Mean path length inside non-scattering refractive objects

TL;DR

This paper investigates the mean path length of light rays inside refractive objects, revealing differences between zero-scattering and low-scattering cases and deriving new analytic results for simple shapes.

Contribution

It demonstrates that the mean path length varies at zero-scattering, contrasting previous claims of independence, and explains the role of trapped rays in this behavior.

Findings

Mean path length differs at zero-scattering compared to low-scattering.

Trapped ray trajectories cause the discontinuity in path length.

New analytic formulas derived for simple refractive shapes.

Abstract

It has recently been argued that the geometric-optics mean path length of rays inside a refractive object under Lambertian illumination is independent of the scattering strength of the medium [Savo et al., Science 358, 765 (2017)]. We here show that it is in fact different in the case of zero-scattering. We uncover and explain the role of trapped ray trajectories in creating this unexpected discontinuity from zero- to low-scattering. This allows us to derive new analytic results for the zero-scattering mean path length of simple refractive shapes. This work provides a fresh perspective on the study of path length inside refractive objects, with possible applications in for example the study of scattering by large particles or the design of optical systems.