A general analysis of geodesic luneberg lenses

Geodesic lenses have been developed which give a collimated beam diametrically opposite the focal point and at an arbitrary angle relative to the plane of the lens rim. The lenses may have an arbitrary variation of the index of refraction; however, only the constant index lenses are considered in detail. Experimental results are in good agreement with the theory. The practical importance of these lenses is that as a result of their circular symmetry a lens antenna may scan a full by feed movement alone or simultaneous coverage in many directions may be accomplished by use of multiple feeds.