TOROIDAL dual reflector antenna is similar to Gregorian reflector in shape, but the basic formula differs from it.
The sub-reflector of Toroidal antenna is from a virtual toroid, but the main reflector is analogous to an ellipsoid.
There is no parabolic formula. This system has a convex - concave sub-reflector. This sub-reflector is convex in one
plane and concave in orthogonal plane. The complete shape of them are obtained through elaborate mathematical and physical calculation.