Abstract
A new model is presented for a reflector producing a shaped narrow beam when illuminated by a point feed. The deviation from an idealised (Dunbar) model which has zero beam width in the geometrical optics approximation is regulated by a single arbitrary function tau , introduced to enhance the physical optics performance. In terms of tau , the phase distribution on a plane aperture is readily computed. Reflector profiles are then calculated by integration along the characteristics of a first order non-linear partial differential equation, leading to explicit formulae involving only ordinary quadratures. Initial data arises naturally on the central-section curve. It is shown that for continuous reflectors a well-known design due to Brunner (1971), frequently used in surveillance radar, is mathematically inconsistent.
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