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

arXiv: https://arxiv.org/abs/1803.03259 · HTML: https://mlsanity.com/paper/1803.03259/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2018.

## Built on by (most cited first, 2 of 2)

- [Objects as volumes: A stochastic geometry view of opaque solids](https://mlsanity.com/paper/2312.15406/) (2023)
- [Generalized non-exponential Gaussian splatting](https://mlsanity.com/paper/2603.02887/) (2026)

## Abstract (arXiv)

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-path-length 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 transmittance 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 negatively-correlated suspensions of monodispersive hard spheres in bounded two-dimensional domains and demonstrate improved performance relative to previous work. We also derive new, exact, reciprocal, single-scattering solutions for plane-parallel half-spaces over a variety of non-exponential media types.