Modified Luneburg lenses

The radial refractive index law in a Luneburg lens can be generalised so that a refractive index greater than unity is obtained at the surface, the analysis remaining exact. The feed radiation is limited to the value which gives total internal reflection at the surface and the reduction in aperture is compensated for by increased efficiency. A resultant non-parallelism among the radiated rays gives an ignorably small phase front perturbation