Mechanical description of subreflector and lens corrector profiles for optical antennas

The mechanical drawing method, well known in the case of the ellipse, is adapted, by a theorem of Leibniz, to the case of extended caustics. By matching the caustic of a reflector in a receiving mode to the caustic of a subreflector, focusing requirements for any situation can be met. The method is then extendable to the drawing methods for hyperbolas and refracting elements such as the Cartesian oval. Two-dimensional surfaces can be created section by section by applying the method to individual planes of a complete antenna. The method is illustrated by the design of a subreflector for a paraboloid with an offset beam and other optical systems. This includes the design of completely general double reflector antennas by choice of an arbitrary originating caustic.