Initial design with L2 Monge-Kantorovich theory for the Monge–Ampère equation method of freeform optics

Rengmao Wu; Yaqin Zhang; Pablo Benítez; Juan C. Miñano

doi:10.1117/12.2072370

17 December 2014 Initial design with L² Monge-Kantorovich theory for the Monge–Ampère equation method of freeform optics

Rengmao Wu, Yaqin Zhang, Pablo Benítez, Juan C. Miñano

Author Affiliations +

Proceedings Volume 9293, International Optical Design Conference 2014; 92930M (2014) https://doi.org/10.1117/12.2072370
Event: International Optical Design Conference, 2014, Kohala Coast, Hawaii, United States

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 L² Monge-Kantorovich (LMK) theory, and introduce an efficient approach for finding the optimal mapping of the LMK problem. 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.

Citation Download Citation

Rengmao Wu, Yaqin Zhang, Pablo Benítez, and Juan C. Miñano "Initial design with L² Monge-Kantorovich theory for the Monge–Ampère equation method of freeform optics", Proc. SPIE 9293, International Optical Design Conference 2014, 92930M (17 December 2014); https://doi.org/10.1117/12.2072370

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