Backscattering radiance calculation in a turbid medium with anisotropic scattering by spherical harmonics method

Abstract

In actual mediums with anisotropic scattering in small angle approximation (SA) is possible simply and accurately to calculate light field radiance in forward from a source directions. The backscattering calculation in these mediums by any known method is complex and has no sufficient precision for practical problems: spherical harmonics (SH) method has strong oscillation, Monte-Carlo method has a large variance, concerned with improbable event with large weight, and the first iteration from SA has uncontrollable precision and validity range. In suggested solution the refinement of SA is found by SH method. The SA solution is taken in small angle modification of SH method. This allows receiving analytical solution in the form of an exponential of matrix. Last circumstance requires numerical calculation under the obtained expression, however in the most unfavorable case the amount of terms in the refinement does not exceed 21 harmonics. The solution is practically smooth at any sharpness of a scattering phase function. Calculation time on the obtained algorithm is almost equivalent to time of calculation on SA. In addition, algorithm improving radiance distributions in a forward hemisphere.