# Inverse Acoustic and Electromagnetic Scattering Theory

@inproceedings{Colton1992InverseAA, title={Inverse Acoustic and Electromagnetic Scattering Theory}, author={David Colton and Rainer Kress}, year={1992} }

Introduction.- The Helmholtz Equation.- Direct Acoustic Obstacle Scattering.- III-Posed Problems.- Inverse Acoustic Obstacle Scattering.- The Maxwell Equations.- Inverse Electromagnetic Obstacle Scattering.- Acoustic Waves in an Inhomogeneous Medium.- Electromagnetic Waves in an Inhomogeneous Medium.- The Inverse Medium Problem.-References.- Index

## 4,801 Citations

A point source method for inverse acoustic and electromagnetic obstacle scattering problems

- Mathematics, Physics
- 1998

We present the mathematical foundation for a point source method to solve some inverse acoustic and electromagnetic obstacle scattering problems in three dimensions. We investigate the inverse…

The linear sampling method in inverse electromagnetic scattering theory

- Mathematics
- 2003

We survey the linear sampling method for solving the inverse scattering problem for time-harmonic electromagnetic waves at fixed frequency. We consider scattering by an obstacle as well as scattering…

The linear sampling method in inverse electromagnetic scattering theory

- Mathematics
- 2003

We survey the linear sampling method for solving the inverse scattering problem for time-harmonic electromagnetic waves at fixed frequency. We consider scattering by an obstacle as well as scattering…

On uniqueness in inverse acoustic and electromagnetic obstacle scattering problems

- Mathematics
- 2008

We review some of the uniqueness results in inverse acoustic and electromagnetic obstacle scattering problems. The emphasis is given to the recent progress on unique determination of general…

Integral equation methods in electromagnetic scattering from anisotropic media

- Mathematics
- 2000

We investigate scattering of time-harmonic electromagnetic waves by an anisotropic inhomogeneous medium. The problem is equivalently transformed into a system of strongly singular integral equations.…

An inverse electromagnetic scattering problem for a cavity

- Mathematics
- 2011

We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting cavity from measurement of the scattered electric field due to electric-dipole sources on…

Nonlinear integral equations for an inverse electromagnetic scattering problem

- Mathematics
- 2008

We present a new method to solve an inverse scattering problem for time-harmonic electromagnetic waves. The method is based on an equivalence relation of the inverse problem to a system of two…

Reflection principle for the Maxwell equations and its application to inverse electromagnetic scattering

- Mathematics
- 2007

A novel reflection principle for the time-harmonic Maxwell equations is established. It is then used to derive a uniqueness result in inverse electromagnetic obstacle scattering with polyhedral-type…

Integral equation method for acoustic scattering by an inhomogeneous penetrable obstacle in a stratified medium

- Mathematics
- 2014

In this paper, we study the scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a stratified medium. By using the integral equation method, we prove the uniqueness…

Scattering relations for point sources: Acoustic and electromagnetic waves

- Mathematics
- 2002

The problem of scattering of spherical waves by a bounded obstacle is considered. General scattering theorems are proved. These relate the far-field patterns due to scattering of waves from a point…

## References

SHOWING 1-10 OF 29 REFERENCES

On uniqueness in inverse obstacle scattering

- Mathematics
- 1993

The inverse problem we consider in this survey is to reconstruct the shape of an obstacle from the knowledge of the far field pattern for the scattering of time-harmonic acoustic or electromagnetic…

An inverse transmission problem for the Helmholtz equation

- Mathematics, Business
- 1987

The problem considered is that of determining the shape of a three-dimensional scattering object, illuminated by an acoustic field, from a knowledge of scattered far-field data. The far-field data…

The domain derivative and two applications in inverse scattering theory

- Mathematics
- 1993

The author recalls the notion of the domain derivative of a functional. The existence and a characterization of the domain derivative of the far-field pattern for a scattering problem with Dirichlet…

The interior transmission problem and inverse scattering from inhomogeneous media

- Mathematics
- 1991

This paper is concerned with the class of far field patterns corresponding to the scattering of time harmonic acoustic plane waves by an inhomogeneous medium in a bounded domain B, with refractive…

On uniqueness in th invese transmission scattering problem

- Mathematics
- 1990

We give uniqueness results for the inverse scattering problem where the unknown scatterer D is a bounded open set and some coefficients of an elliptic equation are unknown as well. On the boundary of…

Iterative method for multi-dimensional inverse scattering problems at fixed frequencies

- Mathematics
- 1994

Suppose that a medium with slowly changing spatial properties is enclosed in a bounded three-dimensional domain and is subjected to a scattering by plane waves of a fixed frequency. Let measurements…

Inverse Problems in Partial Differential Equations

- Mathematics
- 1990

This workshop brought together mathematicians engaged in dif- ferent aspects of inverse problems for partial differential equations. Classical topics such as the inverse problems of impedance…

Frechet differentiability of boundary integral operators in inverse acoustic scattering

- Mathematics
- 1994

Using integral equation methods to solve the time-harmonic acoustic scattering problem with Dirichlet boundary conditions, it is possible to reduce the solution of the scattering problem to the…

The inverse scattering problem on a fixed energy level for the two-dimensional Schrödinger operator

- Mathematics
- 1992

Uniqueness Theorems for the Inverse Problem of Acoustic Scattering

- Mathematics
- 1983

On a obtenu des theoremes d'unicite pour le probleme de la determination de la forme d'un obstacle dur au son ou mou au son a partir de la connaissance du diagramme en champ lointain ou de la section…