ZERNIPAX: A Fast and Accurate Zernike Polynomial Calculator in Python

Abstract

Zernike polynomials serve as an orthogonal basis on the unit disc, and have proven to be effective in optics simulations, astrophysics, and more recently in plasma simulations. Unlike Bessel functions, Zernike polynomials are inherently finite and smooth at the disc center (r=0), ensuring continuous differentiability along the axis. This property makes them particularly suitable for simulations, requiring no additional handling at the origin. We developed ZERNIPAX, an open-source Python package capable of utilizing CPU/GPUs, leveraging Google's JAX package and available on GitHub as well as the Python software repository PyPI. Our implementation of the recursion relation between Jacobi polynomials significantly improves computation time compared to alternative methods by use of parallel computing while still performing more accurately for high-mode numbers.

References in corpus (4)

• Improved GRAVITY astrometric accuracy from modeling of optical aberrations
• The Three Hundred Project: quest of clusters of galaxies morphology and dynamical state through Zernike Polynomials
• Nonaxisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions
• Balanced Binary Tree Schemes for Computing Zernike Radial Polynomials