Generalized Dual Reflector
The antenna has a main reflector that ranges from a sphere (k = 0) to a parabola (k = 1) finally to a plane (k = 2). The parameter k various continuously but sphere and plane can be only approached asymptotically. The October 2012 issue of IEEE Antenna and Propagation Magazine, Vol. 54, No. 5 contains the article Generalized Dual- Reflector Axisymmetric Antennas by Norayr R. Khachatryan, Ruben V. Ter-Antonyan which discusses an approach to this antenna. Equations are given for a subreflector that focuses rays to a feed point. An executable gerdual that runs in a DOS window designs the antenna and generates input files to GRASP.
K = 0.25, Main diameter = 8, Theta_max = 45, Subreflector center = 2, Feed = 4
K = 0.70, Main diameter = 8, Theta_max = 45, Subreflector center = 0.5, Feed = 2.5
K = 1.20, Main diameter = 8, Theta_max = 45, Subreflector center = -0.2, Feed = 1.0