WIAS Preprint No. 718, (2002)

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.

Appeared in

  • Applicable Analysis 81 (2002), pp. 1307-1328

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