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Elschner, Johannes; Yamamoto, Masahiro

An inverse problem in periodic diffractive optics: Reconstruction of Lipschitz grating profiles. (English) Zbl 1028.78008

Appl. Anal. 81, No. 6, 1307-1328 (2002).
Summary: 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.

Cited in 21 Documents

MSC:

78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
35R30 Inverse problems for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78M50 Optimization problems in optics and electromagnetic theory

Keywords:

diffraction grating; profile reconstruction; optimization method; convergence analysis
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\textit{J. Elschner} and \textit{M. Yamamoto}, Appl. Anal. 81, No. 6, 1307--1328 (2002; Zbl 1028.78008)
Full Text: DOI

References:

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