Abstract

The inverse source problem of the scalar wave equation for a monochromatic source is generalized to the case of an inhomogeneous attenuative medium. The attenuative medium can be a lossy deterministic medium or a lossless random medium in which the coherent field attenuates. Two generalized holographic imaging equations are obtained that are based on the use of two Green’s functions, G+* and G. The kernel for the first equation with G+* is Hermitian and depends on the location and the shape of the recording surface, whereas the equation with G has a non-Hermitian kernel that is independent of the recording surface. The solutions of the integral equations are investigated. The nonuniqueness of the solutions are also related to the nonradiating sources and to the minimum energy solution.

© 1987 Optical Society of America

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