An inverse problem in periodic diffractive optics: Reconstruction of Lipschitz grating profiles
- Elschner, Johannes
- Yamamoto, Masahiro
2010 Mathematics Subject Classification
- 35R30 35J05 78A46 78M50
- Diffraction grating, profile reconstruction, optimization method, convergence analysis
We consider the problem of recovering a two-dimensional periodic structure from scattered waves measured above the structure. Following an approach by Kirsch and Kress, this inverse problem is reformulated as a nonlinear optimization problem. We develop a theoretical basis for the reconstruction method in the case of an arbitrary Lipschitz grating profile. The convergence analysis is based on new perturbation and stability results for the forward problem.
- Applicable Analysis 81 (2002), pp. 1307-1328