hswfs.fast_zernike

This module provides pre-computed numpy versions of the Cartesian derivatives of Zernike polynomials, which can be used to (significantly) speed up the fitting of wavefronts.

Warning

Note: This file / module is automatically generated by the precompute_fast_zernike.py script in the scripts directory!

hswfs.fast_zernike.zernike_derivative_cartesian(m: int, n: int, x: Union[float, ndarray], y: Union[float, ndarray], wrt: Union[str, Symbol]) → Union[float, ndarray][source]

Evaluate the Cartesian derivative of a the Zernike polynomial \(Z^m_n\) at the position(s) x, y. Fast.

Parameters

  • m – Index \(m\) of \(Z^m_n\).

  • n – Index \(n\) of \(Z^m_n\). Default maximum value is \(n_\text{max} = 15\).

  • x – The x-coordinate(s) at which to evaluate the derivative.

  • y – The y-coordinate(s) at which to evaluate the derivative.

  • wrt – A string or sy.Symbol that specifies with respect to which variable the derivative is taken: “x” or “y”.

Returns

The value(s) of the derivative of \(Z^m_n\) with respect to wrt at the given position(s) x, y.