Penetration depth of low-coherence enhanced backscattering photons in the sub-diffusion regime

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 sc L less than the scattering mean free path s l . In order to understand the mechanisms of photon propagation in LEBS in the sub-diffusion 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 ( s l and anisotropy factor g) and strong dependence on the spatial coherence length of illumination, sc L relative to those in the diffusion regime. More importantly, these low order scattering photons typically penetrate less than ls 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. 3 / 1 2 ] [ s s L l π ).