The linear sampling method for the inverse electromagnetic scattering by a partially coated bi-periodic structure

TL;DR

This paper develops a periodic linear sampling method to reconstruct a doubly periodic structure in electromagnetic scattering using near field data, advancing inverse problem techniques for coated periodic surfaces.

Contribution

It introduces a periodic linear sampling approach for inverse electromagnetic scattering, specifically tailored for partially coated doubly periodic structures.

Findings

Successfully reconstructs periodic structures from near field data.

Replaces far field equations with a linear integral equation on a plane.

Provides a new method for inverse problems involving coated periodic surfaces.

Abstract

In this paper, we consider the inverse problem of recovering a doubly periodic Lipschitz structure through the measurement of the scattered field above the structure produced by point sources lying above the structure. The medium above the structure is assumed to be homogenous and lossless with a positive dielectric coefficient. Below the structure is a perfect conductor partially coated with a dielectric. A periodic version of the linear sampling method is developed to reconstruct the doubly periodic structure using the near field data. In this case, the far field equation defined on the unit ball of R^3 is replaced by the near field equation which is a linear integral equation of the first kind defined on a plane above the periodic surface.