American Institute of Mathematical Sciences

Advanced
May  2009, 3(2): 295-307. doi: 10.3934/ipi.2009.3.295

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

Emre Kiliç 1, , Mehmet Çayören 1, , Ali Yapar 1, and  Íbrahim Akduman 1,

1. 

Istanbul Technical University, Electrical and Electronics Engineering Faculty, 34469 Maslak, Istanbul, Turkey, Turkey, Turkey, Turkey

Received  December 2008 Revised  March 2009 Published  May 2009

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: impedance boundary condition., rough surface reconstruction, Inverse scattering problems.
Mathematics Subject Classification: Primary: 78A46; Secondary: 65N2.
Citation: Emre Kiliç, Mehmet Çayören, Ali Yapar, Íbrahim Akduman. Reconstruction of perfectly conducting rough surfaces by the use of inhomogeneous surface impedance modeling. Inverse Problems & Imaging, 2009, 3 (2) : 295-307. doi: 10.3934/ipi.2009.3.295
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