arbitrary_basis

poppy.zernike.arbitrary_basis(aperture, nterms=15, rho=None, theta=None, outside=nan)

Orthonormal basis on arbitrary aperture, via Gram-Schmidt

Return a cube of Zernike-like terms from 1 to N, calculated on an arbitrary aperture, each as a 2D array showing the value at each point. (Regions outside the unit circle on which the Zernike is defined are initialized to zero.)

This implements Gram-Schmidt orthonormalization numerically, starting from the regular Zernikes, to generate an orthonormal basis on some other aperture

Parameters:

aperture2D array_like

2D array representing the arbitrary aperture. All positive nonzero values are considered within the aperture; any pixels with zero, negative, or NaN values will be considered outside the aperture, and set equal to the ‘outside’ parameter value.

ntermsint, optional

Number of Zernike terms to return, starting from piston. (e.g. nterms=1 would return only the Zernike piston term.) Default is 15.

rho, thetaarray_like, optional

Image plane coordinates. rho should be 0 at the origin and 1.0 at the edge of the pupil. theta should be the angle in radians.

outsidefloat

Value for pixels outside the specified aperture. Default is np.nan, but you may also find it useful for this to be 0.0 sometimes.