Identification of generalized impedance boundary conditions in inverse scattering problems

Laurent Bourgeois 1 Houssem Haddar 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
2 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : In the context of scattering problems in the harmonic regime, we consider the problem of identification of some Generalized Impedance Boundary Conditions (GIBC) at the boundary of an object (which is supposed to be known) from far field measurements associated with a single incident plane wave at a fixed frequency. The GIBCs can be seen as approximate models for thin coatings, corrugated surfaces or highly absorbing media. After pointing out that uniqueness does not hold in the general case, we propose some additional assumptions for which uniqueness can be restored. We also consider the question of stability when uniqueness holds. We prove in particular Lipschitz stability when the impedance parameters belong to a compact subset of a finite dimensional space.
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Laurent Bourgeois, Houssem Haddar. Identification of generalized impedance boundary conditions in inverse scattering problems. Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2010, 4 (1), pp.19-38. ⟨10.3934/ipi.2010.4.19⟩. ⟨hal-00739327⟩

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