We will take two, RR and LL, waves that will incident on hyperboloidal subreflector and converge as well after reflection.
The cartesian coordinates of the rays reflected by the hyperboloidal subreflector are given by.
y]/[partial derivative](x, y)] for all four rays, reflected from hyperboloidal subreflector, which are given below.
In order to calculate the zone plate efficiency, the chord length squared (proportional to zone plate intensity at the focus) is divided by the corresponding arc length squared (proportional to hyperboloidal lens focal contribution).
Since the zone plate is thinner than a lens, it has lower dielectric loss, lower weight and smaller volume than a lens, and because of planar construction, is easier to fabricate, especially compared to an ideal lens with hyperboloidal curvature.