Light scattering by randomly oriented axially symmetric particles

Abstract

Light scattering by ensembles of independently scattering, randomly oriented, axially symmetric particles is considered. The elements of the scattering matrices are expanded in (combinations of) generalized spherical functions; this is advantageous in computations of both single and multiple light scattering. Waterman’s T-matrix approach is used to develop a rigorous analytical method to compute the corresponding expansion coefficients. The main advantage of this method is that the expansion coefficients are expressed directly in some basic quantities that depend on only the shape, morphology, and composition of the scattering axially symmetric particle; these quantities are the elements of the T matrix calculated with respect to the coordinate system with the z axis along the axis of particle symmetry. Thus the expansion coefficients are calculated without computing beforehand the elements of the scattering matrix for a large set of particle orientations and scattering angles, which minimizes the numerical calculations. Like the T-matrix approach itself, the method can be used in computations for homogeneous and composite isotropic particles of sizes not too large compared with a wavelength. Computational aspects of the method are discussed in detail, and some illustrative numerical results are reported for randomly oriented homogeneous dielectric spheroids and Chebyshev particles. Results of timing tests are presented; it is found that the method described is much faster than the commonly used method of numerical angle integrations.