The No Response Test for the reconstruction of polyhedral objects in electromagnetics

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article; Proceedings Paper

Potthast, Roland¹  Sini, Mourad² 

[1] Univ Reading, Dept Math, Reading RG6 6AX, Berks, England

[2] Austrian Acad Sci, RICAM, Linz, Austria

关键词: Electromagnetic waves;    Maxwell equations;    Inverse scattering;    Object reconstruction;    Sampling method;    No Response Test;   

DOI  :  10.1016/j.cam.2009.08.023

来源: Elsevier

【 摘 要 】

We develop a No Response Test for the reconstruction of a polyhedral obstacle from two or few time-harmonic electromagnetic incident waves in electromagnetics. The basic idea of the test is to probe some region in space with waves which are small on some test domain and, thus, do not generate a response when the scatterer is inside of this test domain. We will prove that the No Response Test checks analytic continuability of a time-harmonic field from the far field pattern into the domain B-e := R-3 \ (B) over bar for a non-vibrating test domain B. We show that two incident waves, defined by one incident direction and two appropriately chosen directions of polarization, are enough to recover the convex hull of polyhedrals. Based on this uniqueness result, we build up the No Response Test and we prove convergence in the sense that it fully reconstructs a convex polyhedral scatterer D or the convex hull of an arbitrary polyhedral scatterer. Further, we will describe the algorithmic realization of the No Response Test and show the feasibility of the method by reconstruction of convex polyhedral objects in three dimensions. This is the first formulation of the No Response Test for electromagnetics. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free