Abstract

We propose an approach to deal with the problem of freeform surface illumination design without assuming any symmetry based on the concept that this problem is similar to the problem of optimal mass transport. With this approach, the freeform design is converted into a nonlinear boundary problem for the elliptic Monge–Ampére equation. The theory and numerical method are given for solving this boundary problem. Experimental results show the feasibility of this approach in tackling this freeform design problem.

© 2013 Optical Society of America

Influence of the characteristics of a light source and target on the Monge–Ampére equation method in freeform optics design

Rengmao Wu, Pablo Benítez, Yaqin Zhang, and Juan C. Miñano
Opt. Lett. 39(3) 634-637 (2014)

Initial design with L² Monge-Kantorovich theory for the Monge–Ampère equation method in freeform surface illumination design

Rengmao Wu, Yaqin Zhang, Mohamed M. Sulman, Zhenrong Zheng, Pablo Benítez, and Juan C. Miñano
Opt. Express 22(13) 16161-16177 (2014)

Freeform surface off-axis illumination design with the Monge–Ampère equation method in optical lithography

Yaqin Zhang, Rengmao Wu, and Zhenrong Zheng
Appl. Opt. 53(31) 7296-7303 (2014)

Designing illumination lenses and mirrors by the numerical solution of Monge–Ampère equations

Kolja Brix, Yasemin Hafizogullari, and Andreas Platen
J. Opt. Soc. Am. A 32(11) 2227-2236 (2015)

A mathematical model of the single freeform surface design for collimated beam shaping

Rengmao Wu, Peng Liu, Yaqin Zhang, Zhenrong Zheng, Haifeng Li, and Xu Liu
Opt. Express 21(18) 20974-20989 (2013)