A reciprocal formulation of non-exponential radiative transfer with uncorrelated sources, detectors and boundaries. 1: Sketch and motivation
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Recent proposals to permit non-exponential free-path statistics in radiative transfer have not included support for volume and boundary sources that are 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 distributions between correlated medium particles and the free-path-lengths beginning at locations not correlated to medium particles, such as boundary surfaces, imbedded occlusions and uncorrelated emitters. Reciprocity requires that the uncorrelated free-path distributions are simply the normalized extinction of the correlated free path lengths. We perform Monte Carlo analysis of minimum Poisson-disk blue noise scatterers in infinite and semi-infinite configurations and show that our reciprocal formulation of correlated transport is more accurate than alternative proposals. We also derive new exact, recriprocal single-scattering solutions for plane-parallel half-spaces over a variety of non-exponential media types.
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