Diffraction tomography and the stochastic inverse scattering problem

The Fourier diffraction theorem is the basis of diffraction tomography. The theorem states that the field scattered by a semitransparent object maps onto arcs in the Fourier space of the object. In this paper, the stochastic analog is derived to the theorem for a general anisotropic, statistically homogeneous random continuum. By acoustically probing the random medium from various angles, the second-order statistics of the medium can be recovered from the second-order statistics of the perturbed field. The robust nature of the result is confirmed by numerical experiments using finite arrays and autocorrelation estimation theory.