Abstract
We show the existence of a lens, when its lower face is given, such that it refracts radiation emanating from a planar source, with a given field of directions, into the far field that preserves a given distribution of energies. Conditions are shown under which the lens obtained is physically realizable. It is shown that the upper face of the lens satisfies a pde of Monge-Ampère type.
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Gutiérrez, C.E., Sabra, A. Freeform Lens Design for Scattering Data with General Radiant Fields. Arch Rational Mech Anal 228, 341–399 (2018). https://doi.org/10.1007/s00205-017-1196-y
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DOI: https://doi.org/10.1007/s00205-017-1196-y