Small‐angle light scattering from an anisotropic sphere: The mueller matrix approach

Abstract

AbstractThe explicit form of the Mueller scattering matrix, which characterizes the small‐angle light scattering from an anisotropic sphere when the requirements of the Rayleigh‐Gans‐Debye (RGD) approximation are fulfilled, contains all information obtainable about the RGD scattering from an anisotropic sphere taken as a model for a spherulite. A comparison of angular dependences of single matrix elements for the Lorenz‐Mie sphere, the Rayleigh particle, and the simplified form of the presented matrix (taking a sphere without inherent anisotropy, i.e., Δn = 0) shows very good agreement within the limits of RGD approximations. The polarized small‐angle light scattering intensities Hυ and Vυ are combinations of the single matrix elements. Their explicit form is in accord with the expressions for Hυ and Vυ intensities recently rederived from a 2 × 2 amplitude scattering matrix. It has been shown that the angular dependence of matrix elements is determined by the (n̄ — 1)/Δn parameter, where n — is the mean refractive index andδ n is the anisotropy, both measured relative to the surrounding medium. The expressions for Hυ and Vυ intensities derived by Stein and Rhodes fail for a sphere without inherenet anisotropy ( δ n = 0); and the commonly used procedure of size determination from a maximum of Hυ intensity has limited validity (it holds only approximately under the condition of a small phase shift and small (n̄‐1)/ δ n). Further theoretical work must be done to understand and construct scattering models for situations where the RGD approximately is inappropriate.