Kim Arnold D
Department of Mathematics, Stanford University, Stanford, California 94305-2125, USA.
Appl Opt. 2004 Jan 20;43(3):555-63. doi: 10.1364/ao.43.000555.
We study light propagation in biological tissue containing an absorbing obstacle. In particular, we solve the infinite-domain problem in which an absorbing plate of negligible thickness prevents a portion of the light from the source from reaching the detector plane. Inasmuch as scattering in the medium is sharply peaked in the forward direction, we replace the governing radiative transport equation with the Fokker-Planck equation. The problem is solved first by application of the Kirchhoff approximation to determine the secondary source distribution over the surface of the plate. That result is propagated to the detector plane by use of Green's function. The Green's function is given as an expansion of plane-wave modes that are calculated numerically. The radiance is shown to obey Babinet's principle. Results from numerical computations that demonstrate this theory are shown.
我们研究光在含有吸收障碍物的生物组织中的传播。特别地，我们解决了一个无限域问题，其中一个厚度可忽略不计的吸收板阻止了一部分来自光源的光到达探测器平面。由于介质中的散射在向前方向上急剧峰值化，我们用福克 - 普朗克方程代替主导的辐射传输方程。首先通过应用基尔霍夫近似来确定板表面上的二次源分布，从而解决该问题。该结果通过使用格林函数传播到探测器平面。格林函数表示为通过数值计算得到的平面波模式的展开。结果表明辐射率服从巴比涅原理。展示了证明该理论的数值计算结果。
