High accuracy solution of the time-dependent radiative transfer equation for pulse propagation in obscuring 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. Two subjects are discussed in more detail: (i) spectrum and eigensolutions of the RTE in its integral form and in a discretized integro-differential form; and (ii) a possible way of enhancing the early-time diffusion signal by constructing sources coupled more strongly to the RTE eigenmodes responsible for early-time diffusion than to the late-time diffusion modes.