Inequalities in inverse scattering theory

F. Cakoni, D. Colton

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous dielectric medium that is partially coated by a thin metallic layer in ℝ2. We use far field pattern of the scattered waves at a fixed frequency as data to determine the support D of the inhomogeneous obstacle, the surface conductivity that characterizes the coating and the relative permittivity. No a prior information on the material properties of the scatterer is needed. The support D is determined by the linear sampling method which is based on the approximate solution of the far field equation. This solution is also used to obtain lower bounds for the surface conductivity and relative permittivity. The techniques for solving this inverse scattering problem rely on the analysis of a non standard boundary value problem known as the interior transmission problem.

Original languageEnglish (US)
Pages (from-to)483-491
Number of pages9
JournalJournal of Inverse and Ill-Posed Problems
Volume15
Issue number5
DOIs
StatePublished - Sep 20 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

  • Electromagnetic waves
  • Inhomogeneous medium
  • Interior transmission problem
  • Inverse scattering problem
  • Mixed boundary value problems
  • Qualitative approaches in inverse scattering

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