WIAS Preprint No. 769, (2002)

A two-step algorithm for the reconstruction of perfectly reflecting periodic profiles


  • Bruckner, Gottfried
  • Elschner, Johannes

2010 Mathematics Subject Classification

  • 35R30 35J05 78A46 78M50


  • diffraction grating, profile reconstruction, Tikhonov regularization, optimization method, Gauss-Newton method




We consider the inverse problem of recovering a 2D periodic structure from scattered waves measured above the structure. First, following [5], the inverse problem is reformulated as an optimization problem which consists of two parts: a linear severely ill-posed problem and a nonlinear well--posed one. Then, contrary to [5], here the two problems are solved separately to diminish the computational effort by exploiting their special properties. Numerical results for exact and noisy data demonstrate the practicability of the inversion algorithm.

Appeared in

  • Inverse Problems 19 (2003), pp. 315-329

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