A new treatment for the problem of perfectly imaging geodesic lenses is presented that provides a uniform mathematical description for full aperture as well as for nonfull aperture media. A family of the existing particular solutions is surveyed and completed with novel results. The proposed formulation is in some aspects similar to the mathematical description of the Luneburg lens, which may be of some convenience for those familiar with the Luneburg lens theory.
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Jacek Sochacki (1986) studied this question.
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