In this paper, we consider the inverse problem of recovering a doublyperiodic Lipschitz structure through the measurement of the scattered fieldabove the structure produced by point sources lying above the structure. Themedium above the structure is assumed to be homogenous and lossless with apositive dielectric coefficient. Below the structure is a perfect conductorpartially coated with a dielectric. A periodic version of the linear samplingmethod is developed to reconstruct the doubly periodic structure using the nearfield data. In this case, the far field equation defined on the unit ball ofR^3 is replaced by the near field equation which is a linear integral equationof the first kind defined on a plane above the periodic surface.
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