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DOE OSTI · 2586597

ZERNIPAX: A fast and accurate Zernike polynomial calculator in Python

Elmacioglu, Yigit Gunsur [Princeton Univ., NJ (United States)] (ORCID:0009000277472834)·Conlin, Rory [Univ. of Maryland, College Park, MD (United States); Princeton Univ., NJ (United States)] (ORCID:0000000183662111)·Dudt, Daniel W. [Thea Energy, Kearny, NJ (United States); Princeton Univ., NJ (United States)] (ORCID:0000000245573529)·Panici, Dario [Princeton Univ., NJ (United States)] (ORCID:0000000307364360)·Kolemen, Egemen [Princeton Univ., NJ (United States); Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)] (ORCID:0000000342123247)
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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. Furthermore, 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.

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AstrophysicsJAXCPU/GPU computingOpticsPythonSpectral simulationsZernike polynomials

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Elmacioglu, Yigit Gunsur [Princeton Univ., NJ (United States)] (ORCID:0009000277472834), Conlin, Rory [Univ. of Maryland, College Park, MD (United States); Princeton Univ., NJ (United States)] (ORCID:0000000183662111), Dudt, Daniel W. [Thea Energy, Kearny, NJ (United States); Princeton Univ., NJ (United States)] (ORCID:0000000245573529), Panici, Dario [Princeton Univ., NJ (United States)] (ORCID:0000000307364360), Kolemen, Egemen [Princeton Univ., NJ (United States); Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)] (ORCID:0000000342123247). 2025-05-22. ZERNIPAX: A fast and accurate Zernike polynomial calculator in Python. https://doi.org/10.1016/j.amc.2025.129534

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