WIAS Preprint No. 888, (2003)

The numerical solution of an inverse periodic transmission problem


  • Bruckner, Gottfried
  • Elschner, Johannes

2010 Mathematics Subject Classification

  • 78A46 78M50 35R30 35J05


  • Diffraction grating, TE transmission problem, profile reconstruction, Tikhonov regularization, optimization method


We consider the inverse problem of recovering a 2D periodic structure from scattered waves measured above and below the structure. We discuss convergence and implementation of an optimization method for solving the inverse TE transmission problem, following an approach first developed by Kirsch and Kress for acoustic obstacle scattering. The convergence analysis includes the case of Lipschitz grating profiles and relies on variational methods and solvability properties of periodic boundary integral equations. Numerical results for exact and noisy data demonstrate the practicability of the inversion algorithm.

Appeared in

  • Math. Methods Appl. Sci., 28 (2005) pp. 757--778.

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