Fishkin J B, Gratton E
Department of Physics, University of Illinois, Urbana-Champaign 61801.
J Opt Soc Am A. 1993 Jan;10(1):127-40. doi: 10.1364/josaa.10.000127.
Light propagation in strongly scattering media can be described by the diffusion approximation to the Boltzmann transport equation. We have derived analytical expressions based on the diffusion approximation that describe the photon density in a uniform, infinite, strongly scattering medium that contains a sinusoidally intensity-modulated point source of light. These expressions predict that the photon density will propagate outward from the light source as a spherical wave of constant phase velocity with an amplitude that attenuates with distance r from the source as exp(-alpha r)/r. The properties of the photon-density wave are given in terms of the spectral properties of the scattering medium. We have used the Green's function obtained from the diffusion approximation to the Boltzmann transport equation with a sinusoidally modulated point source to derive analytic expressions describing the diffraction and the reflection of photon-density waves from an absorbing and/or reflecting semi-infinite plane bounded by a straight edge immersed in a strongly scattering medium. The analytic expressions given are in agreement with the results of frequency-domain experiments performed in skim-milk media and with Monte Carlo simulations. These studies provide a basis for the understanding of photon diffusion in strongly scattering media in the presence of absorbing and reflecting objects and allow for a determination of the conditions for obtaining maximum resolution and penetration for applications to optical tomography.
强散射介质中的光传播可以用玻尔兹曼输运方程的扩散近似来描述。我们基于扩散近似推导了解析表达式，这些表达式描述了在均匀、无限、强散射介质中包含正弦强度调制点光源时的光子密度。这些表达式预测，光子密度将作为具有恒定相速度的球面波从光源向外传播，其振幅随距光源距离r按exp(-αr)/r衰减。光子密度波的特性由散射介质的光谱特性给出。我们利用从具有正弦调制点光源的玻尔兹曼输运方程的扩散近似中得到的格林函数，推导了描述光子密度波从浸没在强散射介质中的直边界定的吸收和/或反射半无限平面的衍射和反射的解析表达式。给出的解析表达式与在脱脂牛奶介质中进行的频域实验结果以及蒙特卡罗模拟结果一致。这些研究为理解在存在吸收和反射物体的情况下强散射介质中的光子扩散提供了基础，并允许确定在光学层析成像应用中获得最大分辨率和穿透深度的条件。
