Dielectric function parameterization by penalized splines
Dmitriy V. Likhachev · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2017
In this article, we investigate the penalized spline (P-spline) approach to restrict flexibility of dielectric function parameterization by B-splines and prevent overfitting of the ellipsometric data. The penalty degree is easily controlled by a certain smoothing parameter. The P-spline approach offers a number of advantages over well-established B-spline parameterization. First of all, it typically uses an equidistant knot arrangement which simplifies the construction of the roughness penalties and makes it computationally efficient. Since P-splines possess the “power of the penalty” property, a selection of the number of knots is no longer crucial, as long as there is a minimum knot number to capture all significant spatial variability of the data curves. We demonstrate the proposed approach by real-data application with ellipsometric spectra from aluminum-coated sample.