Orthogonal basis with a conicoid first mode for shape specification of optical surfaces
Abstract
A 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.
Keywords
Cite
@article{arxiv.1606.06327,
title = {Orthogonal basis with a conicoid first mode for shape specification of optical surfaces},
author = {Chelo Ferreira and Jose L. Lopez and Rafael Navarro and Ester Perez Sinusia},
journal= {arXiv preprint arXiv:1606.06327},
year = {2016}
}
Comments
This paper has been withdrawn by the author due to an error in the computation of the coefficients used in Example 1. This error affects later computations and pictures and translates into the necessity of a complete modification of the conclusions