© 2021 Optical Society of America under the terms of the OSA Open Access Publishing AgreementRestrepo, R.Belenguer Dávila, T.González Fernández, M.Sánchez - Valdepeñas García - Moreno, Jesús2022-02-112022-02-112021-02-01OSA Continuum 4(2): 542-555(2021)http://hdl.handle.net/20.500.12666/5182021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement (https://opg.optica.org/library/license_v1.cfm#VOR-OA)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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Q-polynomial basisZernike basisFreeform surfacesinfo:eu-repo/semantics/article10.1364/OSAC.4103042578-7519http://dx.doi.org/10.13039/501100010687info:eu-repo/semantics/openAccess