"[F]or the bare hyperboloid, both real and Lambertian sources are in the same plane. This is a limitation in certain applications; however, we can manipulate these positions with lenses to place the sources at more convenient locations. ...this is an ideal concentrator. ...we have postulated an ideal lens while the hyperboloid is an ideal concentrator, albeit operating on a virtual source. The design considerations readily follow from the geometry of the hyperbola."
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Sources
, Juan C. Miñano, Pablo BenÃtez, Nonimaging Optics (2005) Ch. 6, The Flow-line Method for Designing Nonimaging Optical Systems
https://en.wikiquote.org/wiki/Hyperboloid
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Hyperboloid
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