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

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.