B-spline parameterization of the dielectric function and information criteria: the craft of non-overfitting

Dmitriy V. Likhachev

doi:10.1117/12.2270249

26 June 2017 B-spline parameterization of the dielectric function and information criteria: the craft of non-overfitting

Dmitriy V. Likhachev

Author Affiliations +

Proceedings Volume 10330, Modeling Aspects in Optical Metrology VI; 103300B (2017) https://doi.org/10.1117/12.2270249
Event: SPIE Optical Metrology, 2017, Munich, Germany

Abstract

Johs and Hale developed the Kramers–Kronig consistent B-spline formulation for the dielectric function modeling in spectroscopic ellipsometry data analysis. In this article we use popular Akaike, corrected Akaike and Bayesian Information Criteria (AIC, AICc and BIC, respectively) to determine an optimal number of knots for B-spline model. These criteria allow finding a compromise between under- and overfitting of experimental data since they penalize for increasing number of knots and select representation which achieves the best fit with minimal number of knots. Proposed approach provides objective and practical guidance, as opposite to empirically driven or “gut feeling” decisions, for selecting the right number of knots for B-spline models in spectroscopic ellipsometry. AIC, AICc and BIC selection criteria work remarkably well as we demonstrated in several real-data applications. This approach formalizes selection of the optimal knot number and may be useful in practical perspective of spectroscopic ellipsometry data analysis.

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Dmitriy V. Likhachev "B-spline parameterization of the dielectric function and information criteria: the craft of non-overfitting", Proc. SPIE 10330, Modeling Aspects in Optical Metrology VI, 103300B (26 June 2017); https://doi.org/10.1117/12.2270249

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