个良好的近似。非均匀性仅限于与螺旋路径方位对齐且在背景介质上具有吸收或散射系数正或负对比度的异常情况。对于弱对比度异常，通过在柱坐标系中应用成熟的微扰分析来找到其对沿螺旋路径的光子注量率的微扰。对于强对比度异常，使用有限元方法计算其对沿螺旋路径的光子注量率的变化。对于所研究的非均匀介质情况，沿均匀介质相关螺旋路径的光子注量率在宏观上与平面半无限界面上直线的光子注量率无法区分，并且在微观上与之接近。
