Abstract
The problem under consideration is a first-order approximation (Born or Rytov) of the scattering problem for the scalar Helmholtz equation with a fixed real-valued free-space wavenumber and a complex valued compactly supported potential. The only boundary condition is the Sommerfield radiation condition. It is assumed that for every direction of an irradiating plane wave the corresponding scattered wave (its amplitude (Born) or phase (Rytov)) is known on certain hyperplanes outside the scatterer. As is well known, a band-limited approximation of the scatterer can be given in terms of such data via Fourier transforms. For the case of two space dimensions, exact integral representation of the scatterer in terms of the data are derived from an analysis of the so-called evanescent waves generated by the high-frequency components of the scatterer. This analysis also leads to some insight into the connection between forward scattering and backscattering.
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