Retrieval of a Green's Function with Reflections from Partly Coherent Waves Generated by a Wave Packet Using Cross Correlations

We analyze the “field-field” cross correlation associated with partly coherent scattered waves generated by a wave packet. The configuration consists of a slab in which random medium fluctuations occur; the bottom of the slab is bounded by a deterministic discontinuity (a smooth reflector). Following the dyadic parabolic scaling of wave packets, and scaling the random fluctuations appropriately, we arrive at a description in terms of a system of linear Itô-Schrödinger diffusion models. Studying the Wigner distributions of the fields generated by these models, leads to a “blurring” transformation providing a complete characterization of the cross correlation. We obtain a description of the cross correlation in terms of this transformation applied to the effective transmission operator arising as a solution of the Itô-Schrödinger model. Most of the analysis is focussed on the interaction of the deterministic reflector with the random fluctuations through the waves in the regime of fine scales.