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The inverse electromagnetic scattering problem for a partially coated dielectric
 J. Comp. Appl. Math
"... Abstract. The inverse electromagnetic scattering problem for anisotropic media plays a special role in inverse scattering theory due to the fact that the (matrix) index of refraction is not uniquely determined from the far field pattern of the scattered field even if multifrequency data is availabl ..."
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Abstract. The inverse electromagnetic scattering problem for anisotropic media plays a special role in inverse scattering theory due to the fact that the (matrix) index of refraction is not uniquely determined from the far field pattern of the scattered field even if multifrequency data is available. In this paper we describe how transmission eigenvalues can be determined from the far field pattern and be used to obtain upper and lower bounds on the norm of the index of refraction. Numerical examples will be given for the case when the scattering object is an infinite cylinder and the inhomogeneous medium is orthotropic. 1.
Reconstruction of the shape and surface impedance from acoustic scattering data for arbitrary cylinder
 SIAM J. Appl. Math
"... Abstract. The inverse scattering for an obstacle D ⊂ R 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and noncoated parts of the boundary. We construct some indicator functions for this inverse problem using the farfield pattern ..."
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Abstract. The inverse scattering for an obstacle D ⊂ R 2 with mixed boundary condition can be considered as a prototype for radar detection of complex obstacles with coated and noncoated parts of the boundary. We construct some indicator functions for this inverse problem using the farfield pattern directly, without the necessity of transforming the far field to the near field. Based on careful singularity analysis, these indicator functions enable us to reconstruct the shape of the obstacle and distinguish the coated from the noncoated part of the boundary. Moreover, an explicit representation formula for the surface impedance in the coated part of the boundary is also given. Our reconstruction scheme reveals that the coated part of the obstacle is less visible than the noncoated one, which corresponds to the physical fact that the coated boundary absorbs some part of the scattered wave. Numerics are presented for the reconstruction formulas, which show that both the boundary shape and the surface impedance in the coated part of the boundary can be reconstructed accurately. The theoretical reconstruction techniques proposed in this work can be applied in the practical 3dimensional electromagnetic inverse scattering problems with promising numerical performance. Such problems are of great importance in the design of nondetectable obstacles.
A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media, Inverse Problems and Imaging 1
, 2007
"... (Communicated by David Colton) Abstract. The interior transmission problem plays a basic role in the study of inverse scattering problems for inhomogeneous medium. In this paper we study the interior transmission problem for the Maxwell equations in the electromagnetic scattering problem for an anis ..."
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Cited by 15 (8 self)
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(Communicated by David Colton) Abstract. The interior transmission problem plays a basic role in the study of inverse scattering problems for inhomogeneous medium. In this paper we study the interior transmission problem for the Maxwell equations in the electromagnetic scattering problem for an anisotropic inhomogeneous object. We use a variational approach which extends the method developed in [15] to the case when the index of refraction is less than one as well as for partially coated scatterers. In addition, we also describe the structure of the transmission eigenvalues. 1.
The determination of boundary coefficients from far field measurements
"... Dedicated to Chuck Groetsch for his fundamental contributions to the field of inverse problems. We consider the problem of determining either the surface impedance λ = λ(x) or surface conductivity η = η(x) from far field data corresponding to timeharmonic incident plane waves scattered by a coated ..."
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Dedicated to Chuck Groetsch for his fundamental contributions to the field of inverse problems. We consider the problem of determining either the surface impedance λ = λ(x) or surface conductivity η = η(x) from far field data corresponding to timeharmonic incident plane waves scattered by a coated infinite cylinder. We show that λ and η are uniquely determined from the far field data and provide a numerical algorithm for determining these quantities. 1
Identification of partially coated anisotropic buried objects using electromagnetic Cauchy data
 in "J. Integral Equations and Applications
"... ABSTRACT. We consider the three dimensional electromagnetic inverse scattering problem of determining information about a target buried in a known inhomogeneous medium from a knowledge of the electric and magnetic fields corresponding to time harmonic electric dipoles as incident fields. The scatter ..."
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ABSTRACT. We consider the three dimensional electromagnetic inverse scattering problem of determining information about a target buried in a known inhomogeneous medium from a knowledge of the electric and magnetic fields corresponding to time harmonic electric dipoles as incident fields. The scattering object is assumed to be an anisotropic dielectric that is (possibly) partially coated by a thin layer of highly conducting material. The data is measured at a given surface containing the object in its interior. Our concern is to determine the shape of this scattering object and some information on the surface conductivity of the coating without any knowledge of the index of refraction of the inhomogeneity. No a priori assumption is made on the extent of the coating, i.e., the object can be fully coated, partially coated or not coated at all. Our method, introduced in [14, 17], is based on the linear sampling method and reciprocity gap functional for reconstructing the shape of the scattering object. The algorithm consists in solving a set of linear integral equations of the first kind for several sampling points and three linearly independent polarizations. The solution of these integral equations is also used to determine the surface conductivity. 1. Introduction. The
Open problems in the qualitative approach to inverse electromagnetic scattering theory
 European Jour. Applied Math
"... We formulate a number of open problems for timeharmonic inverse electromagnetic scattering theory focusing on uniqueness theorems, the determination of the support of a scattering object and the determination of material parameters 1 ..."
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We formulate a number of open problems for timeharmonic inverse electromagnetic scattering theory focusing on uniqueness theorems, the determination of the support of a scattering object and the determination of material parameters 1
Recent developments in the qualitative approach to inverse scattering theory
 12:1 WSPC/Trim Size: 9in x 6in for Proceedings CakoniGreece05
"... We consider the inverse scattering problem of determining both the shape and some of the physical properties of the scattering object from a knowledge of the (measured) electric and magnetic fields due to the scattering of an incident time harmonic electromagnetic wave at fixed frequency. We shall d ..."
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Cited by 3 (1 self)
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We consider the inverse scattering problem of determining both the shape and some of the physical properties of the scattering object from a knowledge of the (measured) electric and magnetic fields due to the scattering of an incident time harmonic electromagnetic wave at fixed frequency. We shall discuss the linear sampling method for solving the inverse scattering problem which does not require any a priori knowledge of the geometry and the physical properties of the scatterer. Included in our discussion is the case of partially coated objects and inhomogeneous background. We give references for numerical examples for each problem discussed in this paper. Key words: Electromagnetic inverse scattering, inverse scattering problem, linear sampling method, mixed boundary value problem. 1
Inequalities in Inverse Scattering Theory
 J. of Inverse and Illposed Problems
"... 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 R 2. We use far field pattern of the scattered waves at a fixed frequency as data to determine the support D of the inh ..."
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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 R 2. 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. Key words. Inverse scattering problem, inhomogeneous medium, interior transmission problem, electromagnetic waves, mixed boundary value problems, qualitative approaches in inverse scattering. AMS classification. 35P25, 35R30, 78A45. 1.