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Description:
The paper is devoted to the inverse problem of recovering a 2D periodic structure from scattered waves measured above and below the structure. We show that measurements corresponding to a finite number of refractive indices above or below the grating profile, uniquely determine the periodic interface in the inverse TE transmission problem. If a priori information on the height of the diffraction grating is available, then we also obtain upper bounds of the required number of wavenumbers by using the Courant-Weyl min-max principle for a fourth-order elliptic problem. This extends uniqueness results by Hettlich and Kirsch [11] to the inverse transmission problem.