Solving inverse problems appearing in design and metrology of diffractive optical elements by using Bayesian optimization

Martin Hammerschmidt; Philipp-Immanuel Schneider; Xavier Garcia Santiago; Lin Zschiedrich; Martin Weiser; Sven Burger

doi:10.1117/12.2315468

28 May 2018 Solving inverse problems appearing in design and metrology of diffractive optical elements by using Bayesian optimization

Martin Hammerschmidt, Philipp-Immanuel Schneider, Xavier Garcia Santiago, Lin Zschiedrich, Martin Weiser, Sven Burger

Author Affiliations +

Proceedings Volume 10694, Computational Optics II; 1069407 (2018) https://doi.org/10.1117/12.2315468
Event: SPIE Optical Systems Design, 2018, Frankfurt, Germany

Abstract

For optimizing specific functionalities of optical components which include structures on a micrometer or nanometer scale, typically high-dimensional optimization problems have to be solved. We use Gaussian process regression to this aim. Gaussian processes can be viewed as machine-learning algorithms where results from evaluations at specific points in the parameter space (training data) are used to predict values and their uncertainty in the full parameter space. The forward-problem (evaluation at a given point in parameter space) requires to rigorously solve Maxwell’s equations, i.e. to compute light propagation in a specific setup. We use our finite-element method (FEM) implementation JCMsuite to this aim. The general framework of FEM allows to employ adaptive numerical resolution and accurate geometry modelling for arbitrary shapes. We discuss application of Bayesian optimization for the inverse problem in parameter retrieval from scatterometric data.

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Martin Hammerschmidt, Philipp-Immanuel Schneider, Xavier Garcia Santiago, Lin Zschiedrich, Martin Weiser, and Sven Burger "Solving inverse problems appearing in design and metrology of diffractive optical elements by using Bayesian optimization", Proc. SPIE 10694, Computational Optics II, 1069407 (28 May 2018); https://doi.org/10.1117/12.2315468

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