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J Opt Soc Am A Opt Image Sci Vis. 2011 Feb 1;28(2):284-9. doi: 10.1364/JOSAA.28.000284.

Reflection, refraction, and the Legendre transform.

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  • 1Dipartimento di Matematica e Informatica, Universita di Cagliari, Via Ospedale, n 72 09124 Cagliari, Italy.


We construct in dimension two a mirror that reflects collimated rays into a set of directions that amplify the image and an optical lens so that collimated rays are refracted into a set of directions with a prescribed magnification factor. The profiles of these optical surfaces are given by explicit formulas involving the Legendre transformation.

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