TY - BOOK

T1 - A numerical method for the design of free-form reflectors for lighting applications

AU - Prins, C.R.

AU - Thije Boonkkamp, ten, J.H.M.

AU - Roosmalen, van, J.

AU - IJzerman, W.L.

AU - Tukker, T.W.

PY - 2013

Y1 - 2013

N2 - 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

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

M3 - Report

T3 - CASA-report

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

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -