A numerical method for the design of free-form reflectors for lighting applications

C.R. Prins, J.H.M. Thije Boonkkamp, ten, J. Roosmalen, van, W.L. IJzerman, T.W. Tukker

Onderzoeksoutput: Boek/rapportRapportAcademic

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In this article we present a method for the design of fully free-form reflectors for illumination systems. We derive an elliptic partial differential equation of the Monge-Ampère type for the surface of a reflector that converts an arbitrary parallel beam of light into a desired intensity output pattern. The differential equation has an unusual boundary condition known as the transport boundary condition. We find a convex or concave solution to the equation using a state of the art numerical method. The method uses a nonstandard discretization based on the diagonalization of the Hessian. The discretized system is solved using standard Newton iteration. The method was tested for a circular beam with uniform intensity, a street light and a uniform beam that is transformed into a famous Dutch painting. The reflectors were verified using commercial ray tracing software. Key words: illumination optics, nonimaging optics, Monge-Ampère equation, optimal mass transport, nonlinear partial differential equation, reflector design, convex solution, wide stencil
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijTechnische Universiteit Eindhoven
Aantal pagina's21
StatusGepubliceerd - 2013

Publicatie series

NaamCASA-report
Volume1322
ISSN van geprinte versie0926-4507

Vingerafdruk

illuminating
reflectors
partial differential equations
illumination
elliptic differential equations
optics
boundary conditions
streets
ray tracing
newton
iteration
differential equations
computer programs
output

Citeer dit

Prins, C. R., Thije Boonkkamp, ten, J. H. M., Roosmalen, van, J., IJzerman, W. L., & Tukker, T. W. (2013). A numerical method for the design of free-form reflectors for lighting applications. (CASA-report; Vol. 1322). Eindhoven: Technische Universiteit Eindhoven.
Prins, C.R. ; Thije Boonkkamp, ten, J.H.M. ; Roosmalen, van, J. ; IJzerman, W.L. ; Tukker, T.W. / A numerical method for the design of free-form reflectors for lighting applications. Eindhoven : Technische Universiteit Eindhoven, 2013. 21 blz. (CASA-report).
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abstract = "In this article we present a method for the design of fully free-form reflectors for illumination systems. We derive an elliptic partial differential equation of the Monge-Amp{\`e}re type for the surface of a reflector that converts an arbitrary parallel beam of light into a desired intensity output pattern. The differential equation has an unusual boundary condition known as the transport boundary condition. We find a convex or concave solution to the equation using a state of the art numerical method. The method uses a nonstandard discretization based on the diagonalization of the Hessian. The discretized system is solved using standard Newton iteration. The method was tested for a circular beam with uniform intensity, a street light and a uniform beam that is transformed into a famous Dutch painting. The reflectors were verified using commercial ray tracing software. Key words: illumination optics, nonimaging optics, Monge-Amp{\`e}re equation, optimal mass transport, nonlinear partial differential equation, reflector design, convex solution, wide stencil",
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Prins, CR, Thije Boonkkamp, ten, JHM, Roosmalen, van, J, IJzerman, WL & Tukker, TW 2013, A numerical method for the design of free-form reflectors for lighting applications. CASA-report, vol. 1322, Technische Universiteit Eindhoven, Eindhoven.

A numerical method for the design of free-form reflectors for lighting applications. / Prins, C.R.; Thije Boonkkamp, ten, J.H.M.; Roosmalen, van, J.; IJzerman, W.L.; Tukker, T.W.

Eindhoven : Technische Universiteit Eindhoven, 2013. 21 blz. (CASA-report; Vol. 1322).

Onderzoeksoutput: Boek/rapportRapportAcademic

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AB - In this article we present a method for the design of fully free-form reflectors for illumination systems. We derive an elliptic partial differential equation of the Monge-Ampère type for the surface of a reflector that converts an arbitrary parallel beam of light into a desired intensity output pattern. The differential equation has an unusual boundary condition known as the transport boundary condition. We find a convex or concave solution to the equation using a state of the art numerical method. The method uses a nonstandard discretization based on the diagonalization of the Hessian. The discretized system is solved using standard Newton iteration. The method was tested for a circular beam with uniform intensity, a street light and a uniform beam that is transformed into a famous Dutch painting. The reflectors were verified using commercial ray tracing software. Key words: illumination optics, nonimaging optics, Monge-Ampère equation, optimal mass transport, nonlinear partial differential equation, reflector design, convex solution, wide stencil

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Prins CR, Thije Boonkkamp, ten JHM, Roosmalen, van J, IJzerman WL, Tukker TW. A numerical method for the design of free-form reflectors for lighting applications. Eindhoven: Technische Universiteit Eindhoven, 2013. 21 blz. (CASA-report).