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Point Source Regularization of the Finite Source Reflector Problem

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBenamou, Jean-David
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChazareix, Guillaume
hal.structure.identifierHigh Tech Campus Eindhoven
dc.contributor.authorIjzerman, Wilbert
hal.structure.identifierInria de Paris
dc.contributor.authorRukhaia, Giorgi
dc.date.accessioned2021-10-27T09:08:16Z
dc.date.available2021-10-27T09:08:16Z
dc.date.issued2022
dc.identifier.issn0021-9991
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22107
dc.language.isoenen
dc.subjectInverse reflector problem
dc.subjectOptimal transportation
dc.subjectNon-linear optimization
dc.subject.ddc515en
dc.titlePoint Source Regularization of the Finite Source Reflector Problem
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe address the “freeform optics” inverse problem of designing a reflector surface mapping a prescribed source distribution of light to a prescribed far field distribution, for a finite light source. When the finite source reduces to a point source, the light source distribution has support only on the optics ray directions. In this setting the inverse problem is well posed for arbitrary source and target probability distributions. It can be recast as an Optimal Transportation problem and has been studied both mathematically and nu-merically. We are not aware of any similar mathematical formulation in the finite source case: i.e. the source has an “´etendue” with support both in space and directions. We propose to leverage the well-posed variational formulation of the point source problem to build a smooth parameterization of the reflec-tor and the reflection map. Under this parameterization we can construct a smooth loss/misfit function to optimize for the best solution in this class of reflectors. Both steps, the parameterization and the loss, are related to Optimal Transportation distances. We also take advantage of recent progress in the numerical approximation and resolution of these mathematical objects to perform a numerical study.
dc.relation.isversionofjnlnameJournal of Computational Physics
dc.relation.isversionofjnlissue456
dc.relation.isversionofjnldate2022
dc.relation.isversionofdoi10.1016/j.jcp.2022.111032
dc.relation.isversionofjnlpublisherElsevier
dc.subject.ddclabelAnalyseen
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2023-01-02T14:56:49Z
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