The design of correcting secondary reflectors

A computer program called DERIVE is described for the design of the reflecting surfaces of two-mirror radio telescopes. It calculates the shape of a secondary reflector to any given primary by use of geometrical optics, yielding zero path length errors for all paraxial rays. The only condition to be fulfilled is (for Cassegrain types) that incoming rays, after reflection at the primary, do not cross each other before reaching the secondary. Equations for this condition are given. This method can be used to improve existing telescopes at short wavelengths by correcting for the surface deviations of the primary reflector with a specially shaped secondary. The results of 17 calculated examples are described, for various types of deviations