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DOE OSTI2025

ZERNIPAX: A fast and accurate Zernike polynomial calculator in Python

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.

Astrophysics↗

DOE OSTI2025

Modal focal adaptive optics for Bessel-focus two-photon fluorescence microscopy

Adaptive optics (AO) improves the spatial resolution of microscopy by correcting optical aberrations. While its application has been well established in microscopy modalities utilizing a circular pupil, its adaptation to systems with non-circular pupils, such as Bessel-focus two-photon fluorescence microscopy (2PFM) with an annular pupil, remains relatively uncharted. Herein, we present a modal focal AO (MFAO) method for Bessel-focus 2PFM. Measuring and correcting aberration using a spatial light modulator placed in conjugation with the focal plane of the microscope objective, MFAO employs Zernike annular polynomials — a first in AO implementation — to achieve performance on par with a previous zonal AO method, but with a notably simplified optical configuration. We validated the performance of MFAO in correcting artificial and sample-induced aberrations, as well as in in vivo imaging of zebrafish larvae and mouse brains. By expanding the application of modal AO to annular pupils as well as aberration measurement and correction to a wavefront modulator at the objective focal plane, MFAO represents a notable advancement in the implementation of AO in microscopy.

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