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

aperture : 2D 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.

nterms : int, 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, theta : array_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.

outside : float

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.