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Recovery of Small Inhomogeneities from the Scattering Amplitude at a Fixed Frequency

Summary: Recovery of Small Inhomogeneities from the Scattering
Amplitude at a Fixed Frequency
Habib Ammari  Ekaterina Lakovleva y Shari Moskow z
September 17, 2001
We derive rigorously the leading order term in the asymptotic expansion of the
scattering amplitude of a collection of nite number of dielectric inhomogeneities of
small diameter. We then apply this asymptotic formula for the purpose of identifying
the location and certain properties of the shapes of the small inhomogeneities from
scattering amplitude measurements at a xed frequency. Our main idea is to reduce
this reconstruction problem to the calculation of an inverse Fourier transform.
Key words. Inverse scattering problem, scattering amplitude, Helmholtz equation,
dielectric imperfections, reconstruction
2000 AMS subject classi cations. 35R30, 78A46
1 Introduction
In this paper we consider three-dimensional electromagnetic scattering from a collec-
tion of small dielectric inhomogeneities. We suppose that there is a nite number of
dielectric imperfections in R 3 , each of the form z j + B j , where B j  R 3 is a bounded,
smooth (C 1 ) domain containing the origin. This regularity assumption could be con-
siderably weakened. The total collection of imperfections thus takes the form


Source: Ammari, Habib - Centre de Mathématique Appliquées, École Polytechnique


Collections: Mathematics