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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 20974–20989

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  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 20974-20989 (2013)
http://dx.doi.org/10.1364/OE.21.020974


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Abstract

Incoherent collimated beam has a wide application, and reshaping the collimated beam with freeform optics has become a popular and challenging topic of noniamging design. In this paper, we address this issue, embedded in three-dimensional space without any symmetry, with a freeform surface from a new perspective. A mathematical model is established for achieving the one-freeform surface design based on the problem of optimal mass transport. A numerical technique for solving this design model is disclosed for the first time, and boundary conditions for balancing light are presented. Besides, some key issues in achieving complex illuminations are addressed, and the influence of caustic surface on this design model is also discussed. Design examples are given to verify these theories. The results show elegance of the design model in tackling complex illumination tasks. The conclusions obtained in this paper can be generalized to achieve LED illumination and tackle multiple freeform surfaces illumination design.

© 2013 OSA

OCIS Codes
(220.1250) Optical design and fabrication : Aspherics
(080.1753) Geometric optics : Computation methods
(220.2945) Optical design and fabrication : Illumination design
(220.4298) Optical design and fabrication : Nonimaging optics

ToC Category:
Geometric Optics

History
Original Manuscript: June 14, 2013
Revised Manuscript: August 22, 2013
Manuscript Accepted: August 22, 2013
Published: August 30, 2013

Citation
Rengmao Wu, Peng Liu, Yaqin Zhang, Zhenrong Zheng, Haifeng Li, and Xu Liu, "A mathematical model of the single freeform surface design for collimated beam shaping," Opt. Express 21, 20974-20989 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20974


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