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Updated: Jun 24, 2025

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
Published on: August 19, 2021
Fast Zernike fitting of freeform surfaces using the Gauss-Legendre quadrature
Abstract:
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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