Theory of imaging of Cassegrainian and Gregorian antennas

The formation of an image by an eilipsoidal reflector under illumination from one of its foci is discussed. The transformation relating the field distributions over two conjugate surfaces
\Sigma_{0}
and
\Sigma
is determined. It is shown that the image produced by the reflected field
E
over
\Sigma
is not an exact replica of the illumination of
\Sigma_{0}
, but
E = E_{i} + \delta E
, where
E_{i}
is the image according to geometric optics. The distortion
\delta E
is primarily due to the nonzero angle of incidence
i
on the reflector. If
i = 0
then
\delta E \simeq 0
, in agreement with Fresnel's diffraction theory for an optical system of revolution. The theory applies in general to any multireflector arrangement derived from quadric surfaces of revolution and, in particular, to Cassegrainian and Gregorian antennas. As an application, a simple solution to the classical problem of illuminating efficiently the aperture of a reflector antenna is proposed. A horn of relatively small aperture is combined with an imaging reflector. The imaging reflector, an ellipsoid, transforms the horn aperture distribution into a magnified image illuminating efficiently the main reflector, with negligible spillover over a wide frequency range.