A variety of structures in the form of spheres can provide sharp focusing and directivity gains comparable to those from a circular piston with the same diameter. With an isotropic refractive sphere, spherical aberration does not impair focusing except for angular resolutions of the order of a few degrees and less. Luneberg lenses with compliant tubes or refractive liquid packets eliminate spherical aberration, but the focal distance may change as a result of dispersion in the resultant index of refraction. The outer shell of a Luneberg lens alone, and without the inner core, provides an angular resolution which is comparable to that for the full lens, but with a decrease in the directivity gain which is not as great as the reduction in the amount of refractive matter. Primary feeds with considerable directivity are essential for all types of lenses except those with the focus near the outer surface of the lens.
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W. J. Toulis (1963) studied this question.