WIAS Preprint No. 682, (2001)

An optimization method for grating profile reconstruction


  • Bruckner, Gottfried
  • Elschner, Johannes
  • Yamamoto, Masahiro

2010 Mathematics Subject Classification

  • 35R30 35J05 78A46 78M50


  • diffraction grating, profile reconstruction, Tikhonov regularization, optimization method, Levenberg-Marquardt algorithm.




We consider the inverse diffraction problem to recover a two-dimensional periodic structure from scattered waves measured above the structure. Following an approach by Kirsch and Kress, the inverse problem is reformulated as a nonlinear optimization problem. The resulting Tikhonov regularized least squares problem is then solved iteratively by the Levenberg-Marquardt algorithm. Numerical results for synthetic data demonstrate the practicability of the inversion algorithm. We also present some convergence results for the Tikhonov regularization of the reconstruction problem and for the optimization method.

Appeared in

  • Progress in Analysis, Proceed. 3rd ISAAC congress, World Scientific, Singapore, 2003, pp. 1391-1404

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