illum_parabolic

pyoof.aperture.illum_parabolic(x, y, I_coeff, pr)

Illumination function, \(E_\mathrm{a}(x, y)\), parabolic taper on a pedestal, sometimes called apodization, taper or window. Represents the distribution of light in the primary reflector. The illumination reduces the side lobe effect in the FT and it is a (feed) receiver property.

Parameters

xQuantity

Grid value for the \(x\) variable in length units.

yQuantity

Grid value for the \(y\) variable in length units.

I_coefflist

List which contains 5 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, q, x0, y0], with units as dimensionless, decibels and length, respectively. The coefficient q varies between 1 and 2 for reflector antennas.

prastropy.units.quantity.Quantity

Primary reflector radius in length units.

Returns

Eandarray

Illumination function, \(E_\mathrm{a}(x, y)\).

Notes

The parabolic taper on a pedestal has the following mathematical formula,

\[E_{\mathrm{a}} (\rho') = C + (1 - C) \cdot \left[ 1 - \left( \frac{\rho'}{R} \right)^2 \right]^q,\]

\[C=10^{\frac{c_\mathrm{dB}}{20}}.\]