e_rs¶

pyoof.aperture.e_rs(phase, circ=False)[source]¶

Computes the random-surface-error efficiency, \(\varepsilon_\mathrm{rs}\), using the Ruze’s equation.

Parameters

phaseQuantity: The phase-error, \(\varphi(x, y)\), is a two dimensional array ( one of the solutions from the pyoof package). Its amplitude values are in radians. The input must be in radians or angle units.
circbool: If True it will take the phase.shape[0] as the diameter of a circle and calculate the root-mean-square only in that portion.

Notes

Ruze’s equation was derived empirically from a test reflector with Gaussian distributed errors, and it expressed as,

\[\varepsilon_\mathrm{rs} = \mathrm{e}^{-(4\pi\delta_\mathrm{rms}/\lambda)^2}.\]

Where \(\delta_\mathrm{rms}\) corresponds to the root-mean-squared deviation. The Python function uses the key phase because the term \(4\pi\delta_\mathrm{rms}/\lambda\) corresponds to the phase-error. Notice that this equation only works for a parabolic reflector and with a Cassegrain geometry, the term \(2\pi/\lamda\) converts the surface errors to phase and the additional \(2\) accounts for the two-way path of the reflected rays.

Examples

Simply add the a phase value and define the limits of the phase-error map.

>>> import numpy as np
>>> from astropy import units as u
>>> from pyoof import aperture
>>> pr = 50 * u.m
>>> K_coeff = np.array([0.1] * 21)  # see aperture.phase
>>> x, y, phi = aperture.phase(
...    K_coeff=K_coeff, pr=pr, piston=False, tilt=False
...    )
>>> aperture.e_rs(phase=phi, circ=True)
<Quantity 0.27564826>

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e_rs¶