Electromagnetic scattering by spheroidal particles: Applications to the atmosphere

Hans Arthur Eide
Wed, 22 Apr 2026 18:26:46 PDT

An efficient and reliable method is presented for computing the expansion coefficients in the eigenfunction series representing the prolate and oblate spheroidal functions. While the traditional method is based on recurrence relations, infinite continued fractions, and a variational procedure, the new method is based on reformulating the computational task as an eigenvalue problem. In contrast with the traditional method, the new method requires no initial estimates of the eigenvalues, and the computations can be performed using readily available computer library routines. The new method is shown to produce accurate expansion coefficients for the spheroidal functions required to study scattering by particles with a wide range of shapes, sizes, and complex refractive indices [1]. In a previous study in which the scattering characteristics of Polar Stratospheric Clouds (PSCs) were calculated using randomly oriented monodispersions of prolate spheroids [2], the scattering signature of the main types of PSC particles was related to particles of a certain shape and size range. Here these results are used as a reference for testing a new method for calculating the scattering characteristics of PSC like clouds. The method is based on finding the single scattering solution for spheroids using the rigorous Separation of Variables Method (SVM), and then from it obtain the so called T-matrix The following question is addressed: Can the backscatter depolarization returns be used together with other remote sensing techniques to determine either basic shape (degree of needle- or disc-like asphericity) or size information of ice cloud particles? To this end the SVM is again utilized to obtain the T-matrix for a variety of size, shape, and size-shape distributions of ensembles of randomly oriented spheroidal particles. The results indicate that single-wavelength depolarization lidar returns are insufficient to uniquely determine both the size and the shape of the particles in an ice cloud. However, a combination of an NIR depolarization lidar and additional information obtained by complementing instruments---from which either size or shape can be estimated---has the potential for determining the mean size and shape of particles in an ice cloud.