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Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape

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Rodríguez Ibáñez, Diego and Gómez Pedrero, José Antonio and Alonso Fernández, José and Quiroga Mellado, Juan Antonio (2016) Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape. Optics Express, 24 (6). pp. 5918-5933. ISSN 1094-4087

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Official URL: https://www.osapublishing.org/oe/abstract.cfm?uri=oe-24-6-5918



Abstract

A new method for fitting a series of Zernike polynomials to point clouds defined over connected domains of arbitrary shape defined within the unit circle is presented in this work. The method is based on the application of machine learning fitting techniques by constructing an extended training set in order to ensure the smooth variation of local curvature over the whole domain. Therefore this technique is best suited for fitting points corresponding to ophthalmic lenses surfaces, particularly progressive power ones, in non-regular domains. We have tested our method by fitting numerical and real surfaces reaching an accuracy of 1 micron in elevation and 0.1 D in local curvature in agreement with the customary tolerances in the ophthalmic manufacturing industry.


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En abierto en la web del editor.
Received 7 Oct 2015; revised 4 Feb 2016; accepted 9 Feb 2016; published 9 Mar 2016
© 2016 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.

Uncontrolled Keywords:Surfaces ; Aspherics ; Ophthalmic optics and devices ; Algorithms ; Artificial intelligence ; Learning systems ; Numerical methods ; Arbitrary shape ; Connected domains ; Fitting techniques ; Local curvature ; Manufacturing industries ; Ophthalmic lens ; Robust fittings ; Zernike polynomials
Subjects:Sciences > Physics > Optics
Medical sciences > Optics > Visual perception
Medical sciences > Optics > Optoelectronics
ID Code:37782
Deposited On:20 May 2016 07:51
Last Modified:09 Mar 2017 00:01

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