Multiple Scattering and Diffraction Tomography

Abstract

Multiple scattering processes are often considered to be the limiting factor in the application of diffraction tomography techniques in practice. However, it is relatively easy to conceive idealised examples where such a statement does not strictly apply. For example, consider a typical (one dimensioanl) impediography setup, where a varying impedance is to be recovered from a backscattering experiment. In this case, the contributions of the various orders of multiple scattering processes to the backscattering may be explicitly calculated, and even summed. The standard impediography inversion technique may be applied, and, provided the appropriate boundary conditions are known, and the impedance profile may be recovered from the backscattering. However, the extension of the technique to higher dimensions is fraught with ambiguities, and it is widely felt that a convincing case cannot be built on such an idealised example.