Freeform lens design for scattering data with general radiant fields
type: Item
instance of: scholarly article
title: Freeform lens design for scattering data with general radiant fields
zbMATH Open document ID: 1393.78002
author: Cristian E. Gutiérrez
author: Ahmad Sabra
published in: Archive for Rational Mechanics and Analysis
publication date: 2018-04-17T00:00:00Z
review text: The authors prove the existence of a lens that refracts radiation which emanates from a planar source for a given set of directions. The surfaces constructed by the authors are free form and not necessarily rotationally symmetric. Precise conditions are given for which the lens is realizable. A general theory is developed to solve an illumination problem with two refracting surfaces, a planar source of radiation, and an arbitrary incident field. Aleksandrov solutions to this problem are also discussed. Finally, the upper face of the constructed lens is shown to satisfy a nonlinear partial differential equation of Monge-Ampère type.
reviewed by: Eric Stachura
Mathematics Subject Classification ID: 78A05
Mathematics Subject Classification ID: 35J96
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35R06
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 78A45
zbMATH DE Number: 6860754
zbMATH Keywords: freeform lens design
zbMATH Keywords: planar source
zbMATH Keywords: Monge-Ampère equation
zbMATH Keywords: Aleksandrov solutions
Wikidata QID: Q59610190
MaRDI profile type: Publication
full work available at URL: s00205-017-1196-y
OpenAlex ID: W2768433522
cites work: \(C^{1, \alpha}\) estimates for the parallel refractor
cites work: On the numerical solution of the far field refractor problem
cites work: Q4229031
cites work: Optimal design of an optical lens
cites work: The refractor problem in reshaping light beams
cites work: The near field refractor
cites work: The refractor problem with loss of energy
cites work: The reflector problem and the inverse square law
cites work: Aspherical lens design and imaging
cites work: The Parallel Refractor
cites work: Local near field refractors and reflectors
cites work: Regularity for the near field parallel refractor and reflector problems
cites work: The Monge-Ampère equation
cites work: An inverse problem for the refractive surfaces with parallel lighting
cites work: On the reflector shape design
cites work: Determination of reflector surfaces from near-field scattering data
cites work: On the local theory of prescribed Jacobian equations
cites work: On the design of a reflector antenna
cites work: Geometrical optics and blackbody radiation
DOI: 10.1007/S00205-017-1196-Y
description: scientific article; zbMATH DE number 6860754