ZERNIPAX: A fast and accurate Zernike polynomial calculator in Python

Yigit Gunsur Elmacioglu, Rory Conlin, Daniel W. Dudt, Dario Panici and Egemen Kolemen

Applied Mathematics and Computation, 2025, vol. 505, issue C

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.

Keywords: Zernike polynomials; Optics; Astrophysics; Spectral simulations; Python; JAX; CPU/GPU computing (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300325002607
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:505:y:2025:i:c:s0096300325002607

DOI: 10.1016/j.amc.2025.129534

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().