The identification of a penetrable obstacle with mixed transmission conditions from far field measurements

Fioralba Cakoni; Gen Nakamura; Mourad Sini; Noam Zeev

doi:10.1080/00036810903437820

The identification of a penetrable obstacle with mixed transmission conditions from far field measurements

Fioralba Cakoni, Gen Nakamura, Mourad Sini, Noam Zeev

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We consider the two-dimensional electromagnetic inverse scattering problem for a dielectric medium partially coated with a thin layer of highly conductive material. Using the linear sampling method, we show that the approximate solution of the far field equation can be used to reconstruct the support of the coating in addition to the shape of the scattering obstacle. We also deduce formulaes providing point-wise reconstruction of the surface conductivity on the coated portion and the real index of refraction on the uncoated portion of the boundary. Numerical examples are given for the case with constant surface conductivity and index of refraction showing the viability of our reconstruction procedure.

Original language	English (US)
Pages (from-to)	67-86
Number of pages	20
Journal	Applicable Analysis
Volume	89
Issue number	1
DOIs	https://doi.org/10.1080/00036810903437820
State	Published - Jan 2010
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

Keywords

Inhomogeneous medium
Inverse scattering
Linear sampling
Mixed transmission conditions

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10.1080/00036810903437820

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title = "The identification of a penetrable obstacle with mixed transmission conditions from far field measurements",

abstract = "We consider the two-dimensional electromagnetic inverse scattering problem for a dielectric medium partially coated with a thin layer of highly conductive material. Using the linear sampling method, we show that the approximate solution of the far field equation can be used to reconstruct the support of the coating in addition to the shape of the scattering obstacle. We also deduce formulaes providing point-wise reconstruction of the surface conductivity on the coated portion and the real index of refraction on the uncoated portion of the boundary. Numerical examples are given for the case with constant surface conductivity and index of refraction showing the viability of our reconstruction procedure.",

keywords = "Inhomogeneous medium, Inverse scattering, Linear sampling, Mixed transmission conditions",

author = "Fioralba Cakoni and Gen Nakamura and Mourad Sini and Noam Zeev",

note = "Funding Information: F. Cakoni gratefully acknowledges the support of the U.S. Air Force Office of Scientific Research under Grant FA9550-08-1-0138. M. Sini gratefully acknowledges the support of the FWF under the SFB 013 project.",

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T1 - The identification of a penetrable obstacle with mixed transmission conditions from far field measurements

AU - Cakoni, Fioralba

AU - Nakamura, Gen

AU - Sini, Mourad

AU - Zeev, Noam

N1 - Funding Information: F. Cakoni gratefully acknowledges the support of the U.S. Air Force Office of Scientific Research under Grant FA9550-08-1-0138. M. Sini gratefully acknowledges the support of the FWF under the SFB 013 project.

PY - 2010/1

Y1 - 2010/1

N2 - We consider the two-dimensional electromagnetic inverse scattering problem for a dielectric medium partially coated with a thin layer of highly conductive material. Using the linear sampling method, we show that the approximate solution of the far field equation can be used to reconstruct the support of the coating in addition to the shape of the scattering obstacle. We also deduce formulaes providing point-wise reconstruction of the surface conductivity on the coated portion and the real index of refraction on the uncoated portion of the boundary. Numerical examples are given for the case with constant surface conductivity and index of refraction showing the viability of our reconstruction procedure.

AB - We consider the two-dimensional electromagnetic inverse scattering problem for a dielectric medium partially coated with a thin layer of highly conductive material. Using the linear sampling method, we show that the approximate solution of the far field equation can be used to reconstruct the support of the coating in addition to the shape of the scattering obstacle. We also deduce formulaes providing point-wise reconstruction of the surface conductivity on the coated portion and the real index of refraction on the uncoated portion of the boundary. Numerical examples are given for the case with constant surface conductivity and index of refraction showing the viability of our reconstruction procedure.

KW - Inhomogeneous medium

KW - Inverse scattering

KW - Linear sampling

KW - Mixed transmission conditions

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The identification of a penetrable obstacle with mixed transmission conditions from far field measurements

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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