Dual offset reflectors shaped for zero cross-polarisation and prescribed aperture illumination

The problem of shaping dual offset reflectors, fed by a linearly polarised rotationally symmetric feed horn, to produce a parallel beam over a non-circular aperture with zero cross-polarisation, is considered under the assumptions of geometrical optics. The condition for zero cross-polarisation leads to a partial differential equation, which hitherto has been solved numerically, but is shown here to possess an analytical solution. For uniqueness an additional constraint is put on systems with a plane of symmetry by prescribing the power distribution along the aperture line of symmetry. A suitable choice yields a uniform aperture edge illumination.