Marinyuk V V, Remizovich V S, Sheberstov S V
J Opt Soc Am A Opt Image Sci Vis. 2020 Mar 1;37(3):501-510. doi: 10.1364/JOSAA.385178.
We study the angular distribution of light diffusely reflected from a turbid medium with large (compared to the light wavelength) inhomogeneities. Using Monte Carlo radiative transfer simulations, we calculate the azimuthally averaged bidirectional reflectance for an optically thick plane-parallel medium and analyze its dependence on the parameters of the scattering phase function. To model single scattering in the medium, we take advantage of the Reynolds-McCormick phase function. For grazing angles of incidence, we find that the angular distribution of reflected light becomes very sensitive to the angular profile of the scattering phase function. The more elongated the phase function, the more pronounced the peak that arises around the specular reflection angle. Comparison of our numerical results with an analytic solution of the radiative transfer equation is performed, and it is shown that the bidirectional reflectance can be decomposed into two contributions, namely, the diffusion contribution and the contribution from light experiencing multiple scattering through small angles. The latter relates directly to the angular profile of the scattering phase function and is responsible for the peak in the angular distribution of reflected light. An explicit analytic formula for the azimuthally averaged bidirectional reflectance is obtained.
我们研究了从具有大尺度（与光波长相比）不均匀性的混浊介质漫反射光的角分布。利用蒙特卡罗辐射传输模拟，我们计算了光学厚平面平行介质的方位角平均双向反射率，并分析了其对散射相函数参数的依赖性。为了模拟介质中的单次散射，我们利用了雷诺兹 - 麦考密克相函数。对于掠入射角，我们发现反射光的角分布对散射相函数的角分布变得非常敏感。相函数越细长，在镜面反射角附近出现的峰值就越明显。将我们的数值结果与辐射传输方程的解析解进行了比较，结果表明双向反射率可以分解为两个贡献，即扩散贡献和经历小角度多次散射的光的贡献。后者直接与散射相函数的角分布相关，并导致反射光角分布中的峰值。得到了方位角平均双向反射率的显式解析公式。
