radiation_pattern

pyoof.aperture.radiation_pattern(K_coeff, I_coeff, d_z, wavel, illum_func, telgeo, resolution, box_factor)

Spectrum or (field) radiation pattern, \(F(u, v)\), it is the FFT2 computation of the aperture distribution, \(\underline{E_\mathrm{a}} (x, y)\), in a rectangular grid. Passing the majority of arguments to the aperture distribution except the FFT2 resolution.

Parameters:

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].

resolution : int

Fast Fourier Transform resolution for a rectangular grid. The input value has to be greater or equal to the telescope resolution and with power of 2 for faster FFT processing. It is recommended a value higher than resolution = 2 ** 8.

box_factor : int

Related to the FFT resolution (resolution key), defines the image pixel size level. It depends on the primary radius, pr, of the telescope, e.g. a box_factor = 5 returns x = np.linspace(-5 * pr, 5 * pr, resolution), an array to be used in the FFT2 (fft2).

Returns:

u_shift : ndarray

\(u\) wave-vector in 1 / m units. It belongs to the \(x\) coordinate in meters from the aperture distribution, \(\underline{E_\mathrm{a}}(x, y)\).

v_shift : ndarray

\(v\) wave-vector in 1 / m units. It belongs to the y coordinate in meters from the aperture distribution, \(\underline{E_\mathrm{a}}(x, y)\).

F_shift : ndarray

Output from the FFT2 (fft2), \(F(u, v)\), unnormalized solution in a grid, defined by resolution and box_factor keys.

Notes

The (field) radiation pattern is the direct Fourier Transform in two dimensions of the aperture distribution, hence,

\[F(u, v) = \mathcal{F} \left[ \underline{E_\mathrm{a}}(x, y) \right].\]