zernpy 0.0.4

Calculation of Zernike polynomial value, their sums and basic plotting of their values in polar coordinates

zernpy - package for calculation Zernike polynomials

This project is intended for calculation of Zernike polynomials using recursive equations, that might be the faster way to calculate polynomials with high orders in comparison to calculation using exact equation.
Several useful transformations (e.g., from OSA / ANSI index to Noll one) are implemented as the methods of the main class.

Setup instructions

Basic installation

For installation of this package, use the command: pip install zernpy

Running tests for the code from the repository

Using the library pytest just run in the root folder for this code: pytest
It should collect 5 tests and automatically runs them.

Requirements

For installation the numpy and matplotlib libraries are required.

A few examples of the library features usage

Initialization of base class instance

The useful calculation methods are written as the instance and static methods. The first ones are accessible after initialization of instance class by providing the relevant characteristic orders (see the Zernike polynomial definition, e.g. in Wiki):

from zernpy import ZernPol
zp = ZernPol(m=-2, n=2)  

Alternative initializations using other indices: ZernPol(osa_index=3), ZernPol(noll_index=5), ZernPol(fringe_index=6)

Some useful class instance methods:

1. For getting all characteristic indices for the initialized polynomial: zp.get_indices()
   This method returns the following tuple: ((azimuthal order, radial order), OSA index, Noll index, Fringe index)
2. For getting the string name of the initialized polynomial (up to 7th order): zp.get_polynomial_name()
3. For calculating polynomial value for polar coordinates (r, theta): zp.polynomial_value(r, theta)
   Note that r and theta are accepted as float numbers or numpy.ndarrays with the equal shape.

Some useful static methods of ZernPol class:

1. For getting tuple as (azimuthal order, radial order) for OSA index i: ZernPol.index2orders(osa_index=i)
   Same for Fringe and Noll indices: ZernPol.index2orders(noll_index=i) or ZernPol.index2orders(fringe_index=i)
2. Conversion between indices: ZernPol.osa2noll(osa_index), with similar signature: noll2osa(...), osa2fringe(...), osa2fringe(...), fringe2osa(...)
3. Calculation of Zernike polynomials sum: ZernPol.sum_zernikes(coefficients, polynomials, r, theta, get_surface)
   It calculates the sum of initialized Zernike polynomials (ZernPol) using coefficients and (r, theta) polar coordinates. The variable get_surface allows returning for vector polar coordinates with different shapes the values as for mesh of these coordinates. The details of acceptable values - see the docstring of this method or the API Dictionary.
4. Plotting the initialized Zernike polynomial (ZernPol): ZernPol.plot_zernike_polynomial(polynomial)
   It plots the Zernike polynomial on unit circle polar coordinates (blocked non-interactive call of matplotlib.pyplot.show())
5. Plotting Zernike polynomials sum: ZernPol.plot_sum_zernikes_on_fig(...) - check the list of parameters in the docstring. By using only default parameters, this method will plot sum of Zernike polynomials specified in the list with their coefficients on the provided figure (expected as an instance of the class matplotlib.pyplot.Figure).