phase¶

pyoof.aperture.phase(K_coeff, pr, piston, tilt, resolution=1000)[source]¶

Aperture phase distribution (or phase-error), \(\varphi(x, y)\), for an specific telescope primary reflector. In general, the tilt (average slope in \(x\)- and \(y\)-directions, related to telescope pointings) is subtracted from its calculation. Function used to show the final results from the fit procedure.

Parameters

K_coeffndarray: Constants coefficients, \(K_{n\ell}\), for each of them there is only one Zernike circle polynomial, \(U^\ell_n(\varrho, \varphi)\).
prfloat: Primary reflector radius in length units.
pistonbool: Boolean to include or exclude the piston coefficient in the aperture phase distribution. The Zernike circle polynomials are related to piston through \(U^{0}_0(\varrho, \varphi)\).
tiltbool: Boolean to include or exclude the tilt coefficients in the aperture phase distribution. The Zernike circle polynomials are related to tilt through \(U^{-1}_1(\varrho, \varphi)\) and \(U^1_1(\varrho, \varphi)\).
resolutionint: Resolution for the phase-error map, usually used resolution = 1000 in the pyoof package.

Returns

xndarray: \(x\)-axis dimensions for the primary reflector in meters.
yndarray: \(y\)-axis dimensions for the primary reflector in meters.
phiQuantity: Aperture phase distribution, \(\varphi(x, y)\), for an specific primary reflector radius, measured in radians.

Notes

The aperture phase distribution or phase-error, \(\varphi(x, y)\) is related to the wavefront (aberration) distribution, from classical optics, through the expression,

\[\varphi(x, y) = 2\pi \cdot W(x, y) = 2\pi \cdot \sum_{n, \ell} K_{n\ell}U^\ell_n(\varrho, \vartheta).\]

Examples

To use compute the aperture phase distribution, \(\varphi(x, y)\), first a set of coefficients need to be generated, K_coeff, then simply execute the phase function.

>>> import numpy as np
>>> from astropy import units as u
>>> import matplotlib.pyplot as plt
>>> from pyoof import aperture
>>> pr = 50 * u.m                       # primary relfector
>>> n = 5                               # order polynomial
>>> N_K_coeff = (n + 1) * (n + 2) // 2  # max polynomial number
>>> K_coeff = np.random.normal(0., .1, N_K_coeff)
>>> x, y, phi = aperture.phase(
...    K_coeff=K_coeff, pr=pr, piston=False, tilt=False
...    )

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phase¶