Revision of path-integral approach to radiative transfer

Abstract

During the last decades, a number of publications have appeared, which dealt with applications of path-integral methods in modeling of radiative/light transfer through various turbid media. This approach seems to be an elegant way how to incorporate multiple scattering effects into calculations of radiometric quantities and thus provides an alternative to time-consuming numerical simulations or to too simplifying approximations. However, some of the published works are based on incorrect mathematical assumptions and the functions derived there actually yield infinite value results in particular calculations. They appear to be unusable without some additional ad hoc normalization. It is therefore questionable, how plausible the conclusions drawn in those works are. This paper revises the derivations of a path-integral form of the Green’s function in radiative transfer problems, reveals their critical points, and compares the resulting formulas with the formulas obtained by an alternative probabilistic approach. Moreover, it provides at least an approximate expressions usable for radiance calculations in turbid media.