Reconstruction of Local Perturbations in Periodic Surfaces
For researchers in inverse scattering and periodic structures, this provides a method to handle non-periodic scattered fields, though it is an incremental extension of existing techniques.
This paper tackles the inverse scattering problem of reconstructing local perturbations in periodic surfaces. The proposed two-step numerical method (initialization via support localization, then Newton-CG optimization) successfully reconstructs perturbations, with numerical examples demonstrating efficiency.
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 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, shows the efficiency of the numerical method.