Abstract
Analytic closed form expressions for orthonormal polynomials exhibiting both rotational and Gaussian symmetries are derived for both circular and elliptical geometries. They exhibit a close correspondence to the Zernike polynomials but are of Gaussian shape and orthogonal over the (x,y) plane. Consequently, they may be expressed in terms of Laguerre polynomials. Formulas for calculating the centroid of a real function are also presented and, along with the analytic expressions for the polynomials, may prove to be of especial use in reconstruction of the intensity distribution incident on a Shack–Hartmann wavefront sensor.
© 2022 Optica Publishing Group
Full Article | PDF ArticleMore Like This
Spencer W. Jolly and Miguel A. Porras
Opt. Lett. 47(15) 3632-3635 (2022)
Virendra N. Mahajan and Guang-ming Dai
Opt. Lett. 31(16) 2462-2464 (2006)
Jakub Czuchnowski and Robert Prevedel
Opt. Lett. 46(14) 3480-3483 (2021)