Fast online inverse scattering with Reduced Basis Method (RBM) for a 3D phase grating with specific line roughness

Bernd H. Kleemann; Julian Kurz; Jochen Hetzler; Jan Pomplun; Sven Burger; Lin Zschiedrich; Frank Schmidt

doi:10.1117/12.889364

23 May 2011 Fast online inverse scattering with Reduced Basis Method (RBM) for a 3D phase grating with specific line roughness

Bernd H. Kleemann, Julian Kurz, Jochen Hetzler, Jan Pomplun, Sven Burger, Lin Zschiedrich, Frank Schmidt

Author Affiliations +

Proceedings Volume 8083, Modeling Aspects in Optical Metrology III; 808309 (2011) https://doi.org/10.1117/12.889364
Event: SPIE Optical Metrology, 2011, Munich, Germany

Abstract

Finite element methods (FEM) for the rigorous electromagnetic solution of Maxwell's equations are known to be very accurate. They possess a high convergence rate for the determination of near field and far field quantities of scattering and diffraction processes of light with structures having feature sizes in the range of the light wavelength. We are using FEM software for 3D scatterometric diffraction calculations allowing the application of a brilliant and extremely fast solution method: the reduced basis method (RBM). The RBM constructs a reduced model of the scattering problem from precalculated snapshot solutions, guided self-adaptively by an error estimator. Using RBM, we achieve an efficiency accuracy of about 10^-4 compared to the direct problem with only 35 precalculated snapshots being the reduced basis dimension. This speeds up the calculation of diffraction amplitudes by a factor of about 1000 compared to the conventional solution of Maxwell's equations by FEM. This allows us to reconstruct the three geometrical parameters of our phase grating from "measured" scattering data in a 3D parameter manifold online in a minute having the full FEM accuracy available. Additionally, also a sensitivity analysis or the choice of robust measuring strategies, for example, can be done online in a few minutes.

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Bernd H. Kleemann, Julian Kurz, Jochen Hetzler, Jan Pomplun, Sven Burger, Lin Zschiedrich, and Frank Schmidt "Fast online inverse scattering with Reduced Basis Method (RBM) for a 3D phase grating with specific line roughness", Proc. SPIE 8083, Modeling Aspects in Optical Metrology III, 808309 (23 May 2011); https://doi.org/10.1117/12.889364

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