A new look at fundamentals of the photometric light transport and scattering theory. Part 3: Bridges to multi-dimensional problems

In previous two parts of the article, one-dimensional (1D) scattering processes were taken into detailed consideration. All main typical 1D scattering problems of different complexities were discussed and solved using different approaches. It gave the opportunity to find ways to improve the theory, two-fluxes Kubelka — Munk approach, in particular. It was shown that scattering and absorption processes inside the light-scattering medium are not independent, so the formulation of first coefficients of transport differential equations as the simplest sum of scattering and absorption coefficients is wrong. Inaccuracy in this formulation leads to inaccuracies in results. In this final part of the article, as a completion, the analysis of some spatial light-scattering problems, mainly two-dimensional (2D) problems as the simplest multidimensional problems for consideration, is presented. The detailed analysis of several important 2D approximations, such as a pure backscattering approximation, single-scattering one for a pencil-like beam, and an orthogonal-scattering approach opens the way to have a new look at several nuances of formulation of the 2D or 3D initial transport equations, as well. For example, a new unknown form of the radiative transport equation of the fourth-order is proposed for the case of the orthogonal scattering approach.