illum_pedestal

pyoof.aperture.illum_pedestal(x, y, I_coeff, pr, q=2)

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 lobes in the FT and it is a property of the receiver.

Parameters:

x : ndarray

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

y : ndarray

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

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].

pr : float

Primary reflector radius in meters.

q : int

Order of the parabolic taper on a pedestal, it is commonly set at \(q = 2\).

Returns:

Ea : ndarray

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

Notes

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

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

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