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Parameter reconstruction is a common problem in optical nano metrology. Itgenerally involves a set of measurements, to which one attempts to fit anumerical model of the measurement process. The model evaluation typicallyinvolves to solve Maxwell's equations and is thus time consuming. This makesthe reconstruction computationally demanding. Several methods exist for fittingthe model to the measurements. On the one hand, Bayesian optimization methodsfor expensive black-box optimization enable an efficient reconstruction bytraining a machine learning model of the squared sum of deviations. On theother hand, curve fitting algorithms, such as the Levenberg-Marquardt method,take the deviations between all model outputs and corresponding measurementvalues into account which enables a fast local convergence. In this paper wepresent a Bayesian Target Vector Optimization scheme which combines these twoapproaches. We compare the performance of the presented method against astandard Levenberg-Marquardt-like algorithm, a conventional Bayesianoptimization scheme, and the L-BFGS-B and Nelder-Mead simplex algorithms. As astand-in for problems from nano metrology, we employ a non-linear least-squareproblem from the NIST Standard Reference Database. We find that the presentedmethod generally uses fewer calls of the model function than any of thecompeting schemes to achieve similar reconstruction performance.

Recent advances in Bayesian optimization with applications to parameter reconstruction in optical nano-metrology