Direct demonstration of the concept of unrestricted effective-medium approximation.

The modified unrestricted effective-medium refractive index is defined as one that yields accurate values of a representative set of far-field scattering characteristics (including the scattering matrix) for an object made of randomly heterogeneous materials. We validate the concept of the modified unrestricted effective-medium refractive index by comparing numerically exact superposition T-matrix results for a spherical host randomly filled with a large number of identical small inclusions and Lorenz-Mie results for a homogeneous spherical counterpart. A remarkable quantitative agreement between the superposition T-matrix and Lorenz-Mie scattering matrices over the entire range of scattering angles demonstrates unequivocally that the modified unrestricted effective-medium refractive index is a sound (albeit still phenomenological) concept provided that the size parameter of the inclusions is sufficiently small and their number is sufficiently large.

Calculation of the reflection function of an optically thick scattering layer for a Henyey-Greenstein phase function.

Simple analytical methods are proposed for calculating the reflection function of a semi-infinite and conservative scattered layer, the value of which is needed to solve many atmospheric optics problems. The methods are based on approximations of the exact values obtained with a strict numerical method. For a Henyey-Greenstein phase function, knowledge of the zeroth and sixth higher harmonics appears to be sufficient for a quite accurate approximation of the angle range, which is acceptable for solution of direct and inverse problems in atmospheric optics when a plane atmosphere is assumed.