pyzernike-polynomials 2.3.1

Zernike polynomials computation and visualization.

pyzernike

Description

pyzernike is a Python package to compute Zernike polynomials and their derivatives. See the documentation below for more informations.

The Zernike polynomials are defined as follows:

with :

where n is the radial order, m is the azimuthal frequency, \rho is the normalized radial coordinate (\rho in [0, 1]) and \theta is the azimuthal angle.

All input arrays are automatically converted to numpy.float64 so that every calculation is performed in double‑precision, guaranteeing numerical stability throughout the library.

Usage

import numpy
from pyzernike import zernike_polynomial

rho = numpy.linspace(0, 1, 100)
theta = numpy.linspace(0, 2*numpy.pi, 100)
result = zernike_polynomial(rho, theta, n=[2], m=[0])
polynomial = result[0]  # result is a list, we take the first element

Also compute the symbolic sympy expression and display the polynomials as follow :

Authors

• Artezaru [e-mail]

• Git Plateform: https://github.com/Artezaru/pyzernike.git

• Online Documentation: https://Artezaru.github.io/pyzernike

Installation

Install with pip

pip install pyzernike-polynomials

pip install git+https://github.com/Artezaru/pyzernike.git

Clone with git

git clone https://github.com/Artezaru/pyzernike.git

License

Copyright 2025 Artezaru

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.