e_rs

pyoof.aperture.e_rs(phase)

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

Parameters:

phase : ndarray

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.

Notes

Ruze’s equation is derived empirically from a fat 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.

Examples

>>> import numpy as np
>>> pr = 50  # m, Effelsberg primary dish radius
>>> box_factor = 5
>>> resolution = 2 ** 8
>>> # then the x and y array will be defined
>>> x = np.linspace(-5 * pr, 5 * pr, resolution)
>>> x.size
256