Theory of wave-front-distortion correction by phase conjugation

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Abstract
A phase-conjugate mirror (PCM) has the remarkable property of correcting the distortions introduced into a wave field when it interacts with a lossless scatterer. We examine this phenomenon of distortion correction, or the socalled healing effect, exhibited by the PCM and present a theoretical analysis of the PCM operation based on a scattering-matrix formulation. We show how the infinitely many terms arising as a result of multiple scattering between the scatterer and the PCM can be conveniently summed in a closed form and that the criteria for a total correction of the distortion introduced into the wave field by a scatterer can be readily derived from this closedform expression. We also present a self-consistent formulation in which the multiple interactions can be conveniently accounted for by means of a boundary condition describing the function of the PCM. The self-consistent formulation is applied to both the closed-region and open-region scattering problems, the latter using a new generalized spectral-domain scattering-matrix representation.