Mean path length inside nonscattering refractive objects

It was recently 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 alternative analytic results for the zero scattering mean path length of simple refractive shapes. We believe 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.

Automated summary

Recent research has shown that the mean path length of rays inside refractive objects under Lambertian illumination is not independent of the medium's scattering strength, particularly in the case of zero scattering. Trapped ray trajectories play a crucial role in creating an unexpected discontinuity from zero to low scattering. This study provides alternative analytic results for the mean path length of simple refractive shapes under zero scattering conditions.