A reciprocal formulation of non-exponential radiative transfer. 1: Sketch and motivation

Previous proposals to permit non-exponential free-path statistics in radiative transfer have not included support for volume and boundary sources that are spatially uncorrelated from the scattering events in the medium. Birth-collision free paths are treated identically to collision-collision free paths and application of this to general, bounded scenes with inclusions leads to non-reciprocal transport. Beginning with reciprocity as a desired property, we propose a new way to integrate non-exponential transport theory into general scenes. We distinguish between the free-path-length statistics between correlated medium particles and the free-pathlength statistics beginning at locations not correlated to medium particles, such as boundary surfaces, inclusions and uncorrelated sources. Reciprocity requires that the uncorrelated free-path distributions are simply the normalized extinction of the correlated free-path distributions. The combination leads to an equilibrium imbedding of a previously derived generalized transport equation into bounded domains. We compare predictions of this approach to Monte Carlo simulation of multiple scattering from negativelycorrelated suspensions of monodispersive hard spheres in bounded two-dimensional domains and demonstrate improved performance relative to previous work. We also derive new, exact, recriprocal, single-scattering solutions for plane-parallel half-spaces over a variety of non-exponential media types.