Double reflector systems with a spherical main reflector

A simple ray tracing scheme is developed for evaluating the contour of a subreflector from phase conditions in the design of a spherical reflector system. The position of the focus feed in the spherical reflector system and the distance separating the subreflector vertex from the focus feed are traced in the aperture plane as the major characteristic parameters of the system. Equations of the beam, phase surfaces, and caustic are derived from the ray-tracing geometry. Several types of appropriate reflectors (e.g., Gregory reflectors) are considered, and five distinct types of subreflectors are found by considering different reflector contours.