Ferreira Chelo, López José L, Navarro Rafael, Sinusía Ester Pérez
Opt Express. 2016 Mar 7;24(5):5448-5462. doi: 10.1364/OE.24.005448.
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.
提出了一个严谨且强大的理论框架，以获得用于表示光学表面的正交函数（或形状模式）系统。该方法具有通用性，因此可应用于不同的初始形状和不同的多项式。在此，当第一个基函数（模式）为二次曲面时，我们给出了具有圆形孔径表面的结果。对于具有旋转对称性的非球面系统，通过对勒让德多项式进行适当的变量变换来获得，而对于一般自由形式的情况，通过对球谐函数应用类似的过程来获得。进行并讨论了与标准系统（如福布斯多项式和泽尼克多项式）的数值比较。
