A New Look at Fundamentals of the Photometric Light Transport and Scattering Theory. Part 2: One-Dimensional Scattering with Absorption

Authors: Persheyev S., Rogatkin D.A. Published: 22.11.2017
Published in issue: #6(75)/2017  
DOI: 10.18698/1812-3368-2017-6-65-78

Category: Physics | Chapter: Optics  
Keywords: scattering, absorption, light transport, radiative transport equations, Kubelka — Munk approach, single scattering approximation, multiple scattering

In the first part of the article, one-dimensional (1D) pure scattering processes were taken into detailed consideration. It allowed to prove that the scattering coefficient is not just a real optical property of a turbid medium, but also is a parameter of the mathematical description of the problem. It depends on the approximation, which is applied to solve the problem. Therefore, in different approaches it can vary. More real and close to realistic practical problems are scattering problems with absorption. This second part of the article describes the 1D scattering problems with absorption. It is shown, that scattering and absorption processes inside the light-scattering medium are not independent in most cases, so a formulation of the first coefficients of initial differential equations, which mathematically describe the problem, as the simplest superposition of scattering and absorption coefficients is wrong. Inaccuracy in this formulations leads to inaccuracies in final results. More correct formulation, for example, in application to the classical two-flux Kubelka --- Munk (KM) approach, which is a good 1D limit for the radiative transport equation, allows one to obtain the exact analytical solution for boundary radiant fluxes (backscattered and transmitted ones), contrary to the classic KM approximation. In addition, it leads to the need for revision of definitions of a number of basic terms in the general radiative transport theory, especially of the albedo, which plays a key role in Monte-Carlo simulations


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