Penetration depth of low-coherence enhanced backscattered light in sub-diffusion regime

TL;DR

This paper investigates photon penetration depth in the sub-diffusion regime using low-coherence enhanced backscattering, deriving models and simulations showing weak dependence on medium properties and a penetration depth scaling with the coherence volume.

Contribution

It develops analytical and numerical models for photon penetration depth in LEBS within the sub-diffusion regime, highlighting the role of spatial coherence length.

Findings

Photon penetration depth is weakly dependent on medium properties.

Penetration depth scales with the one-third power of the coherence volume.

Monte Carlo simulations support the analytical results.

Abstract

The mechanisms of photon propagation in random media in the diffusive multiple scattering regime have been previously studied using diffusion approximation. However, similar understanding in the low-order (sub-diffusion) scattering regime is not complete due to difficulties in tracking photons that undergo very few scatterings events. Recent developments in low-coherence enhanced backscattering (LEBS) overcome these difficulties and enable probing photons that travel very short distances and undergo only a few scattering events. In LEBS, enhanced backscattering is observed under illumination with spatial coherence length L_sc less than the scattering mean free path l_s. In order to understand the mechanisms of photon propagation in LEBS in the subdiffusion regime, it is imperative to develop analytical and numerical models that describe the statistical properties of photon trajectories. Here we derive the probability distribution of penetration depth of LEBS photons and report Monte Carlo numerical simulations to support our analytical results. Our results demonstrate that, surprisingly, the transport of photons that undergo low-order scattering events has only weak dependence on the optical properties of the medium (l_s and anisotropy factor g) and strong dependence on the spatial coherence length of illumination, L_sc, relative to those in the diffusion regime. More importantly, these low order scattering photons typically penetrate less than l_s into the medium due to low spatial coherence length of illumination and their penetration depth is proportional to the one-third power of the coherence volume (i.e. [l_s \pi L_sc^2 ]^1/3).