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Inverse scattering for shape and impedance. (English) Zbl 0985.35109

Summary: We consider the inverse problem of determining both the shape and the impedance of a two-dimensional scatterer from a knowledge of the far-field pattern of the scattering of time-harmonic acoustic or electromagnetic waves by solving the ill-posed nonlinear equations for the operator that maps the boundary and the boundary impedance of the scatterer onto the far-field pattern. We establish results on the injectivity of the linearized map and obtain satisfactory reconstructions by a regularized Newton iteration.

MSC:

35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
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