Inverse scattering for periodic structures: Stability of polygonal interfaces
- Elschner, Johannes
- Schmidt, Gunther
2010 Mathematics Subject Classification
- 78A46 35R30 35Q60
- Inverse problem, diffraction grating, local stability, material derivative
We consider the two-dimensional TE and TM diffraction problems for a time harmonic plane wave incident on a periodic grating structure. An inverse diffraction problem is to determine the grating profile from measured reflected and transmitted waves away from the structure. We present a new approach to this problem which is based on the material derivative with respect to the variation of the dielectric coefficient. This leads to local stability estimates in the case of interfaces with corner points.
- Inverse Problems 17 (2001), pp. 1817-1829