### 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-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

Original language | English |
---|---|

Place of Publication | Eindhoven |

Publisher | Technische Universiteit Eindhoven |

Number of pages | 21 |

Publication status | Published - 2013 |

### Publication series

Name | CASA-report |
---|---|

Volume | 1322 |

ISSN (Print) | 0926-4507 |

## Fingerprint Dive into the research topics of 'A numerical method for the design of free-form reflectors for lighting applications'. Together they form a unique fingerprint.

## Cite this

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). Technische Universiteit Eindhoven.