Adaptive focusing in scattering media through sound-speed inhomogeneities: The van Cittert Zernike approach and focusing criterion

An original formalism that allows a thorough understanding of cross-correlation-based phase aberration correction techniques in a scattering medium is developed. This formalism is based on the analysis of the second-order statistics of the pressure field scattered by a random distribution of scatterers. One of the major interests of this analysis is the ability it provides to evaluate and monitor the convergence of phase aberration correction techniques. This is achieved by the computation of a single parameter C that serves as a focusing criterion. The theoretical developments are validated experimentally.