Zernike-like Laguerre-Gaussian orthonormal polynomials for optical field reconstruction

Posted on 22.11.2022 - 14:24
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. Formulae 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.

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Strycker, Benjamin (2022): Zernike-like Laguerre-Gaussian orthonormal polynomials for optical field reconstruction. Optica Publishing Group. Collection. https://doi.org/10.6084/m9.figshare.c.6276888.v2
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