Abstract

A method using a freeform surface lens for LED secondary optic design is proposed in this paper. By Snell’s Law, the differential equations are given to build the relationship between the normal direction of a freeform surface and its input/output ray vectors. Runge–Kutta formulas are used to calculate the differential equations to design the freeform surface. Moreover, the optical model for uniform illumination is simulated and optical performance is analyzed. A practical freeform surface lens for LED uniform illumination is fabricated using an injection molding method. By the process, our system demonstrates a uniform illumination with a divergence half-angle of 6° and an efficiency of 78.6%.

© 2009 Optical Society of America

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References

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  1. Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16, 12958-12966(2008).
    [CrossRef]
  2. J. Bullough, “Lighting answers: LED lighting systems,” http://www.lrc.rpi.edu/nlpip/publicationDetails.asp?id=885&type=2.
  3. B. Yang and Y. T. Wang, “Computer aided design of free form reflector,” Proc. SPIE 5942, 88-96 (2004).
  4. R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier Academic, 2005).
  5. H. Ries, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19, 590-595 (2002).
    [CrossRef]
  6. R. Winston and H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” Proc. SPIE 2016, 2-11(1993).
    [CrossRef]
  7. W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
    [CrossRef]
  8. F. Zhao, “Practical reflector design and calculation for general illumination,” Proc. SPIE 5942, 59420J (2005).
    [CrossRef]
  9. Philips Lumileds Lighting Company, “Secondary optics design considerations for SuperFlux LEDs,” http://www.philipslumileds.com/pdfs/AB20-5.PDF.
  10. B. Huang, Design of Lens for Large Area, High Brightness LEDs (Taiwan: National Central University, 2003).
  11. S. Kudaev and P. Schreiber, “Optimization of symmetrical free-shape non-imaging concentrators for LED light source applications,” Proc. SPIE 5942, 594209 (2005).
    [CrossRef]
  12. W. Tai and R. Schwarte, “Design of an aspherical lens to generate ahomogenous irradiance for three-dimensional sensors with a light-emitting-diode source,” Appl. Opt. 39, 5801-5805(2000).
    [CrossRef]
  13. F. H. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Marcel Dekker, 2000).
  14. J. R. Dromand, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19-26 (1980).
    [CrossRef]
  15. I. Moreno, M. Avendano-Alejo, and R. I. Tzonchev, “Designing LED arrays for uniform near-field irradiance,” Appl. Opt. 45, 2265-2272 (2006).
    [CrossRef]
  16. W. A. Parkyn and D. G. Pelka, “Auxiliary lens to modify the output flux distribution of a TIR lens,” U.S. patent 5,577,493 (26 November 1996).

2008

2006

2005

F. Zhao, “Practical reflector design and calculation for general illumination,” Proc. SPIE 5942, 59420J (2005).
[CrossRef]

S. Kudaev and P. Schreiber, “Optimization of symmetrical free-shape non-imaging concentrators for LED light source applications,” Proc. SPIE 5942, 594209 (2005).
[CrossRef]

2004

B. Yang and Y. T. Wang, “Computer aided design of free form reflector,” Proc. SPIE 5942, 88-96 (2004).

2003

W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
[CrossRef]

2002

2000

1993

R. Winston and H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” Proc. SPIE 2016, 2-11(1993).
[CrossRef]

1980

J. R. Dromand, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19-26 (1980).
[CrossRef]

Anselm, C.

W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
[CrossRef]

Avendano-Alejo, M.

Benitez, P.

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier Academic, 2005).

Bullough, J.

J. Bullough, “Lighting answers: LED lighting systems,” http://www.lrc.rpi.edu/nlpip/publicationDetails.asp?id=885&type=2.

Dickey, F. H.

F. H. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Marcel Dekker, 2000).

Ding, Y.

Dromand, J. R.

J. R. Dromand, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19-26 (1980).
[CrossRef]

Gu, P. F.

Holswade, S. C.

F. H. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Marcel Dekker, 2000).

Huang, B.

B. Huang, Design of Lens for Large Area, High Brightness LEDs (Taiwan: National Central University, 2003).

Knoflach, C.

W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
[CrossRef]

Kudaev, S.

S. Kudaev and P. Schreiber, “Optimization of symmetrical free-shape non-imaging concentrators for LED light source applications,” Proc. SPIE 5942, 594209 (2005).
[CrossRef]

Liu, X.

Minano, J. C.

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier Academic, 2005).

Moreno, I.

Muschaweck, J. A.

W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
[CrossRef]

Parkyn, W. A.

W. A. Parkyn and D. G. Pelka, “Auxiliary lens to modify the output flux distribution of a TIR lens,” U.S. patent 5,577,493 (26 November 1996).

Pelka, D. G.

W. A. Parkyn and D. G. Pelka, “Auxiliary lens to modify the output flux distribution of a TIR lens,” U.S. patent 5,577,493 (26 November 1996).

Pohl, W.

W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
[CrossRef]

Ries, H.

W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
[CrossRef]

H. Ries, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19, 590-595 (2002).
[CrossRef]

R. Winston and H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” Proc. SPIE 2016, 2-11(1993).
[CrossRef]

Schreiber, P.

S. Kudaev and P. Schreiber, “Optimization of symmetrical free-shape non-imaging concentrators for LED light source applications,” Proc. SPIE 5942, 594209 (2005).
[CrossRef]

Schwarte, R.

Tai, W.

Timinger, A. L.

W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
[CrossRef]

Tzonchev, R. I.

Wang, Y. T.

B. Yang and Y. T. Wang, “Computer aided design of free form reflector,” Proc. SPIE 5942, 88-96 (2004).

Winston, R.

R. Winston and H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” Proc. SPIE 2016, 2-11(1993).
[CrossRef]

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier Academic, 2005).

Yang, B.

B. Yang and Y. T. Wang, “Computer aided design of free form reflector,” Proc. SPIE 5942, 88-96 (2004).

Zhao, F.

F. Zhao, “Practical reflector design and calculation for general illumination,” Proc. SPIE 5942, 59420J (2005).
[CrossRef]

Zheng, Z. R.

Appl. Opt.

J. Comput. Appl. Math.

J. R. Dromand, “A family of embedded Runge-Kutta formulae,” J. Comput. Appl. Math. 6, 19-26 (1980).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Proc. SPIE

R. Winston and H. Ries, “Nonimaging reflectors as functionals of the desired irradiance,” Proc. SPIE 2016, 2-11(1993).
[CrossRef]

W. Pohl, C. Anselm, C. Knoflach, A. L. Timinger, J. A. Muschaweck, and H. Ries, “Complex 3D-tailored facets for optimal lighting of facades and public places,” Proc. SPIE 5186, 133-142(2003).
[CrossRef]

F. Zhao, “Practical reflector design and calculation for general illumination,” Proc. SPIE 5942, 59420J (2005).
[CrossRef]

B. Yang and Y. T. Wang, “Computer aided design of free form reflector,” Proc. SPIE 5942, 88-96 (2004).

S. Kudaev and P. Schreiber, “Optimization of symmetrical free-shape non-imaging concentrators for LED light source applications,” Proc. SPIE 5942, 594209 (2005).
[CrossRef]

Other

F. H. Dickey and S. C. Holswade, Laser Beam Shaping Theory and Techniques (Marcel Dekker, 2000).

R. Winston, J. C. Minano, and P. Benitez, Nonimaging Optics (Elsevier Academic, 2005).

Philips Lumileds Lighting Company, “Secondary optics design considerations for SuperFlux LEDs,” http://www.philipslumileds.com/pdfs/AB20-5.PDF.

B. Huang, Design of Lens for Large Area, High Brightness LEDs (Taiwan: National Central University, 2003).

J. Bullough, “Lighting answers: LED lighting systems,” http://www.lrc.rpi.edu/nlpip/publicationDetails.asp?id=885&type=2.

W. A. Parkyn and D. G. Pelka, “Auxiliary lens to modify the output flux distribution of a TIR lens,” U.S. patent 5,577,493 (26 November 1996).

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Figures (15)

Fig. 1
Fig. 1

Geometric relationship of the freeform surface and the rays.

Fig. 2
Fig. 2

Two different illumination models: (a) divergent illumination model, (b) convergent illumination model.

Fig. 3
Fig. 3

Layout of freeform surface lens: (a) 2D layout of the freeform surface lens, (b) partial enlarged detail of freeform.

Fig. 4
Fig. 4

Ray trace model of a freeform surface lens.

Fig. 5
Fig. 5

Analysis result of the illumination by ASAP: (a) illuminance distribution on target plane, (b) angular energy distribution.

Fig. 6
Fig. 6

Influence of the deviation of the target plane.

Fig. 7
Fig. 7

Intensity distribution on the target plane in the extended source case: (a) the source is round, (b) the source is rectangular.

Fig. 8
Fig. 8

Simulation result of efficiency and homogeneity as function of the diameter of the source.

Fig. 9
Fig. 9

Experiment mold: (a) design mold, (b) actual mold.

Fig. 10
Fig. 10

Appearance of the molding lens.

Fig. 11
Fig. 11

Measurement of the freeform surface.

Fig. 12
Fig. 12

Illumination modular with lens.

Fig. 13
Fig. 13

Flux measurement using an integrating sphere.

Fig. 14
Fig. 14

Diagram of the optical uniformity test.

Fig. 15
Fig. 15

Optical uniformity test result.

Tables (1)

Tables Icon

Table 1 Flux Measurement of an LED with a Freeform Surface

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

I ( φ ) = I 0 cos m φ ,
m = ln 2 ln ( cos φ 1 / 2 ) .
ϕ = I ( φ ) d Ω = 4 π I 0 m + 1 ( 1 cos m + 1 φ max ) .
ϕ = I ( φ ) d Ω = 2 π I 0 sin 2 φ max .
[ 1 + n 2 2 n ( Out · In ) ] 1 / 2 · N = Out n · In .
{ Out = ( x d x , H z ) In = ( x , z ) N = ( d z , d x ) .
d z d x = f ( x , z , x d ) = ( n D B ) / ( A n C ) ,
{ A = H z ( x d x ) 2 + ( H z ) 2 B = x d x ( x d x ) 2 + ( H z ) 2 C = z x 2 + z 2 D = x x 2 + z 2 .
ϕ = E · S .
ϕ = ϕ .
x d = R · ( 1 cos m + 1 φ ) 1 cos m + 1 φ max ,
x d = R · 1 1 cos m + 1 φ 1 cos m + 1 φ max ,
u k + 1 = u k + h 6 ( K 1 + K 2 + K 3 + K 4 ) ,
{ K 1 = f ( t k , u k ) K 2 = f ( t k + h 2 , u k + h 2 K 1 ) K 3 = f ( t k + h 2 , u k + h 2 K 2 ) K 4 = f ( t k + h , u k + h K 3 ) .
η = 102.2 130.1 = 78 . 6 % .

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