Abstract

A combined feedback design method based on variable separation mapping is proposed in this paper to design free-form optical systems for an extended LED source with complicated illumination patterns. In this method, macro energy division and micro illuminance distribution feedback modifications are carried out according to the deviation between the simulated illumination results and the target requirements. The free-form optical system is then regenerated, and the deviation could be minimized through multiple iterations. Results indicate that free-form optical system designed by this method could achieve precise energy distribution, high regional illuminance uniformity (89.7%), and high light output efficiency (94.9%) simultaneously.

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  1. Y. Luo, Z. X. Feng, Y. J. Han, and H. T. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18(9), 9055–9063 (2010).
    [CrossRef] [PubMed]
  2. R. Winston, J. C. Miñano, and P. Benítez, eds., with contributions by N. Shatz and J. C. Bortz, eds., Nonimaging Optics (Elsevier, 2005).
  3. Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).
  4. Y. Yi, K. Y. Qian, and Y. Luo, “A novel LED uniform illuminance system based on nonimaging optics,” Opt. Technol. 33(1), 110–112 (2007).
  5. H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
    [CrossRef] [PubMed]
  6. A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
    [CrossRef]
  7. V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207 (2005).
    [CrossRef]
  8. J. Bortz and N. Shatz, “Generalized functional method of nonimaging optical design,” Proc. SPIE 6338, 633805 (2006).
    [CrossRef]
  9. L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007).
    [CrossRef] [PubMed]
  10. Y. J. Han, X. Zhang, Z. Feng, K. Qian, H. Li, Y. Luo, G. Huang, and B. Zhu, “Variable-separation three dimensional freeform nonimaging optical system design based on target-to-source mapping and micro belt surface construction,” Sciencepaper Online 1–9 (2010). http://www.paper.edu.cn/en/paper.php?serial_number=201002-443

2010 (1)

2008 (1)

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

2007 (2)

Y. Yi, K. Y. Qian, and Y. Luo, “A novel LED uniform illuminance system based on nonimaging optics,” Opt. Technol. 33(1), 110–112 (2007).

L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007).
[CrossRef] [PubMed]

2006 (1)

J. Bortz and N. Shatz, “Generalized functional method of nonimaging optical design,” Proc. SPIE 6338, 633805 (2006).
[CrossRef]

2005 (1)

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207 (2005).
[CrossRef]

2003 (1)

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

2002 (1)

Bortz, J.

J. Bortz and N. Shatz, “Generalized functional method of nonimaging optical design,” Proc. SPIE 6338, 633805 (2006).
[CrossRef]

Deng, G.

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Feng, Z. X.

Han, Y. J.

Y. Luo, Z. X. Feng, Y. J. Han, and H. T. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18(9), 9055–9063 (2010).
[CrossRef] [PubMed]

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Hu, F.

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Lee, W.

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Li, H. T.

Luo, Y.

Y. Luo, Z. X. Feng, Y. J. Han, and H. T. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18(9), 9055–9063 (2010).
[CrossRef] [PubMed]

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Y. Yi, K. Y. Qian, and Y. Luo, “A novel LED uniform illuminance system based on nonimaging optics,” Opt. Technol. 33(1), 110–112 (2007).

L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007).
[CrossRef] [PubMed]

Muschaweck, J.

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

Muschaweck, J. A.

Oliker, V.

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207 (2005).
[CrossRef]

Qian, K. Y.

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Y. Yi, K. Y. Qian, and Y. Luo, “A novel LED uniform illuminance system based on nonimaging optics,” Opt. Technol. 33(1), 110–112 (2007).

L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007).
[CrossRef] [PubMed]

Ries, H.

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002).
[CrossRef] [PubMed]

Shatz, N.

J. Bortz and N. Shatz, “Generalized functional method of nonimaging optical design,” Proc. SPIE 6338, 633805 (2006).
[CrossRef]

Timinger, A.

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

Wang, L.

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007).
[CrossRef] [PubMed]

Yang, Y.

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Yi, Y.

Y. Yi, K. Y. Qian, and Y. Luo, “A novel LED uniform illuminance system based on nonimaging optics,” Opt. Technol. 33(1), 110–112 (2007).

Zhang, O.

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Zhang, X.

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

Appl. Opt. (1)

Chin. J. Lasers (1)

Y. Luo, X. Zhang, L. Wang, Y. Yang, F. Hu, K. Y. Qian, Y. J. Han, W. Lee, O. Zhang, and G. Deng, “Non-imaging optics and its application in solid state lighting,” Chin. J. Lasers 35(7), 964–971 (2008).

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Opt. Technol. (1)

Y. Yi, K. Y. Qian, and Y. Luo, “A novel LED uniform illuminance system based on nonimaging optics,” Opt. Technol. 33(1), 110–112 (2007).

Proc. SPIE (3)

A. Timinger, J. Muschaweck, and H. Ries, “Designing tailored free-form surfaces for general illumination,” Proc. SPIE 5186, 128–132 (2003).
[CrossRef]

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed illuminance properties,” Proc. SPIE 5942, 594207 (2005).
[CrossRef]

J. Bortz and N. Shatz, “Generalized functional method of nonimaging optical design,” Proc. SPIE 6338, 633805 (2006).
[CrossRef]

Other (2)

R. Winston, J. C. Miñano, and P. Benítez, eds., with contributions by N. Shatz and J. C. Bortz, eds., Nonimaging Optics (Elsevier, 2005).

Y. J. Han, X. Zhang, Z. Feng, K. Qian, H. Li, Y. Luo, G. Huang, and B. Zhu, “Variable-separation three dimensional freeform nonimaging optical system design based on target-to-source mapping and micro belt surface construction,” Sciencepaper Online 1–9 (2010). http://www.paper.edu.cn/en/paper.php?serial_number=201002-443

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Figures (9)

Fig. 1
Fig. 1

Energy matrix, area matrix, and the corresponding (u,v) and (x,y) divisions.

Fig. 2
Fig. 2

Different accuracy of construction: (a) high construction accuracy with small source angle division, (b) low construction accuracy with large source angle division.

Fig. 3
Fig. 3

Mesh grid mismatch between the area matrix and the prescribed illuminance matrix.

Fig. 4
Fig. 4

Combined feedback process: (a) frame curves established, (b) regional curves established.

Fig. 5
Fig. 5

Design example: (a) design parameters, (b) prescribed illuminance distribution pattern.

Fig. 6
Fig. 6

Simulated results: (a) initial result of feedback with fixed A , (b) final result of feedback with fixed A , (c) initial result of feedback with fixed E , (d) final result of feedback with fixed E , (e) initial result of combined feedback design, (f) final result of combined feedback design.

Fig. 7
Fig. 7

Comparisons between simulated results on three parameters: (a) total energy ratio between white and blue regions, (b) average regional illuminance uniformity, (c) light output efficiency (Fresnel loss ignored).

Fig. 8
Fig. 8

Profiles of the final optical system models designed by three feedback methods: (a) cross-sectional profiles in the y-z plane (x = 0), (b) cross-sectional profiles in the x-z plane (y = 0).

Fig. 9
Fig. 9

3-D geometry of the final optical system model designed by the combined feedback method.

Equations (8)

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u min u k + 1 J ( u ) cos u d u u min u max J ( u ) cos u d u = i = 1 k j = 1 n E ( i , j ) i = 1 m j = 1 n E ( i , j ) ,
v min v s + 1 k + 1 J ( v ) cos v d v v min v max J ( v ) cos v d v = j = 1 s E ( k , j ) j = 1 n E ( k , j ) ,
x min x k + 1 J ( x ) d x x min x max J ( x ) d x = i = 1 k j = 1 n A ( i , j ) i = 1 m j = 1 n A ( i , j ) ,
y min y s + 1 k + 1 J ( y ) d y y min y max J ( y ) d y = j = 1 s A ( k , j ) j = 1 n A ( k , j ) ,
E k ( i , j ) = P p r e k 1 ( i , j ) P s i m k 1 ( i , j ) P p r e k 2 ( i , j ) P s i m k 2 ( i , j ) P p r e 0 ( i , j ) P s i m 0 ( i , j ) E 0 ( i , j ) , i = 1... m , j = 1... n ,
A k ( i , j ) = P s i m k 1 ( i , j ) P p r e k 1 ( i , j ) P s i m k 2 ( i , j ) P p r e k 2 ( i , j ) P s i m 0 ( i , j ) P p r e 0 ( i , j ) A 0 ( i , j ) , i = 1... m , j = 1... n ,
E w k ( i , j ) = E w 0 ( i , j ) E w s i m k 1 ( i , j ) E w 0 ( i , j ) E w s i m k 2 ( i , j ) E w 0 ( i , j ) E w s i m 0 ( i , j ) E w 0 ( i , j ) , i = 1... m w , j = 1... n w ,
A s k ( i , j ) = P s i m s k 1 ( i , j ) P p r e s k 1 ( i , j ) P s i m s k 2 ( i , j ) P p r e s k 2 ( i , j ) P s i m s 0 ( i , j ) P p r e s 0 ( i , j ) A s 0 ( i , j ) , i = 1... m s , j = 1... n s , s = 1... m w × n w ,

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