title: Initial design with L(2) Monge-Kantorovich theory for the Monge-Ampère equation method in freeform surface illumination design.
abstract: The Monge-Ampère (MA) equation arising in illumination design is highly nonlinear so that the convergence of the MA method is strongly determined by the initial design. We address the initial design of the MA method in this paper with the L(2)-Kantorovich (LMK) theory. An efficient approach is proposed to find the optimal mapping of the LMK problem. The characteristics of the new approach are introduced and the limitations of the LMK theory in illumination design are presented. Three examples, including the beam shaping of collimated beam and point light source, are given to illustrate the potential benefits of the LMK theory in the initial design. The results show the MA method converges more stably and faster with the application of the LMK theory in the initial design.
authors: Rengmao
authors: R
authors: Wu
authors: Yaqin
authors: Y
authors: Zhang
authors: Mohamed M
authors: MM
authors: Sulman
authors: Zhenrong
authors: Z
authors: Zheng
authors: Pablo
authors: P
authors: Benítez
authors: Juan C
authors: JC
authors: Miñano