It was shown in a paper by Morgan [J. Appl. Phys.29, 1358–1368 (1958)] that there exist an infinite number of spherically symmetric, perfect‐focusing lenses of which the Luneburg lens is but one example. Using the Helmholtz formulation of diffraction theory, we examine the farfield radiation characteristics of these lenses for both the case of an omnidirectional source and a particular directional source.