From one of the 80's-era Radio-Electronics magazines in the pile that was sitting on the table at the station today, I noticed a very interesting article about the design of a flat 'dish' antenna for UHF reception.
The design uses the approach to RF that a flat 'Fresnel' lens does in visual light to magnify a book page for example. The article explains the concept in detail as well as providing a simple BASIC program to design your own.
Apparently this is called a zone plate antenna. There is a Wikipedia page about it that mentions a prototype for 6 GHz that was developed at Bell Labs in 1946. It consisted of a 10 ft × 10 ft vertical lattice of parallel metal strips in the form of a Fresnel lens and, this is what I found fascinating, the antenna feed is behind the lens requiring the wavefront to pass through it.
An interesting article from 1985. See attached
Dave K3DFD