Welcome to pyzernike’s documentation!#

Description of the package#

Zernike polynomials computation and visualization.

The Zernike polynomials are defined as follows:

\[Z_{n}^{m}(\rho, \theta) = R_{n}^{m}(\rho) \cos(m \theta) \quad \text{if} \quad m \geq 0\]
\[Z_{n}^{m}(\rho, \theta) = R_{n}^{-m}(\rho) \sin(-m \theta) \quad \text{if} \quad m < 0\]

with :

\[R_{n}^{m}(\rho) = \sum_{k=0}^{(n-m)/2} \frac{(-1)^k (n-k)!}{k! ((n+m)/2 - k)! ((n-m)/2 - k)!} \rho^{n-2k}\]

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

Contents#

The documentation is divided into the following sections:

  • Installation: This section describes how to install the package.

  • API Reference: This section contains the documentation of the package’s API.

  • Usage: This section contains the documentation of how to use the package.

Contents:

A terminal commmand is created to plot the first zernike polynomials. The command is called pyzernike and can be used as follows:

pyzernike
_images/zernike_display.png

Author#

The package pyzernike was created by the following authors:

You can access the package and the documentation with the following URL:

License#

Please refer to the [LICENSE] file for the license of the package.