Freeform Lens Design for Scattering Data with General Radiant Fields

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 realiz...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2018-05, Vol.228 (2), p.341-399
Main Authors: Gutiérrez, Cristian E., Sabra, Ahmad
Format: Article
Language:English
Subjects:
Classical Mechanics
Complex Systems
Fluid- and Aerodynamics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-017-1196-y