Abstract

Light flux from LED must be redistributed to meet the needs of lighting in most cases, a new method is proposed for its secondary optic design. Based on refractive equation and energy conservation, a set of first-order partial differential equations which represent the characters of LED source and desired illumination were presented. The freeform lens was constructed by solving these equations numerically. The numerical results showed that we can get a freeform lens for the illumination of uniformity near to 90%, with considerable high computation speed. This method can shorten the designing time of the freeform lens with high accepted tolerance.

© 2008 Optical Society of America

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References

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  1. P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).
  2. M. Shen, H. F. Li, W. Lu, and X. Liu, "Method of reflective fly eye lens design for LED illuminating projection system," Acta Photonica Sinica 35,93-95 (2006).
  3. J. Bortz, N. Shatz, and D. Pitou, "Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target," Proc. SPIE 4092, 130-138 (2000).
    [CrossRef]
  4. B. A. Jacobson and R. D. Gengelbach, "Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source," Proc. SPIE 4446, 130-138 (2002).
  5. B. Parkyn and D. Pelka, "Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm," Proc. SPIE 6338, 633808 (2005).
    [CrossRef]
  6. H. Ries and J. Muschaweck, "Tailoring freeform lenses for illumination," Proc. SPIE 6338, 633808 (2001).
  7. H. Ries and J. Muschaweck, "Tailored freeform optical surfaces," J. Opt. Soc. Am. A 19, 590-595 (2002).
    [CrossRef]
  8. Y. Ding and P. F. Gu, "The Freeform Reflector for Uniform Illumination," Acta Optica Sinica 27, 540-544 (2007).
  9. Y. Ding, X. Liu, H. F. Li, and P. F. Gu, "The design of the freeform reflector for uniform illumination," in Proceedings of Asia Display 2007, Volume 1. (Shanghai, China, 2007), pp. 735-738.
  10. J. Schruben, "Formulation of a reflector design problem for a lighting fixture," J. Opt. Soc. Am 62, 1498-1501 (1972).
    [CrossRef]
  11. W. H. Chen, Introduction of Differential Geometry (Beijing University, 1990), Chap. 4.
  12. Y. C. Su and Q. G. Wu, Numerical Solutions of Partial Differential Equations (Weather, 1989), Chap. 1.
  13. Lumileds LED technical data sheet, "Luxeon star technical data sheet" (Lumileds, 2006). http://www.lumileds.com/pdfs/DS23.pdf.
  14. W. A. Parkyn, "Segmented illumination lenses for steplighting and wall-washing," Proc. SPIE 3779, 363-370 (1999).
    [CrossRef]
  15. H. Chase, "Optical Design with Rotationally Symmetric NURBS," Proc. SPIE 4832, 10-24 (2002).
    [CrossRef]
  16. T. L. R. Davenport, "3D NURBS representation of surface for illumination," Proc. SPIE 4832, 293-301 (2002).
    [CrossRef]
  17. T. L. R. Davenport, " Generation of NC Tool Path for Subdivision Surface," in Proceedings of CAD/Graphics 2001, Q. Peng, ed. (International Academic, Kunming, China, 2001), pp. 1-7.
  18. Precitech product features, "Freeform 700G" (Precitech, 2006). http://www.precitech.com/Precitech_ff700G_features.html.
  19. Y. Z. Wang and L. J. Chen, "A real-time NURBS surface interpolator for 5-axis surface machining," Chinese Journal of Aeronautics 18, 263-272 (2005).
    [CrossRef]

2007

Y. Ding and P. F. Gu, "The Freeform Reflector for Uniform Illumination," Acta Optica Sinica 27, 540-544 (2007).

2006

M. Shen, H. F. Li, W. Lu, and X. Liu, "Method of reflective fly eye lens design for LED illuminating projection system," Acta Photonica Sinica 35,93-95 (2006).

2005

B. Parkyn and D. Pelka, "Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm," Proc. SPIE 6338, 633808 (2005).
[CrossRef]

Y. Z. Wang and L. J. Chen, "A real-time NURBS surface interpolator for 5-axis surface machining," Chinese Journal of Aeronautics 18, 263-272 (2005).
[CrossRef]

2004

P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).

2002

B. A. Jacobson and R. D. Gengelbach, "Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source," Proc. SPIE 4446, 130-138 (2002).

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

H. Chase, "Optical Design with Rotationally Symmetric NURBS," Proc. SPIE 4832, 10-24 (2002).
[CrossRef]

T. L. R. Davenport, "3D NURBS representation of surface for illumination," Proc. SPIE 4832, 293-301 (2002).
[CrossRef]

2001

H. Ries and J. Muschaweck, "Tailoring freeform lenses for illumination," Proc. SPIE 6338, 633808 (2001).

2000

J. Bortz, N. Shatz, and D. Pitou, "Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target," Proc. SPIE 4092, 130-138 (2000).
[CrossRef]

1999

W. A. Parkyn, "Segmented illumination lenses for steplighting and wall-washing," Proc. SPIE 3779, 363-370 (1999).
[CrossRef]

1972

J. Schruben, "Formulation of a reflector design problem for a lighting fixture," J. Opt. Soc. Am 62, 1498-1501 (1972).
[CrossRef]

Bortz, J.

J. Bortz, N. Shatz, and D. Pitou, "Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target," Proc. SPIE 4092, 130-138 (2000).
[CrossRef]

Chase, H.

H. Chase, "Optical Design with Rotationally Symmetric NURBS," Proc. SPIE 4832, 10-24 (2002).
[CrossRef]

Chen, L. J.

Y. Z. Wang and L. J. Chen, "A real-time NURBS surface interpolator for 5-axis surface machining," Chinese Journal of Aeronautics 18, 263-272 (2005).
[CrossRef]

Davenport, T. L. R.

T. L. R. Davenport, "3D NURBS representation of surface for illumination," Proc. SPIE 4832, 293-301 (2002).
[CrossRef]

Ding, Y.

Y. Ding and P. F. Gu, "The Freeform Reflector for Uniform Illumination," Acta Optica Sinica 27, 540-544 (2007).

Gengelbach, R. D.

B. A. Jacobson and R. D. Gengelbach, "Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source," Proc. SPIE 4446, 130-138 (2002).

Gu, P. F.

Y. Ding and P. F. Gu, "The Freeform Reflector for Uniform Illumination," Acta Optica Sinica 27, 540-544 (2007).

P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).

Jacobson, B. A.

B. A. Jacobson and R. D. Gengelbach, "Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source," Proc. SPIE 4446, 130-138 (2002).

Li, H. F.

M. Shen, H. F. Li, W. Lu, and X. Liu, "Method of reflective fly eye lens design for LED illuminating projection system," Acta Photonica Sinica 35,93-95 (2006).

P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).

Lin, Y. X.

P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).

Liu, X.

M. Shen, H. F. Li, W. Lu, and X. Liu, "Method of reflective fly eye lens design for LED illuminating projection system," Acta Photonica Sinica 35,93-95 (2006).

Lu, W.

M. Shen, H. F. Li, W. Lu, and X. Liu, "Method of reflective fly eye lens design for LED illuminating projection system," Acta Photonica Sinica 35,93-95 (2006).

P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).

Muschaweck, J.

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

H. Ries and J. Muschaweck, "Tailoring freeform lenses for illumination," Proc. SPIE 6338, 633808 (2001).

Parkyn, B.

B. Parkyn and D. Pelka, "Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm," Proc. SPIE 6338, 633808 (2005).
[CrossRef]

Parkyn, W. A.

W. A. Parkyn, "Segmented illumination lenses for steplighting and wall-washing," Proc. SPIE 3779, 363-370 (1999).
[CrossRef]

Pelka, D.

B. Parkyn and D. Pelka, "Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm," Proc. SPIE 6338, 633808 (2005).
[CrossRef]

Pitou, D.

J. Bortz, N. Shatz, and D. Pitou, "Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target," Proc. SPIE 4092, 130-138 (2000).
[CrossRef]

Ries, H.

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

H. Ries and J. Muschaweck, "Tailoring freeform lenses for illumination," Proc. SPIE 6338, 633808 (2001).

Schruben, J.

J. Schruben, "Formulation of a reflector design problem for a lighting fixture," J. Opt. Soc. Am 62, 1498-1501 (1972).
[CrossRef]

Shatz, N.

J. Bortz, N. Shatz, and D. Pitou, "Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target," Proc. SPIE 4092, 130-138 (2000).
[CrossRef]

Shen, M.

M. Shen, H. F. Li, W. Lu, and X. Liu, "Method of reflective fly eye lens design for LED illuminating projection system," Acta Photonica Sinica 35,93-95 (2006).

Wang, Y. Z.

Y. Z. Wang and L. J. Chen, "A real-time NURBS surface interpolator for 5-axis surface machining," Chinese Journal of Aeronautics 18, 263-272 (2005).
[CrossRef]

Zheng, Z. R.

P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).

Zhou, P.

P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).

Acta Optica Sinica

P. Zhou, W. Lu, Y. X. Lin, Z. R. Zheng, H. F. Li, and P. F. Gu, "Fly eye lens array used in liquid crystal projection display with high light efficiency," Acta Optica Sinica 24, 587-591 (2004).

Y. Ding and P. F. Gu, "The Freeform Reflector for Uniform Illumination," Acta Optica Sinica 27, 540-544 (2007).

Acta Photonica Sinica

M. Shen, H. F. Li, W. Lu, and X. Liu, "Method of reflective fly eye lens design for LED illuminating projection system," Acta Photonica Sinica 35,93-95 (2006).

Chinese Journal of Aeronautics

Y. Z. Wang and L. J. Chen, "A real-time NURBS surface interpolator for 5-axis surface machining," Chinese Journal of Aeronautics 18, 263-272 (2005).
[CrossRef]

J. Opt. Soc. Am

J. Schruben, "Formulation of a reflector design problem for a lighting fixture," J. Opt. Soc. Am 62, 1498-1501 (1972).
[CrossRef]

J. Opt. Soc. Am. A

Proc. SPIE

W. A. Parkyn, "Segmented illumination lenses for steplighting and wall-washing," Proc. SPIE 3779, 363-370 (1999).
[CrossRef]

H. Chase, "Optical Design with Rotationally Symmetric NURBS," Proc. SPIE 4832, 10-24 (2002).
[CrossRef]

T. L. R. Davenport, "3D NURBS representation of surface for illumination," Proc. SPIE 4832, 293-301 (2002).
[CrossRef]

J. Bortz, N. Shatz, and D. Pitou, "Optimal design of a nonimaging projection lens for use with an LED source and a rectangular target," Proc. SPIE 4092, 130-138 (2000).
[CrossRef]

B. A. Jacobson and R. D. Gengelbach, "Lens for uniform LED illumination: an example of automated optimization using Monte Carlo ray-tracing of an LED source," Proc. SPIE 4446, 130-138 (2002).

B. Parkyn and D. Pelka, "Free-form illumination lens designed by a pseudo-rectangular lawnmower algorithm," Proc. SPIE 6338, 633808 (2005).
[CrossRef]

H. Ries and J. Muschaweck, "Tailoring freeform lenses for illumination," Proc. SPIE 6338, 633808 (2001).

Other

W. H. Chen, Introduction of Differential Geometry (Beijing University, 1990), Chap. 4.

Y. C. Su and Q. G. Wu, Numerical Solutions of Partial Differential Equations (Weather, 1989), Chap. 1.

Lumileds LED technical data sheet, "Luxeon star technical data sheet" (Lumileds, 2006). http://www.lumileds.com/pdfs/DS23.pdf.

T. L. R. Davenport, " Generation of NC Tool Path for Subdivision Surface," in Proceedings of CAD/Graphics 2001, Q. Peng, ed. (International Academic, Kunming, China, 2001), pp. 1-7.

Precitech product features, "Freeform 700G" (Precitech, 2006). http://www.precitech.com/Precitech_ff700G_features.html.

Y. Ding, X. Liu, H. F. Li, and P. F. Gu, "The design of the freeform reflector for uniform illumination," in Proceedings of Asia Display 2007, Volume 1. (Shanghai, China, 2007), pp. 735-738.

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Figures (11)

Fig. 1.
Fig. 1.

Vectors in refraction.

Fig. 2.
Fig. 2.

The LED refractive illumination system.

Fig. 3.
Fig. 3.

The topological mapping from source to target plane.

Fig. 4.
Fig. 4.

The freeform lens.

Fig. 5.
Fig. 5.

The simulated results using MM1D as the source. oe-16-17-12958-i001 across the center; — across the quarter.

Fig. 6.
Fig. 6.

The simulated results of an octagon illumination.

Fig. 7.
Fig. 7.

The simulated results using a 1×1 mm2 Lambertian rectangle as the source. oe-16-17-12958-i002 across the center; — across the quarter.

Fig. 8.
Fig. 8.

The illumination distribution when the source was translated for 0.1mm. oe-16-17-12958-i003 along +x axis; —along +y axis; oe-16-17-12958-i004 along +z axis; oe-16-17-12958-i005 along -z axis.

Fig. 9.
Fig. 9.

The simulated results when the source was tilted 3°. oe-16-17-12958-i006 rotation round x axis; — rotation round y axis; oe-16-17-12958-i007 rotation round vector (1,1,0).

Fig. 10.
Fig. 10.

The simulated results when F is 0.1µm. oe-16-17-12958-i008 T=100; — T=50; oe-16-17-12958-i009 T=10.

Fig. 11.
Fig. 11.

The simulated results when F is 2µm. oe-16-17-12958-i010 illumination along x axis; ·illumination along y axis.

Equations (15)

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

N = ( N x i , N y j , N z k ) .
I = ( I x i , I y j , I z k ) .
O = ( t p ) t p .
x = N x [ n o ( z p z ) n I I z t p ] ( n o N z ) + p x + n I n o I x t p .
y = N y [ n o ( z p z ) n I I z t p ] ( n o N z ) + p y + n I n o I y t p .
N = ( ρ θ ρ φ ) ρ θ ρ φ .
p = ( p x , p y , p z ) = ( ρ ( θ , φ ) sin φ cos θ , ρ ( θ , φ ) sin φ sin θ , ρ ( θ , φ ) cos φ ) .
0 2 π d θ 0 φ MAX I ( I ( φ ) ) sin φ d φ = E ( t ) d A .
I = ( sin φ I cos θ i , sin φ I sin θ j , cos φ I k ) .
φ I = φ S α 1 + α 2 .
ρ sin ( α 1 α 2 ) = sin ( φ S α 1 ) × R sin φ S sin ( α 1 α 2 φ S + φ ) .
Φ LED = 2 π × ( φ 0 φ 0 + d φ 2 I ( I ( φ 0 ) ) sin φ d φ + n = 1 N 1 φ n d φ 2 φ n + d φ 2 I ( I ( φ n ) ) sin φ d φ + φ N d φ 2 φ N I ( I ( φ N ) ) sin φ d φ ) .
Φ LED = E × 4 × X × Y ( X Y = 4 3 ) .
{ θ = y Y × π 4 θ = X x X × π 4 + π 4 0 θ π 4 π 4 θ π 2 .
φ s = n × d φ ; θ s = i × d θ . n , i = 0 , 1 , 2 . . .

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