Rodríguez Ibáñez, DiegoGómez Pedrero, José AntonioAlonso Fernández, JoséQuiroga Mellado, Juan Antonio2023-06-182023-06-182016-03-211094-408710.1364/OE.24.005918https://hdl.handle.net/20.500.14352/24496En 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.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.engjournal articlehttps://www.osapublishing.org/oe/abstract.cfm?uri=oe-24-6-5918open access537.533.3681.7SurfacesAsphericsOphthalmic optics and devicesAlgorithmsArtificial intelligenceLearning systemsNumerical methodsArbitrary shapeConnected domainsFitting techniquesLocal curvatureManufacturing industriesOphthalmic lensRobust fittingsZernike polynomialsÓptica (Física)Óptica oftálmicaOptoelectrónica2209.19 Óptica Física