Statistics of photon penetration depth in diffusive media

The study of photon migration through highly scattering media opens the way to the non-invasive investigation of biological tissues well below the skin surface. When the medium is addressed in reflectance geometry, a key issue is to maximize the depth reached by migrating photons. By exploiting the Diffusion Approximation of the Radiative Transfer Equation, we calculated the time-resolved and continuous-wave probability density functions for the maximum depth reached by detected photons, for both a homogeneous and a layered laterally-infinite diffusive slab. From the probability density functions it is possible to calculate the mean value of the maximum depth at which detected photons have undergone scattering events.