Marinyuk V V, Sheberstov S V
Appl Opt. 2017 Nov 10;56(32):9105-9113. doi: 10.1364/AO.56.009105.
We study the total bulk reflectance of a turbid medium with large (as compared to the light wavelength) inhomogeneities at grazing angles of light incidence. To model highly forward scattering in the medium, we take advantage of the Reynolds-McCormick scattering phase function. Using the scaling analysis for the small-angle radiative transfer equation, we derive simple analytical formulas for the total reflectance. For grazing incidence angles, we find a range of values of the medium transport coefficients where the total reflectance proves to be a universal function of a single parameter, which is expressed in terms of the incidence angle, the absorption coefficient, and the transport scattering one. The explicit form of this function is governed by the specific angular profile of the scattering phase function. The results obtained are verified by comparison with results of a direct numerical integration of the radiative transfer equation.
我们研究了在掠入射角下具有大尺寸（与光波长相比）不均匀性的浑浊介质的总体反射率。为了模拟介质中的强前向散射，我们利用了雷诺兹 - 麦考密克散射相函数。通过对小角度辐射传输方程进行标度分析，我们推导出了总反射率的简单解析公式。对于掠入射角，我们找到了介质输运系数的一系列值，在这些值下总反射率被证明是一个单一参数的通用函数，该参数用入射角、吸收系数和输运散射系数表示。这个函数的显式形式由散射相函数的特定角分布决定。通过与辐射传输方程的直接数值积分结果进行比较，验证了所得到的结果。
