Limitations and defects of certain inverse scattering theories

Recently some new formulations for the inverse scattering problem were developed resulting in the "exact inverse scattering theory," which promises to be a more general background for different other methods. This theory consists essentially of the construction of "effectal fields" inside a closed surface, on which the monochromatic scattered field and its normal derivative are known. Outgoing from the "effectal fields" several methods were proposed to reconstruct the scattered field, its equivalent sources or just to visualize the scattering geometry. Recent discussions on this subject have issued controversy concerning the exactness, uniqueness, and applicability of these methods. Applying them to synthetic examples and practical problems we are able to confirm the results of Devaney et al. with emphasis on the following facts: in two versions, the "exact inverse scattering theory" is incorrect, and, in another one, it does not yield a better solution than generalized holography. Only broad-band excitation or multiple experiments yield further information about the scatterer, but then, approximations concerning the sources and scatterers have to be introduced.