JournalszaaVol. 26 , No. 2DOI 10.4171/zaa/1316

Uniqueness in Determining Polygonal Periodic Structures

  • Johannes Elschner

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

    University of Tokyo, Japan
Uniqueness in Determining Polygonal Periodic Structures cover

Abstract

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].