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We present a Bayesian inference-based nonlinear least-squares fitting approach developed to reliably fit challenging, noisy data in an automated and robust manner. The advantages of using Bayesian inference for nonlinear fitting are demonstrated by applying this approach to a set of temperature-dependent film thickness h(T) data collected by ellipsometry for thin films of polystyrene (PS) and poly(2-vinylpyridine) (P2VP). The glass transition experimentally presents as a continuous transition in thickness characterized by a change in slope that in thin films with broadened transitions can become particularly subtle and challenging to fit. This Bayesian fitting approach is implemented using existing open-source Python libraries that make these powerful methods accessible with desktop computers. We show how this Bayesian approach is more versatile and robust than existing methods by comparing it to common fitting methods currently used in the polymer science literature for identifying Tg. As Bayesian inference allows for fitting to more complex models than existing methods in the literature do, our discussion includes an in-depth evaluation of the best functional form for capturing the behavior of h(T) data with temperature-dependent changes in thermal expansivity. This Bayesian fitting approach is easily automated, capable of reliably fitting noisy and challenging data in an unsupervised manner, and ideal for machine learning approaches to materials development.
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Fast Zernike fitting of freeform surfaces using the Gauss-Legendre quadrature
Zernike polynomial orthogonality, an established mathematical principle, is leveraged with the Gauss-Legendre quadrature rule in a rapid novel approach to fitting data over a circular domain. This approach provides significantly faster fitting speeds, in the order of thousands of times, while maintaining comparable error rates achieved with conventional least-square fitting techniques. We demonstrate the technique for fitting mid-spatial-frequencies (MSF) prevalent in small-tool-manufacturing typical of aspheric and freeform optics that are poised to soon permeate a wide range of optical technologies.
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- PAR ID:
- 10566218
- Publisher / Repository:
- Optica
- Date Published:
- Journal Name:
- Optics Express
- Volume:
- 32
- Issue:
- 11
- ISSN:
- 1094-4087
- Page Range / eLocation ID:
- 20011
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1364/OE.523022
