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Applied Math Seminar
Imaging by cross correlations of incoherent waves
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We will analyze the waves reflected by a random medium in the case in which the medium has three-dimensional rapid random fluctuations and one-dimensional slow variations. In the presence of a strong interface, the reflected wave is strong and partially coherent and it can be described by a generalized Ito-Schrodinger equation, which in particular predicts the enhanced backscattering phenomenon. In the absence of a strong interface, the reflected wave is weak and incoherent and its second-order statistics is determined by a system of transport equations that depends on the slow variations of the background velocity and the scattering coefficient. By observing the reflected wave, it is possible to invert this system and to reconstruct the parameters of the medium. This is a joint work with Knut Solna (University of California, Irvine). |