prtools.zernike_coeff_legacy#

zernike_coeff_legacy(coeffs, modes=None, order='noll')[source]#

Convert Zernike coefficients between legacy and current orientation conventions.

prtools 2.0.2 and earlier computed Zernike polynomials in a coordinate system mirrored top-to-bottom (y -> -y). This results in modes with negative azimuthal order (sine terms: y tilt, 45 degree astigmatism, y coma, …) having a flipped sign. Modes with zero or positive azimuthal order are unaffected.

This conversion is involutory so it converts legacy coefficients to the current convention and current coefficients to the legacy convention.

Parameters:

coeffs (array_like) – Zernike coefficients. The last axis indexes Zernike modes, so a stack of coefficient vectors (e.g. a time series) can be converted in a single call.
modes (array_like, optional) – Zernike mode indices corresponding to the last axis of coeffs, e.g. the modes passed to zernike_fit(). If None (default), coeffs[..., k] is taken to be the coefficient for mode index k + 1, matching zernike_compose().
order ({'noll', 'fringe', 'ansi'}, optional) – Zernike ordering scheme. Default is ‘noll’.

Returns:

Converted coefficients with the same shape as coeffs.

Return type:

ndarray

Notes

The conversion is exact for masks with an even number of pixels in each dimension. Along any dimension with an odd number of pixels, the legacy coordinate origin was also offset half a pixel from the mask centroid. The effect of that offset on fitted coefficients is small but is not a sign change, so it cannot be undone by this function.

Examples

Convert tip, tilt, and focus coefficients fit with prtools 2.0.2:

>>> prtools.zernike_coeff_legacy([1e-8, 2e-8, 3e-8], modes=[2, 3, 4])
array([ 1.e-08, -2.e-08,  3.e-08])