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Zeitschrift für Analysis und ihre Anwendungen

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Volume 26, Issue 2, 2007, pp. 165–177
DOI: 10.4171/ZAA/1316

Published online: 2007-06-30

Uniqueness in Determining Polygonal Periodic Structures

Johannes Elschner[1] and Masahiro Yamamoto[2]

(1) Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
(2) University of Tokyo, Japan

We consider the inverse problem of recovering a two-dimensional perfectly reflecting diffraction grating from scattered waves measured above the structure. We establish the uniqueness within the class of general polygonal grating profiles by a minimal number of incoming plane waves, without excluding Rayleigh frequencies and further geometric constraints on the profile. This extends and improves the uniqueness results of Elschner, Schmidt and Yamamoto [Inverse Problems 19 (2003), 779--787].

Keywords: Diffraction grating, periodic Helmholtz equation, inverse Dirichlet and Neumann problems, polygonal grating profile

Elschner Johannes, Yamamoto Masahiro: Uniqueness in Determining Polygonal Periodic Structures. Z. Anal. Anwend. 26 (2007), 165-177. doi: 10.4171/ZAA/1316