Please use this identifier to cite or link to this item:
Title: Field aberrations in terms of the Q-polynomial basis and its relationship to the Zernike basis
Authors: García Moreno, A.
Restrepo, R.
Belenguer Dávila, T.
González Fernández, M.
Keywords: Q-polynomial basis;Zernike basis;Freeform surfaces
Issue Date: 1-Feb-2021
Publisher: Optica Publishing Group
DOI: 10.1364/OSAC.410304
Citation: OSA Continuum 4(2): 542-555(2021)
Abstract: The aberrations generated at the image plane of an optical system that includes freeform surfaces described through Q-polynomials can be calculated using nodal aberration theory. By analyzing the definition of each Q-polynomial, they can be compared with Zernike polynomials allowing a relationship between the two bases. This relationship is neither simple nor direct, so a fitting must be made. Once established, the contribution to the aberration field map generated by each surface described through the Q-polynomial can be calculated for any surface that is not at the stop of the system. The Q-polynomials are characterized by their orthogonality in the gradient instead of the surface, which represents an opportunity to restrict the changes in the slope in a simple way and facilitate the manufacturing process. The knowledge of the field aberrations generated by each Q-polynomial allows selecting that which of them are necessary to be introduced as variables in the optimization process for an efficient optimization.
Description: 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement (
E-ISSN: 2578-7519
Appears in Collections:(Espacio) Artículos

This item is licensed under a Creative Commons License Creative Commons