WIAS Preprint No. 785, (2002)

Grating profile reconstruction based on finite elements and optimization techniques


  • Elschner, Johannes
  • Hsiao, George C.
  • Rathsfeld, Andreas
    ORCID: 0000-0002-2029-5761

2010 Mathematics Subject Classification

  • 35R30 35J05 35J05 78A46 78M50


  • Diffraction grating, profile reconstruction, optimization method, conjugate gradient algorithm




We consider the inverse diffraction problem to recover a two-dimensional periodic structure from scattered waves measured above and beneath the structure. The task is reformulated in form of an optimization problem including special regularization terms. The solvability and the dependence on the parameter of regularization is analyzed. Numerical results for synthetic data demonstrate the practicability of the inversion algorithm.

Appeared in

  • SIAM J. Appl. Math. 64 (2003), pp.525-545

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