Wave tomography of time-varying disordered structures

Abstract

An original model based on the first principles is constructed for the temporal correlation of wave fields propagating in random scattering media. The predictions of this model are consistent, in general, with those of the diffusingwave spectroscopy. It is shown that considering the wave vector as a free parameter that can vary at will, one can provide an additional dimension to the data, which results in a tomographic-type reconstruction of the full spacetime dynamics of a complex structure, instead of a plain spectroscopic technique. In the Fourier space the problem is reduced to a spherical mean transform defined for a family of spheres containing the origin and therefore is easily invertible.