lentil.zernike_fit#

lentil.zernike_fit(opd, mask, modes, normalize=True, order='noll', rho=None, theta=None)[source]#

Fit a Zernike basis set to an OPD.

Parameters:

opd (array_like) – OPD to fit.
mask (array_like) – Mask defining the extent to compute the Zernike polynomial over. All nonzero entries are included in the result.
modes (array_like) – List of modes (Noll ordering) to fit.
normalize (bool, optional) – If True (default), the output is normalized according to [1]. If False, the output value ranges [-1, 1] over the mask.
order ({'noll', 'fringe', 'ansi'}, optional) – Zernike ordering scheme. Default is ‘noll’.
rho (array_like, optional) – Radial coordinates of the mask. rho should be 0 at the origin and 1 at the edge of the circle.
theta (array_like, optional) – Angular coordinates of the mask in radians.

Returns:

List of coefficients fit to the supplied OPD over the specified number of Zernike modes.

Return type:

ndarray

Examples

>>> import numpy as np
>>> import lentil
>>> mask = lentil.circle((256,256), 128, antialias=False)
>>> coeffs = np.random.rand(4)*100e-9
>>> opd = lentil.zernike_compose(mask, coeffs)
>>> fit_coeffs = lentil.zernike_fit(opd, mask, np.arange(2,4))
>>> print('Tip/tilt coefficients:', coeffs[1:3])
>>> print('Fit tip/tilt coefficients:', fit_coeffs)

Tip/tilt coefficients: [9.69097470e-08 9.94332699e-08]
Fit tip/tilt coefficients: [9.69545890e-08 9.94781119e-08]