ZernikePy is a minimalistic Python library to compute and visualize Zernike polynomials of any given orders. A typical usage is to generate basis functions for phase modulation in optics.

Installation

pip install ZernikePy

Requirements

numpy
scipy
matplotlib

How to use

After installation, first import the main function from the library

from zernikepy import zernike_polynomials

Examples

Generate a (256, 256)-sized Zernike polynomial of order 4 (defocusing):

p = zernike_polynomials(mode=4, size=256)

or

p = zernike_polynomials(mode='defocusing', size=256)

Generate the first 15 modes and display them:

ps = zernike_polynomials(mode=14, select='all', show=True)

Generate the following selected modes defocusing, vertical coma, oblique astigmatism and display them:

ps = zernike_polynomials(mode=10, select=[4, 'vertical coma', 'oblique astigmatism'], show=True)

Note that regardless of the order of the elements in the list select, the output stores the polynomials in ascending order in the last dimension. Hence, in the output ps[:, :, 0] is oblique astigmatism, ps[:, :, 1] is defocusing and ps[:, :, 2] is vertical coma.

Detailed explanation

The main function zernike_polynomials(mode, size, select, show) takes four variables:

• mode: which (or up to which) order of the polynomial. It follows the OSA standard indexing convention and should be a nonnegative integer. It is also possible to pass a string of the corresponding name for the first 15 modes. Default is 'defocus'.
• size: numerical size of the square Cartesian mesh. It should be a postive integer. Default is 128.
• select: in the case of passing more than one polynomial, i.e. some selected modes up to the given mode, give a list of integers or strings or a mixture of both. A special case is select='all' where all the polynomials up to the given mode is passed. Default is None in which case only a single polynomial of the given mode is passed.
• show: boolen variable to determine whether to display the polynomials. Default is False.

The output is a Numpy array, either 2D for a single mode, or 3D for multiple modes.

Name of the first 15 modes