Plass G N, Kattawar G W, Catchings F E
Appl Opt. 1973 Feb 1;12(2):314-29. doi: 10.1364/AO.12.000314.
An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles including the polar angle theta = 0 degrees ; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions. Both the general theory and its history together with the method of calculation are discussed. As a first example of the method numerous curves are given for both the reflected and transmitted radiance for Rayleigh scattering from a homogeneous layer for a range of optical thicknesses from 0.0019 to 4096, surface albedo A = 0, 0.2, and 1, and cosine of solar zenith angle micro = 1, 0.5397, and 0.1882. It is shown that the matrix operator approach contains the doubling method as a special case.
回顾了一种基于矩阵算子理论求解辐射传输方程的完全严格的方法。该方法的优点如下：（1）反射矩阵和透射矩阵的所有阶数一次性计算得出；（2）任意厚度的层可以合并，从而可以根据任意数量的具有不同特性和厚度的层建立一个逼真的大气模型；（3）对于大光学厚度和具有高度各向异性相函数的情况，计算可以很容易地进行；（4）对于包括表面反照率为1在内的任何所需表面反照率值以及包括极角θ = 0度在内的大量极角和方位角，都能得到结果；（5）所有基本方程都可以立即根据与该问题相关的物理相互作用来解释；（6）可以从相对简单的表达式计算内部点处的向上和向下辐射率。讨论了该一般理论及其历史以及计算方法。作为该方法的第一个示例，给出了一系列曲线，这些曲线表示从均匀层进行瑞利散射时，在光学厚度范围从0.0019到4096、表面反照率A = 0、0.2和1以及太阳天顶角余弦μ = 1、0.5397和0.1882的情况下的反射辐射率和透射辐射率。结果表明，矩阵算子方法包含加倍法作为一种特殊情况。
