Ferreira González, CheloLópez García, José LuisPérez Sinusía, EsterNavarro, Rafael2018-12-142018-12-1420161094-4087 (Electronic)10.1364/OE.24.005448https://academica-e.unavarra.es/handle/2454/31772A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different polynomials. Here we present results for surfaces with circular apertures when the first basis function (mode) is a conicoid. The system for aspheres with rotational symmetry is obtained applying an appropriate change of variables to Legendre polynomials, whereas the system for general freeform case is obtained applying a similar procedure to spherical harmonics. Numerical comparisons with standard systems, such as Forbes and Zernike polynomials, are performed and discussed.17 p.application/pdfeng© 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.Orthogonal functionsOptical surfacesConicoidsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessAcceso abierto / Sarbide irekia