Longwave properties of the orientation averaged Mueller scattering matrix for particles of arbitrary shape. II. Molecular parameters and Perrin symmetry

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Abstract
In Part I of this paper, we started from a dipole array model of elastic light scattering, and found the longwave asymptotic formulas for all 16 elements of the orientation averaged Mueller scattering matrix. However, the Perrin symmetry of the scattering matrix was not obvious from the formulas obtained in Part I. In this paper, Part II, we carry the analysis further, finding the molecular parameter identities which result in the Perrin symmetries. The formulas we present provide a very practical method for model calculations in the longwave limit. After evaluation of ten sums over pairs of the dipolar subunits of the model, the orientation averaged Mueller scattering matrix, as a function of scattering angle, is given by simple trigonometric polynomials. For models containing several hundred subunits the computation is easily carried through by a desktop computer. We verify the asymptotic formulas by numerical comparison with our analytic orientation averaging program PMAT2. We use a helical model with spherical subunits, in which the first Born approximation gives excellent results for the dipole elements (symmetry DSE). In this same model the first, second, and third Born approximations are utterly worthless for calculating the helicity-retardation elements M13 and M23 and their transposes, but fourth Born gives nearly the exact result. These observables therefore use four bounces to feel out the helicity of the array, and may be more sensitive to structural variations than the traditional circular difference observable M14, which responds after only two bounces.