Reconstruction of local perturbations in periodic surfaces. (1st February 2018)

• Record Type: Journal Article
• Authors: Lechleiter, Armin; Zhang, Ruming
• Is Part Of: Inverse problems. Volume 34:Number 3(2018:Mar.)
• Publication Date: 2018-02-01
• Subjects: inverse scattering problems -- Bloch transform -- locally perturbed periodic surfaces -- Newton-CG method; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aaa7b1
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet–Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.