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Inverse Problems and Imaging (IPI)
 

Reconstruction of perfectly conducting rough surfaces by the use of inhomogeneous surface impedance modeling

Pages: 295 - 307, Volume 3, Issue 2, May 2009      doi:10.3934/ipi.2009.3.295

 
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Emre Kiliç - Istanbul Technical University, Electrical and Electronics Engineering Faculty, 34469 Maslak, Istanbul, Turkey (email)
Mehmet Çayören - Istanbul Technical University, Electrical and Electronics Engineering Faculty, 34469 Maslak, Istanbul, Turkey (email)
Ali Yapar - Istanbul Technical University, Electrical and Electronics Engineering Faculty, 34469 Maslak, Istanbul, Turkey (email)
Íbrahim Akduman - Istanbul Technical University, Electrical and Electronics Engineering Faculty, 34469 Maslak, Istanbul, Turkey (email)

Abstract: A new method for the reconstruction of one dimensional profile of a perfectly conducting rough surface is presented. The method is based on the equivalent representation of the rough surface by means of an inhomogeneous impedance plane, whose surface impedance is recovered through the analytical continuation of the measured data. The equivalent problem allows one to calculate the total field in the whole space above the unknown surface. The use of boundary condition that the total electric field vanishes on the unknown surface enables to reduce the problem to the solution of a non-linear equation in terms of the unknown surface function. The non-linear equation is solved iteratively via Newton method and regularization in the least square sense is also applied. The effectiveness of the method has been demonstrated with several numerical simulations.

Keywords:  Inverse scattering problems, rough surface reconstruction, impedance boundary condition.
Mathematics Subject Classification:  Primary: 78A46; Secondary: 65N21.

Received: December 2008;      Revised: March 2009;      Available Online: May 2009.