aperture

pyoof.aperture.aperture(x, y, K_coeff, I_coeff, d_z, wavel, illum_func, telgeo)

Aperture distribution, \(\underline{E_\mathrm{a}}(x, y)\). Collection of individual distribution/functions: i.e. illumination function, \(E_\mathrm{a}(x, y)\), blockage distribution, \(B(x, y)\), aperture phase distribution, \(\varphi(x, y)\) and OPD function, \(\delta(x, y;d_z)\). In general, it is a complex quantity, its phase an amplitude are better understood separately. The FT (2-dim) of the aperture represents the (field) radiation pattern, \(F( u, v)\).

Parameters:

x : ndarray

Grid value for the \(x\) variable in meters.

y : ndarray

Grid value for the \(y\) variable in meters.

K_coeff : ndarray

Constants coefficients, \(K_{n\ell}\), for each of them there is only one Zernike circle polynomial, \(U^\ell_n(\varrho, \varphi)\). The coefficients are between \([-2, 2]\).

I_coeff : ndarray

List which contains 4 parameters, the illumination amplitude, \(A_{E_\mathrm{a}}\), the illumination taper, \(c_\mathrm{dB}\) and the two coordinate offset, \((x_0, y_0)\). The illumination coefficients must be listed as follows, I_coeff = [i_amp, c_dB, x0, y0].

d_z : float

Radial offset, \(d_z\), added to the sub-reflector in meters. This characteristic measurement adds the classical interference pattern to the beam maps, normalized squared (field) radiation pattern, which is an out-of-focus property. It is usually of the order of centimeters.

wavel : float

Wavelength, \(\lambda\), of the observation in meters.

illum_func : function

Illumination function, \(E_\mathrm{a}(x, y)\), to be evaluated with the key I_coeff. The illumination functions available are illum_pedestal and illum_gauss.

telgeo : list

List that contains the blockage distribution, optical path difference (OPD) function, and the primary radius (float) in meters. The list must have the following order, telego = [block_dist, opd_func, pr].

Returns:

E : ndarray

Grid value that contains general expression for aperture distribution, \(\underline{E_\mathrm{a}}(x, y)\).

Notes

The aperture distribution is a collection of distributions/functions, its structure follows,

\[\underline{E_\mathrm{a}}(x, y) = B(x, y)\cdot E_\mathrm{a}(x, y) \cdot \mathrm{e}^{\mathrm{i} \{\varphi(x, y) + \frac{2\pi}{\lambda}\delta(x,y;d_z)\}}.\]

Where it does represent a complex number, with phase: aperture phase distribution, plus OPD function and amplitude the blockage distribution and illumination function.