Hitzfelder S J, Plass G N, Kattawar G W
Appl Opt. 1976 Oct 1;15(10):2489-500. doi: 10.1364/AO.15.002489.
The complete radiation field including polarization is calculated by the matrix operator method for a model of the real atmosphere. The radiance, direction and amount of polarization, and ellipticity are obtained at the top and bottom of the atmosphere for three values of the surface albedo (0, 0.15, 0.90) and five solar zenith angles. Scattering and absorption by molecules (including ozone) and by aerosols are taken into account together with the variation of the number density of these substances with height. All results are calculated for both a normal aerosol number and a distribution that is one-third of the normal amount at all heights. The calculated values show general qualitative agreement with the available experimental measurements. The position of the neutral points of the polarization in the principal plane is a sensitive indicator of the characteristics of the aerosol particles in the atmosphere, since it depends on the sign and value of the single scattered polarization for scattering angles around 20 degrees and 160 degrees for transmitted and reflected photons, respectively. This, in turn, depends on the index of refraction and size distribution of the aerosols. The neutral point position does not depend appreciably on the surface albedo and, over a considerable range, depends little on the solar zenith angle. The value of the maximum polarization in the principal plane depends on the aerosol amount, surface albedo, and solar zenith angle. It could be used to measure the aerosol amount. The details of the ellipticity curves are similar to those for scattering from pure aerosol layers and, thus, are little modified by the Rayleigh scattering. Aerosols could be identified by their characteristic ellipticity curves.
采用矩阵算子法，针对真实大气模型计算了包含偏振的完整辐射场。针对三种地表反照率值（0、0.15、0.90）和五个太阳天顶角，获取了大气顶部和底部的辐射亮度、偏振方向和量以及椭圆率。考虑了分子（包括臭氧）和气溶胶的散射与吸收，以及这些物质的数密度随高度的变化。所有结果均针对正常气溶胶数以及在所有高度均为正常量三分之一的分布进行了计算。计算值与现有的实验测量结果总体上在定性上相符。主平面中偏振中性点的位置是大气中气溶胶颗粒特性的敏感指标，因为它分别取决于透射和反射光子在约20度和160度散射角处单次散射偏振的符号和值。这又取决于气溶胶的折射率和尺寸分布。中性点位置对地表反照率的依赖不明显，并且在相当大的范围内，对太阳天顶角的依赖也很小。主平面中最大偏振值取决于气溶胶量、地表反照率和太阳天顶角。它可用于测量气溶胶量。椭圆率曲线的细节与纯气溶胶层散射的曲线相似，因此，受瑞利散射的影响很小。气溶胶可通过其特征椭圆率曲线来识别。
