Open AccessA mathematical model of the single freeform surface design for collimated beam shaping
Author(s) -
Rengmao Wu,
Peng Liu,
Yaqin Zhang,
Zhenrong Zheng,
Haifeng Li,
Xü Liu
Publication year - 2013
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.21.020974
Subject(s) - collimated light , optics , computer science , surface (topology) , beam (structure) , geometrical optics , physics , mathematics , geometry , laser
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.