An Extension Of The Luneberg-Type Lenses

Abstract
The spherical lens first investigated by Luneberg (Mathematical Theory of Optics, Brown Univ. Lecture Notes, Providence, 1944), for which scanning throughout space without distortion is possible, was generalized to permit the source to lie within the lens, thereby reducing the size of the path followed by the source in scanning. This, and other shperical lenses with complete spherical symmetry that simulate line sources and infinte plane reflectors, appear as special cases of an extension of the class of circularly symmetric circular lenses due to Luneberg. Generally, a point source located within or on the boundary of a circular lens with variable index of refraction appears either as a virtual point source located at an arbitrary point within the lens or as a source whose energy is perfectly collimated in an arbitrary direction.

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