zernike

poppy.zernike.zernike(n, m, npix=100, rho=None, theta=None, outside=nan, noll_normalize=True, **kwargs)

Return the Zernike polynomial Z[m,n] for a given pupil.

For this function the desired Zernike is specified by 2 indices m and n. See zernike1 for an equivalent function in which the polynomials are ordered by a single index.

You may specify the pupil in one of two ways:

zernike(n, m, npix)

where npix specifies a pupil diameter in pixels. The returned pupil will be a circular aperture with this diameter, embedded in a square array of size npix*npix.

zernike(n, m, rho=r, theta=theta)

Which explicitly provides the desired pupil coordinates as arrays r and theta. These need not be regular or contiguous.

The expressions for the Zernike terms follow the normalization convention of Noll et al. JOSA 1976 unless the noll_normalize argument is False.

n, m : int

Zernike function degree

npix : int

Desired diameter for circular pupil. Only used if rho and theta are not provided.

rho, theta : array_like

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

outside : float

Value for pixels outside the circular aperture (rho > 1). Default is np.nan, but you may also find it useful for this to be 0.0 sometimes.

noll_normalize : bool

As defined in Noll et al. JOSA 1976, the Zernike definition is modified such that the integral of Z[n, m] * Z[n, m] over the unit disk is pi exactly. To omit the normalization constant, set this to False. Default is True.

zern : 2D numpy array

Z(m,n) evaluated at each (rho, theta)