Mishchenko M I
Appl Opt. 1993 Aug 20;32(24):4652-66. doi: 10.1364/AO.32.004652.
The ? matrix method, as extended recently to randomly oriented scatterers [J. Opt. Soc. Am. A 8, 871 (1991)], is used to calculate rigorously light scattering by size-shape distributions of randomly oriented axially symmetric particles. The computational scheme is described in detail along with a newly developed convergence procedure that enables one to substantially reduce computer time and storage requirements. It is demonstrated that the elements of the Stokes scattering matrix for a power law size distribution of randomly oriented moderately aspherical spheroids are much smoother than and differ substantially from those of equivalent monodisperse spheroids, and thus averaging over orientations does not eliminate the necessity of averaging over particle sizes. Numerical calculations are reported for volume-equivalent polydispersions of spheres and size-shape distributions of moderately aspherical spheroids with the index of refraction 1.5 + 0.02 i, which is typical of some maritime aero ls. The angular-scattering behavior of the ensembles of nonspherical particles is found to be greatly different from that of the equivalent polydisperse spheres. The size-shape distributions of spheroids exhibit stronger side scattering near 120° and weaker backscattering, the ratio F(22)/F(11), of the elements of the scattering matrix substantially deviates from unity, and the element F(33) is greatly different from F(44). For size distributions of oblate and prolate spheroids of the same aspect ratio, the ratios F(22) /F(11), F(33) /F(11), and F(34)/F(11), can differ substantially and, thus, are indicators of particle shape, whereas the angular patterns of the intensity (F(11)) and linear polarization (-F(12)/F11) are similar. For the size-shape distributions of moderately aspherical spheroids, the optical cross sections, the single-scattering albedo, and the asymmetry parameter of the phase function do not differ substantially from those of equivalent spheres. In general, the elements of the scattering matrix and optical cross sections are more shape dependent for larger particles.
最近扩展到随机取向散射体的矩阵方法[《美国光学学会志A》8, 871 (1991)]，用于严格计算随机取向轴对称粒子的尺寸 - 形状分布引起的光散射。详细描述了计算方案以及新开发的收敛程序，该程序能够大幅减少计算机时间和存储需求。结果表明，对于随机取向的中等非球形椭球体幂律尺寸分布，斯托克斯散射矩阵的元素比等效单分散椭球体的元素平滑得多，且有显著差异，因此对取向进行平均并不能消除对粒径进行平均的必要性。报告了折射率为1.5 + 0.02i（这是一些海洋气溶胶的典型值）的体积等效多分散球体和中等非球形椭球体尺寸 - 形状分布的数值计算结果。发现非球形粒子集合的角散射行为与等效多分散球体的角散射行为有很大不同。椭球体的尺寸 - 形状分布在120°附近表现出更强的侧向散射和较弱的后向散射，散射矩阵元素的比值F(22)/F(11)大幅偏离1，元素F(33)与F(44)有很大差异。对于相同纵横比的扁椭球体和长椭球体的尺寸分布，比值F(22)/F(11)、F(33)/F(11)和F(34)/F(11)可能有显著差异，因此是粒子形状的指标，而强度（F(11)）和线偏振（-F(12)/F11）的角分布相似。对于中等非球形椭球体的尺寸 - 形状分布，光学截面、单次散射反照率和相位函数的不对称参数与等效球体的这些参数没有显著差异。一般来说，对于较大粒子，散射矩阵的元素和光学截面更依赖于形状。
