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On the optimization of knot allocation for B-spline parameterization of the dielectric function in spectroscopic ellipsometry data analysis.
- Source :
- Journal of Applied Physics; 1/21/2021, Vol. 129 Issue 3, p1-15, 15p
- Publication Year :
- 2021
-
Abstract
- Dielectric function representation by B-splines became quite popular and widely used in the context of spectroscopic ellipsometry data interpretation. B-splines are defined by a polynomial degree and a sequence of knots (i.e., the number and positions of knots). Defining the knot sequence is non-trivial, and this task has a significant effect on the actual effectiveness of the B-spline parameterization in spectroscopic ellipsometry data analysis. In this paper, we propose a simple, practical, and systematic knot placement scheme that improves ordinary trial-and-error technique in establishing the knot spacing. The approach suggested here is based on an integral span, a measure introduced in this work. The proposed procedure provides a possibility to determine the knot locations automatically (or, at least, semi-automatically) and excludes widespread modeling ambiguities associated with uncertain knot vector. Moreover, our approach guarantees the absence of non-monotonic behavior of the mean-squared-error function and thereby improves the accuracy of our analysis. The performance of the proposed method has been tested for several real cases of the study. [ABSTRACT FROM AUTHOR]
- Subjects :
- DIELECTRIC function
ELLIPSOMETRY
DATA analysis
PARAMETERIZATION
KNOT theory
Subjects
Details
- Language :
- English
- ISSN :
- 00218979
- Volume :
- 129
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Journal of Applied Physics
- Publication Type :
- Academic Journal
- Accession number :
- 148312461
- Full Text :
- https://doi.org/10.1063/5.0035456