Wu Rengmao, Zhang Yaqin, Sulman Mohamed M, Zheng Zhenrong, Benítez Pablo, Miñano Juan C
Opt Express. 2014 Jun 30;22(13):16161-77. doi: 10.1364/OE.22.016161.
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.
照明设计中出现的蒙日 - 安培（MA）方程具有高度非线性，因此MA方法的收敛性很大程度上取决于初始设计。本文运用L(2)-康托罗维奇（LMK）理论来探讨MA方法的初始设计。提出了一种有效的方法来求解LMK问题的最优映射。介绍了新方法的特点，并阐述了LMK理论在照明设计中的局限性。给出了三个例子，包括准直光束和点光源的光束整形，以说明LMK理论在初始设计中的潜在优势。结果表明，在初始设计中应用LMK理论，MA方法收敛得更稳定、更快。
