Uniqueness in Determining Polygonal Periodic Structures

  • Johannes Elschner

    Weierstrass Institut für Angewandte Analysis und Stochastik, Berlin, Germany
  • Masahiro Yamamoto

    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].

Cite this article

Johannes Elschner, Masahiro Yamamoto, Uniqueness in Determining Polygonal Periodic Structures. Z. Anal. Anwend. 26 (2007), no. 2, pp. 165–177

DOI 10.4171/ZAA/1316