Spherically symmetric lenses

A design procedure is given for finding the index variation of a spherically (or cylindrically) symmetric lens which will produce, with some restrictions, any desired shaped beam pattern. Applications are made to a broad beam Luneberg lens, a bistatic Luneberg reflector, and a bistatic Eaton-Lippmann lens, and other examples are worked out. The practical importance of the index singularity at the center of lenses of the Eaton-Lippmann type is treated.