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The inverse scattering problem for a cylinder†

Published online by Cambridge University Press:  14 November 2011

David Colton
David Colton
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware, U.S.A.
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Synopsis

Let D be a bounded simply connected domain in the plane and Ω the unit disk. Let F(Θ;k) be the far field pattern arising from the scattering of an incoming plane wave by the obstacle D and let an(k) denote the nth Fourier coefficient of F. Then if f conformally maps ℝ2\D onto ℝ2\Ω, a “moment” problem is derived which expresses an(k) in terms of f−1 for small values of the wave number k. The solution of this moment problem then gives the Laurent coefficients of f−1 and hence ∂D.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 84 , Issue 1-2 , 1979 , pp. 135 - 143
Copyright
Copyright © Royal Society of Edinburgh 1979

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