Uniqueness results for an inverse periodic transmission problem
- Elschner, Johannes
- Yamamoto, Masahiro
2010 Mathematics Subject Classification
- 78A46 35R30
- Diffraction grating, periodic Helmholtz equation, inverse transmission problem
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  to the inverse transmission problem.
- Inverse Problems, 20 (2004) pp. 1841--1852.