Freeform reflector design using integrable maps

We propose a design method for freeform reflectors based on source-target maps. The necessity for maps to fulfill the integrability condition to obtain a continuous reflector surface is discussed and demonstrated with various reflector geometries. We also review the advantages and drawbacks of reflectors with step discontinuities that do not require the integrability condition to be satisfied.

[1]  Jannick Rolland,et al.  Optimization of freeform lightpipes for light-emitting-diode projectors. , 2008, Applied optics.

[2]  Shangzhong Jin,et al.  Design of free-form microlens for LED general illumination , 2009, 2009 Asia Communications and Photonics conference and Exhibition (ACP).

[3]  William A. Parkyn.  Segmented illumination lenses for step lighting and wall washing , 1999, Optics & Photonics.

[4]  Harald Ries,et al.  Tailored freeform optical surfaces. , 2002, Journal of the Optical Society of America. A, Optics, image science, and vision.

[5]  T. Frankel.  The geometry of physics : an introduction , 2004 .

[6]  Jannick P Rolland,et al.  Fast freeform reflector generation usingsource-target maps. , 2010, Optics express.

[7]  Xu Liu,et al.  Freeform LED lens for uniform illumination. , 2008, Optics express.

[8]  William B. Elmer.  The optical design of reflectors , 1980 .

[9]  Rama Chellappa,et al.  A Method for Enforcing Integrability in Shape from Shading Algorithms , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Yi Luo,et al.  Discontinuous free-form lens design for prescribed irradiance. , 2007, Applied optics.

[11]  V. Oliker.  Mathematical Aspects of Design of Beam Shaping Surfaces in Geometrical Optics , 2003 .

[12]  Jannick P. Rolland,et al.  Designing freeform reflectors for extended sources , 2009, Optical Engineering + Applications.