Narrowly peaked forward light scattering on particulate media I. Assessment of the multiple scattering contributions to the effective phase function

Abstract

The quasi-ballistic light scattering (QBLS) process induced in a particulate medium by a collimated laser beam is characterized by the effective phase function (EPF) which describes the angular spreading of the scattered photons. The purpose of the first part of our work is to evaluate the accuracy of two approximations of the EPF. The rigorous EPF expression comes out in the form of a sum of an infinite series of terms, indexed by the number of scattering events suffered by the participating photons. One of the approximations is a previously derived, compact, analytical expression (Turcu 2006 Appl. Opt. 45 639–47). The alternative approximation introduced here collects the contribution from the first to the nth order of scattering. To assess the accuracy of the two approximations we introduce a series of minorant–majorant pairs which tightly encompass the EPF. The results of our analysis show that the analytical approximation is not sufficiently accurate in the entire domain of interest. The alternative, more accurate, nth-order sum approximation allows the user to improve the accuracy up to the desired level by increasing the number of scattering orders kept in the approximant.