Abstract

The one-time ray-tracing optimization method is a fast way to design LED illumination systems [Opt. Express 22, 5357 (2014) [CrossRef]  ]. The method optimizes the performance of LED illumination systems by modifying the LEDs’ luminous intensity distribution curve (LIDC) with a freeform lens, instead of modifying the illumination system structure. In finding the LEDs’ LIDC for optimizing the illumination system’s performance, the LEDs’ LIDC found by means of a general gradient descent method can be trapped in a local solution. This study develops a matrix operation method to directly find the global solution of the LEDs’ LIDC for the optimization of the illumination system’s performance for any initial design of an illumination system structure. As compared with the gradient descent method, using the proposed characteristic matrix operation method to find the best LEDs’ LIDC reduces the cost in time by several orders of magnitude. The proposed characteristic matrix operation method ensures that the one-time ray-tracing optimization method is an efficient and reliable method for designing LED illumination systems.

© 2016 Optical Society of America

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References

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  1. F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18(20), 20926–20938 (2010).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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2015 (1)

2014 (1)

2013 (4)

2012 (1)

2011 (2)

2010 (2)

2006 (1)

2004 (1)

I. Moreno, “Configurations of LED arrays for uniform illumination,” Proc. SPIE 5622, 713–718 (2004).
[Crossref]

Aslanov, E. R.

Avendaño-Alejo, M.

Bezus, E. A.

Chen, F.

Chu, S. C.

Deng, L.

Doskolovich, L. L.

Du, K.

Ge, Q.

Hu, S.

Hu, X.

Hu, Y.-W.

Kazanskiy, N. L.

Lee, X.-H.

Liao, Y. H.

Liu, S.

Luo, X.

Ma, Z.

Mei, T.

Moiseev, M. A.

Moreno, I.

Pan, J.-W.

Qian, K.

Qin, Z.

Sun, C.-C.

Tzonchev, R. I.

Wan, L.

Wang, C.

Wang, K.

Wu, D.

Wu, H. Y.

Yang, H. L.

Yang, Y.

Zhai, H.

Zhao, S.

Zhu, N.

Appl. Opt. (2)

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

Opt. Express (8)

K. Wang, D. Wu, Z. Qin, F. Chen, X. Luo, and S. Liu, “New reversing design method for LED uniform illumination,” Opt. Express 19(S4Suppl 4), A830–A840 (2011).
[Crossref] [PubMed]

X.-H. Lee, I. Moreno, and C.-C. Sun, “High-performance LED street lighting using microlens arrays,” Opt. Express 21(9), 10612–10621 (2013).
[Crossref] [PubMed]

Z. Ma, L. Deng, Y. Yang, H. Zhai, and Q. Ge, “Numerical iterative approach for zero-order term elimination in off-axis digital holography,” Opt. Express 21(23), 28314–28324 (2013).
[Crossref] [PubMed]

E. R. Aslanov, L. L. Doskolovich, M. A. Moiseev, E. A. Bezus, and N. L. Kazanskiy, “Design of an optical element forming an axial line segment for efficient LED lighting systems,” Opt. Express 21(23), 28651–28656 (2013).
[Crossref] [PubMed]

S. C. Chu, H. L. Yang, Y. H. Liao, H. Y. Wu, and C. Wang, “One-time ray-tracing optimization method and its application to the design of an illuminator for a tube photo-bioreactor,” Opt. Express 22(5), 5357–5374 (2014).
[Crossref] [PubMed]

S. Hu, K. Du, T. Mei, L. Wan, and N. Zhu, “Ultra-compact LED lens with double freeform surfaces for uniform illumination,” Opt. Express 23(16), 20350–20355 (2015).
[Crossref] [PubMed]

Z. Qin, K. Wang, F. Chen, X. Luo, and S. Liu, “Analysis of condition for uniform lighting generated by array of light emitting diodes with large view angle,” Opt. Express 18(16), 17460–17476 (2010).
[Crossref] [PubMed]

F. Chen, K. Wang, Z. Qin, D. Wu, X. Luo, and S. Liu, “Design method of high-efficient LED headlamp lens,” Opt. Express 18(20), 20926–20938 (2010).
[Crossref] [PubMed]

Opt. Lett. (1)

Proc. SPIE (1)

I. Moreno, “Configurations of LED arrays for uniform illumination,” Proc. SPIE 5622, 713–718 (2004).
[Crossref]

Other (2)

Illumination design software, LightTools, see http://optics.synopsys.com/lighttools/ .

W.-S. Sun and C.-H. Tsuei, “Sunlight and LED hybrid illumination in indoor lighting design,” in Proceedings of International Optical Design Conference (IODC, 2010), paper JMB21.
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Illustration of source zone and target zone divisions for the one-time ray-tracing optimization method. A common edge-lit LED illuminator is used to explain the characteristic matrix operation method.
Fig. 2
Fig. 2 Illustration of two ways of dividing the source zones: (a) Equi-angle division. Each source zone faces over the same extended region of polar angle Δθ; (b) Equi-width division. Each source zone faces over the same lateral region along the y-z cross-section passing the light source center on the bottom of the light guide.
Fig. 3
Fig. 3 Illuminance of target surface resulting from each light source zone when dividing the light source by (a) equi-angle division and (b) equi-width division
Fig. 4
Fig. 4 Illuminance on target surface when the prescribed illumination has a uniform distribution for (a) equi-angle division and (b) equi-width division. Blue, red and orange curves show the prescribed illumination, un-optimized illumination and optimized illumination, respectively.
Fig. 5
Fig. 5 Illuminance on target surface when the prescribed illumination has a Gaussian-like distribution for (a) equi-angle division and (b) equi-width division. Blue, red and orange curves show the prescribed illumination, un-optimized illumination and optimized illumination, respectively.
Fig. 6
Fig. 6 The relation between the illumination system performance and the size of the LED chip adopts in the first example of section 3. (a) The layout of the freeform lens found by Zhao’s method [14] for making a point LED chip possessing optimized LIDC. (b) Optimized LIDC and the LIDCs of freeform lens-constructed light source using different size of LED chip. (c) Illuminance on target surface while using different light source that Fig. 6(b) show.

Tables (3)

Tables Icon

Table 1 The optimized LIDs for two types of prescribed illuminations as using two light source division ways

Tables Icon

Table 2 Time required to perform gradient descent method with different divisions and numbers of target zones and source zones

Tables Icon

Table 3 Time required to perform characteristic matrix operation method with different divisions and numbers of target zones and source zones

Equations (22)

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

F=[ F 1,1 F 1,2 F 1,N F 2,1 F 2,2 F 2,N F M,1 F M,2 F M,N ]
G=[ g 1 , g 2 , ... g M ],
P=GF=[ p 1 , p 2 , ... p N ],
F Nor =[ F 1,1 / ϕ 1 F 1,2 / ϕ 1 ... F 1,N / ϕ 1 F 2,1 / ϕ 2 F 2,2 / ϕ 2 ... F 2,N / ϕ 2 F M,1 / ϕ M F M,2 / ϕ M ... F M,N / ϕ M ],
G Nor =[ n g 1 , n g 2 , ... n g M ],
P Nor = G Nor F Nor =[ n p 1 , n p 2 , ... n p N ],
n p j = i=1 M ( n g i F i,j / ϕ i ) .
p avg =( j=1 N p n j )/N=( j=1 N ( i=1 M n g i F i,j / ϕ i ) )/N=1.
T Nor =[ t n 1 , t n 2 , ... t n N ],
D F =[ F 1,1 / ϕ 1 t n 1 F 1,2 / ϕ 1 t n 2 ... F 1,N / ϕ 1 t n N F 2,1 / ϕ 2 t n 1 F 2,2 / ϕ 2 t n 2 ... F 2,N / ϕ 2 t n N F M,1 / ϕ M t n 1 F M,2 / ϕ M t n 2 ... F M,N / ϕ M t n N ],
G Nor D F × ( G Nor D F ) T = G Nor D F D F T G Nor T = j=1 N ( n p j n t j ) 2 p avg 2 =N ( CV ) 2
G k =[ g k1 , g k2 , ... g kM ],
G k D F D F T G k T = λ k ( G k G k T )=N ( CV ) k 2 .
G global = k=1 M a k G k ,
k=1 M a k =1.
( CV ) 2 = G global D F D F T G global T /N = k=1 M a k 2 ( CV ) k 2
( CV ) 2 = k=1 M1 a k 2 ( CV ) k 2 + ( 1 k=1 M1 a k ) 2 ( CV ) M 2
( CV ) 2 a k =2 a k ( CV ) k 2 +2( l=1 M1 a l 1 ) ( CV ) M 2 =0.
a k = ( 1 l=1 M1 a l ) ( CV ) M 2 ( CV ) k 2 = a M ( CV ) M 2 ( CV ) k 2 .
a 1 : a 2 :...: a M = 1 ( CV ) 1 2 : 1 ( CV ) 2 2 :...: 1 ( CV ) M 2 .
P=G ' global F,
G ' global =[ g k1 / φ 1 , g k2 / φ 2 , ... g kM / φ M ].

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