Abstract

It was previously demonstrated in [Opt. Lett. 38, 229 (2013)] that the problem of freeform surface illumination design can be converted into a nonlinear boundary problem for the elliptic Monge–Ampére equation based on the ideal source assumption. But how the Monge–Ampére equation method is affected by the characteristics of the light source and target was not discussed there. This Letter systematically analyzes the influence of discontinuity, nonconvexity, and connectivity of light source and target on the Monge–Ampére equation method and presents some intrinsic features of this design method. These features are applied in practical examples in freeform optics design.

© 2014 Optical Society of America

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)

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 illumination design: a nonlinear boundary problem for the elliptic Monge–Ampére equation

Rengmao Wu, Liang Xu, Peng Liu, Yaqin Zhang, Zhenrong Zheng, Haifeng Li, and Xu Liu
Opt. Lett. 38(2) 229-231 (2013)

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)

Polar-grids based source-target mapping construction method for designing freeform illumination system for a lighting target with arbitrary shape

Xianglong Mao, Hongtao Li, Yanjun Han, and Yi Luo
Opt. Express 23(4) 4313-4328 (2015)