of the fundamental TE$_{11}$ mode of the horn to unpolarized radiation. By varying the position of the radiator, we can evaluate the response of any feed-horn to near and far field events occurring at varying angular positions with respect to the telescope’s boresight. We do not consider the response to polarized signals in this paper.\
Fig. \[fig:beams\] shows a set of beams for the central feed (top row) and an inner-ring feed. The columns represent the near-field response at varying distances $D$ from the dish, indexed here in terms of the Fresnel number[^2] $n_{\rm f} = \frac{d^2}{4\lambda D}$, where $d$ is the dish diameter, and $\lambda$ is the wavelength. The $n_{\rm f}=0.25$ beams are representative of the far-field response to good accuracy, and for increasing $n_{\rm f}$ (decreasing $D$) the beams get progressively defocused. The far-field FWHM of the central beam in our simulation for the Parkes dish is about 14’.5 at 1.4 GHz which agrees with the quoted value of 14’4 to better than 5%. The first coma lobes for the inner and outer ring feeds in our simulation are respectively at 18 dB and 13.85dB below the peak gain values. The departure of the coma lobe levels from 