Single and multiple electromagnetic scattering by size -shape distributions of small nonspherical particles

Frank Michael Schulz
Wed, 22 Apr 2026 18:26:53 PDT

A comprehensive model for light scattering by size-shape distributions of randomly oriented nonspherical particles is developed. The model uses spheroids as model particles. The vector Helmholtz equation is solved with a new separation of variables (SVM) approach that allows one to calculate the ensemble-averaged single scattering optical properties of ensembles of randomly oriented particles analytically. Since the use of the SVM in spheroidal coordinates properly accounts for the geometry of the particles, the method is applicable to a large range of shapes ranging from elongated prolate needles via spheres to flat oblate disks. The relation between geometric symmetries of particles and symmetry relations of the electromagnetic scattering solution is investigated systematically in the general framework of the theory of point groups. The results are exploited in the model for increasing the computational efficiency. A comprehensive vector radiative transfer model is in part developed in this work. This radiative transfer model takes the output of the single scattering model as input and computes the Stokes vector components in a vertically inhomogeneous, plane parallel medium as a function of polar and azimuth angle and as a function of optical depth. The single scattering model is applied to investigate the impact of particle shape on the optical properties of size-shape distributions of randomly oriented particles, such as aerosol layers or ice clouds in the atmosphere. The optical properties are found to be much more sensitive to a variation in the effective aspect ratio than to a variation in the effective variance of a shape-distribution. The results of this study are used as input to the vector radiative transfer model in order to study the shape-sensitivity of the radiation field in a macroscopic medium containing a size-shape distribution of randomly oriented particles. It is found that both the radiance, and the degree of linear polarization, and the degree of circular polarization are strongly shape-sensitive in most viewing directions.