Expansion of Mie-theory phase functions in series of Legendre polynomials

Abstract

The method of discrete ordinates in the theory of radiative transfer assumes that the scattering phase functions may be expressed as series of Legendre polynomials. Previous efforts to calculate the expansion coefficients of these series have been limited to the phase functions for Rayleigh scattering and the unpolarized Mie-scattering phase function. In this paper, a methodology for calculating the expansion coefficients of the polarized Mie phase functions is developed as a two-step process. The first step is to develop the computation of the expansion coefficients of the Mie angular amplitudes. These angular-amplitude expansion coefficients are then used in the second step to compute the expansion coefficients of the polarized Mie phase functions. Following this, an algorithm suitable for implementing this methodology on a digital computer is developed, and sample calculations are quoted.