Inverse Source and Scattering Problems in Ultrasonics

Abstract

x-v PLANE Abstract-The inverse source problem consists of determining the source term of the inhomogeneous wave equation from field measure- ments performed outside the region of space containing the source. The inverse scattering problem consists of deducing a scattering po- tential from the scattered field generated in one or more scattering experiments employing different incident plane waves. In this paper it is shown that both the inverse source and scattering problems have relevance in a number of diverse applications in ultrasonics. Specific applications addressed in the paper are ultrasonic imaging, acoustic holography, and ultrasonic transmission tomography. Ultrasonic im- aging and acoustic holography are shown to be directly related to the inverse source problem while ultrasonic transmission tomography is shown to be related to the inverse scattering problem. A number of examples are given to illustrate the theoretical material presented in the paper.