Enhancing early-time diffusion through beam collimation in pulse propagation through slabs of discrete random media

This presentation describes an ongoing work by the authors on the solution of the time-dependent radiative transfer equation (RTE) and its application to propagation of short pulses through dilute scattering media (in particular, atmospheric obscurants, such as clouds, fog, or aerosols). It concentrates on exploitation of the “early-time diffusion” phenomenon arising for media in which scatterers are significantly larger than the pulse wavelength. The early time diffusion signature is a sharply rising structure in the time-resolved intensity, immediately following the ballistic (coherent) signal; its rise time is, typically, orders of magnitude shorter than that of the usual “late-time” diffusion and its decay with the propagation distance is significantly slower than for the coherent intensity contribution. Our previous analysis of the early-time diffusion pertained to an infinite random medium. Here we present its generalization to the case of a laterally infinite slab of a finite thickness, and concentrate on an imaging scenario in which the transmitter (collocated with the receiver) and the observed object are located on the opposite sides of the slab. Compared to the infinite medium, the slab geometry offers 1. a possibility of a more direct comparison with typical experimental setups; 2. more favorable circumstances for reducing the effect of back-scattered light as a background for the signal reflected from the object; and 3. an opportunity of exploiting the shower-curtain effect. A general formulation of the problem will be illustrated by preliminary computational results, suggesting improved prospects of applicability of early-time diffusion in remote sensing through atmospheric obscurants, such as clouds, fog, or aerosols.