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Energy Express

  • Editor: Christian Seassal
  • Vol. 22, Iss. S2 — Mar. 10, 2014
  • pp: A365–A375
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Side-illuminating LED luminaires with accurate projection in high uniformity and high optical utilization factor for large-area field illumination

Yi-Chien Lo, Jhih-You Cai, Ming-Shiou Tasi, Zheng-Yu Tasi, and Ching-Cherng Sun  »View Author Affiliations


Optics Express, Vol. 22, Issue S2, pp. A365-A375 (2014)
http://dx.doi.org/10.1364/OE.22.00A365


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Abstract

A novel light luminaire is proposed and experimentally analyzed, which accurately projects light into a large rectangular area to achieve uniform illumination and a high optical utilization factor at the target. Side-illuminating luminaires for large-scale illuminated area are typically set with an elevated tilt angle to enlarge the illuminated area. However, the light pattern is bent thereby reducing the uniformity and optical utilization factor at the target. In this paper, we propose an efficient and useful approach with a rotationally symmetric projection lens that is trimmed to adjust the bending effect and to form a rectangular illumination light pattern on the ground. The design concept is demonstrated and verified. Several potential applications such as highly uniform illumination with fitting shapes for sport courts are analyzed and discussed.

© 2014 Optical Society of America

1. Introduction

Light emitting diodes (LEDs) have been extensively studied for potential applications including indoor and outdoor lighting, and vehicle forward lighting because of competitive features such as compact size, fast response, being free of mercury, wide color range, high efficiency, and long life [1

1. D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron. 8(2), 310–320 (2002). [CrossRef]

3

3. F. Nguyen, B. Terao, and J. Laski, “Realizing LED illumination lighting applications,” Proc. SPIE 5941, 594105 (2005). [CrossRef]

]. In comparison with traditional light source in the lighting devices, LED can provide not only high energy efficiency but also high color rendering index so that more human factors can be installed in an LED lamp. Furthermore, a LED-based design with high optical utilization factor and extremely low light pollution has been proposed [4

4. 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]

]. Consequently, LEDs have successfully replaced most traditional light sources in general lighting. Large-scale area lighting devices are typically used in many specific applications (e.g., street lighting, large plazas and playgrounds) [4

4. 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]

7

7. Y. C. Lo, K. T. Huang, X. H. Lee, and C. C. Sun, “Optical design of a Butterfly lens for a street light based on a double-cluster LED,” Microelectron. Reliab. 52(5), 889–893 (2012). [CrossRef]

]. In general, the illuminating modes for these kinds of applications include two types as shown in Fig. 1: direct-illuminating type, and side-illuminating type. Various optical designs have been proposed for the direct-illuminating type [8

8. Y. Luo, Z. Feng, Y. Han, and H. 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]

10

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

]. For the side-illuminating type, each luminaire is set at an elevated tilt angle to enlarge the illuminated area, but the pattern will be bent and therefore energy is lost to the illuminated area outside the target, as shown in Fig. 1(b). Therefore, the efficiency and uniformity at the target are reduced. Moreover, the unwanted illumination can cause additional light pollution. Using an asymmetric freeform reflector or lens according to the SMS method has been proposed to solve the problem [11

11. R. Winston, J. C. Miñano, and P. Benítez, NonimagingOptics, (Elsevier, 2005).

,12

12. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004). [CrossRef]

]. A collimating system combined with a tilt surface structure diffuser is another solution for side-illuminating type [13

13. 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]

].
Fig. 1 (a) direct-illuminating type, (b) bent pattern from side-illuminating type, and (c) adjusted pattern from specific design.

In this paper, we propose a new and efficient design to adjust the bending effect. The adjusted pattern shown in Fig. 1(c) can meet the rectangular shape of the target and accurately contain most flux in the target to enhance the optical utilization factor (OUF). The accuracy of the design is discussed through simulated and experimental results in the paper. Finally, the general adoptability of the proposed design in various applications is discussed.

2. A novel design for a side-illuminating luminaire

For the basic design, we consider a rectangular shape area as our target and the apparatus is shown in Fig. 2.
Fig. 2 The apparatus of the illuminated.
Fig. 3 CREE XM-L LED: (a) the optical model and (b) a real sample.
The elevated tilt angle is 15° and the height of the lamp is 12 m. The target area is 30 × 40 m2. Single-chip white XM-L LED fabricated by CREE is used, as shown in Fig. 3 [14]. The measured flux is 700 lm with an injection current of 2.4 A. An optical model of the LED is necessary to achieve an accurate design. We follow the mid-field modeling procedure to establish the optical model [15

15. C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M. Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett. 31(14), 2193–2195 (2006). [CrossRef] [PubMed]

17

17. C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express 17(16), 13918–13927 (2009). [CrossRef] [PubMed]

] and the light pattern is simulated through a Monte-Carlo ray tracing program such as ASAP [18]. The angular light patterns are verified through simulations and experiments at different distances in the mid-field region, as shown in Fig. 4.
Fig. 4 Angular pattern at different distances in the mid-field region: (a) 1.5cm, (b) 3cm, (c) 5cm, and (d) 7cm.
Following Fig. 4, we get an accurate model according to the normalized cross correlations (NCC) [15

15. C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M. Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett. 31(14), 2193–2195 (2006). [CrossRef] [PubMed]

] higher than 99.5% at each distance.

The proposed optical module consists of a freeform lens array and a reflector, as shown in Fig. 5.
Fig. 5 The luminaire contains a lens array and a flat reflector.
There are ten segments in the lens array and each segment is combined with a LED with a freeform lens to provide sufficient flux.

Initially, a circular lens based on a single-chip LED is used. According to the feedback modification method [8

8. Y. Luo, Z. Feng, Y. Han, and H. 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]

10

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

], we design a symmetric freeform lens (SFL) which can provide a uniform pattern shown in Fig. 6(a).
Fig. 6 (a) The uniform pattern from the symmetric freeform lens, (b) the pattern from the lens with the diamond-shaped cutting, (c) the tilted lens array module without a planar mirror and the corresponding light pattern, and (d) the tilted lens array module with a planar mirror on one side and the corresponding light pattern.
The optical efficiency of the SFL is 90%. According to the phenomenon illustrated in Fig. 1, the pattern is bent if we only use an axial SFL. Therefore, we modify the off-axis region of the lens with diamond-shape cutting (so-called L-DSC) shown in Fig. 6(b). In Fig. 6(b), the diamond-like shape of the lens can be observed in x-y plane. The cutting shape is a special design to form a specific light pattern on the ground. The specific light pattern can be set as one of the base patterns for a new pattern to meet a certain requirement. Figure 6(c) shows the tilted lens array module and the corresponding light pattern. To control the backward leakage and enhance the OUF, here the new idea is to make beam shaping with a mirror to form a rectangular illumination pattern on the ground. The tilted lens array module with a planar mirror to reflect the pattern of one side and the corresponding light pattern are shown in Fig. 6(d), where a near rectangular light pattern can be observed.

In the optimized design, we have to calculate the suitable shaping anglesθ1 and θ2 of the L-DSC, as illustrated in Fig. 7(a).
Fig. 7 (a) The trapezoid pattern formed by the flat reflector, (b) the new coordinate axis (x',y',z') for the trapezoid pattern, (c) the projective part at x'-z'plane, and (d) the projective part at y'-z' plane.
In Fig. 7(b), we adjust the elevated tilt angle θ of the luminaire so that the trapezoid pattern can be projected as a rectangular pattern on the ground. The dimensions of the rectangular target are set W×L. To calculate the shaping angles θ1 and θ2in Fig. 7(a), the coordinates D1(xd1,0,0) and D2(xd2,yd2,0) must be calculated first. The trapezoid pattern is switched to the new coordinate axis (x',y',z') in Fig. 7(b) because of the elevated tilt angle θ for the luminaire.

According to the new coordinate axis (x',y',z'), D1 and D2are transferred to D1 and D2; and R1 and R2are transferred to R1 and R2. The transfer matrix can be written
[xyz]=[1000cosθsinθ0sinθcosθ][xyzH]+[00H].
(1)
R1(xr1,yr1,0)=(L/2,d,0) and R2(xr2,yr2,0)=(L/2,W+d,0) so that R1(xr1,yr1,zr1) and R2(xr2,yr2,zr2) can be calculated
R1=[xr1yr1zr1]=[L/2dcosθHsinθdsinθHcosθ+H],
(2)
and
R2=[xr2yr2zr2]=[L/2(W+d)cosθHsinθ(W+d)sinθHcosθ+H].
(3)
Because yr1=0, d=Htanθ is obtained. Figure 7(c) and 7(d) show the projected area in x'-z' and y'-z' planes from Fig. 7(b). In Fig. 7(c), D2px and R1pxare the projected points of D2 and R1. In Fig. 7(d), D2pyand R2py are the projected points of D2and R2. Considering the similar triangles OLD1 and AR1D1 in Fig. 7(c), we find
xd1=HH+|zr1|(L/2).
(4)
Based on the similar triangles OLD2pxand AR2pxD2px in Fig. 7(c), we also find
xd2=HH+|zr2|(L/2).
(5)
Besides, considering the similar triangles OLD2py and AR2pyD2py in Fig. 7(d), we find
yd2=HH+|zr2|Wcosθ.
(6)
Finally, the coordinates D1 and D2 can be obtained obtained. Therefore, the shaping angles θ1 and θ2can be written
θ1=cos1[xd1xd2+xd22xd2(xd1xd2)2+yd22]
(7)
and
θ2=2cos1[xd12xd1xd2xd1(xd1xd2)2+yd22].
(8)
With the parameters of H = 12 m, W = 30 m, L = 40 m, we can obtain θ=15°, θ1=113.3° and θ2=133.3°based on Eqs. (7)-(8). In the simulation, PMMA (n = 1.492) is used as the material of the L-DSC, and the reflectivity of the planar mirror with dimensions of 25 × 25 cm2 is set 80%. The optical efficiency of the L-DSC is 87%, which is near the optical efficiency of 90% without cutting. Because the cutting edge of the L-DSC forms a mirror with total internal reflection, it increases the optical efficiency but causes some bright fringes. If the light hitting the cutting edge of the L-DSC are absorbed by the edge, the simulation shows that the optical efficiency decreases to 74.1%. There are 40.2% of the flux from the lens reflected by the planar mirror and the optical efficiency of the whole luminare is approximately 80%. The total flux is measured approximately 5600 lm when the LEDs are driven at 78W. The final pattern of the single luminaire is shown in Fig. 6(d), in which light leakage can be observed, and is highlighted in red. However, the light leakage is compensated when the illuminating system is composed of several luminaires arranged side by side, as shown in Fig. 8(a).
Fig. 8 (a) The array with several luminaires arranged side by side, (b) the pattern with lower loss effect, and (c) the final pattern to meet the target with two luminaires in the opposite side.
When the number of the luminaires is increased, the loss effect decreases. The final pattern for an array with 59 luminaires on each side is shown in Fig. 8(c). The OUF is approximately 70%, where the OUF is the ratio of the flux at the target and the flux from the LEDs.

3. Experimental verification

According to the simulation result, a prototype fabricated through CNC machining is to verify the accuracy. The prototype is shown in Fig. 9(a).
Fig. 9 (a) The prototype by CNC machining, (b) the simulated pattern, and (c) the experimental result.
A distance of 1.3m is used for verification. The simulation and experimental results are compared in Figs. 9(b) and 9(c). The patterns for simulation and experiment are nearly identical. Besides, we need to check the illuminance distribution so the sampling points shown in Fig. 10 are set with a spacing of 50 cm in each line. For the results on the vertical axis in Fig. 11 are set with a spacing of 50 cm in each line. For the results on the vertical axis in Fig. 11, the distributions for each line are similar.
Fig. 10 (a) The sampling points at the vertical axis, (b) the sampling points at horizontal axis.
Fig. 11 The illuminance distribution along (a) the V1 line, (b) the V2 line, (c) the V3 line, (d) the V4 line, and (e) the V5 line.
Fig. 12 The illuminance distribution along (a) the V1 line, (b) the V2 line, (c) the V3 line, (d) the V4 line, and (e) theV5 line.
For the horizontal case in Fig. 12, the difference of the result at H3 is caused by inaccurate alignment, roughness on the surface of each element and manufacturing errors. Based on the comparison, we have confirmed the accuracy of our design.

4. Applications for different requests

In this section, several applications for different playgrounds are discussed based on the DIALUX program [19]. Then, the playgrounds include badminton court, volleyball court, and indoor natatorium in National Central University in Taiwan. According to the illuminance standard in Taiwan, which is called CNS-12112 [20], the average illuminance for different court is defined and the sampling points are set at a plane with a height of 0.85 m. To meet each request, suitable numbers of the luminaires should be confirmed.

4.1 Badminton court

Fig. 13 The dimensions of the badminton court.
The area of the badminton court, as it shown in Fig. 13, is 33 × 39 m2, comprising six racing areas. For normal racing, the range of illuminance is in the range of 300 to 500 lux. To meet the regulation, the number of the luminaires on each side is about 59 pcs. Then, we consider the performance for area A and B because of the symmetry of the apparatus. The analyzed result for the suitable height of the luminaire is shown in Fig. 14.
Fig. 14 The analysis for average illuminance and optical uniformity for (a) section A and (b) section B.
According to the analysis process for the height of the luminaire array, the range for the better choice is in the range of 11 to 13 m. Therefore, we choose the result for the height of 12 m and the simulated scene is shown in Fig. 15.
Fig. 15 The simulated scene: (a) top view and (b) 3D view.
The average illuminace is about 420 lux for section A and 430 lux for section B. The uniformity, defined as the ratio of the minimum and average illuminance, is 78% for section A and 85% for section B.

4.2 Volleyball court

Fig. 16 The dimensions of the volleyball court.
The dimension of the volleyball court shown in Fig. 16 is 32 × 40 m2. Performance is considered only for section A because of the symmetry of the apparatus. To meet the regulation, the number of the luminaires on each side is also about 59 pcs. The analyzed result is shown in Fig. 17.
Fig. 17 The analysis of average illuminance and optical uniformity for section A.
With the same analysis process for the height of the luminaire array, the best choice is near 9.5m. The simulated scene is shown in Fig. 18.
Fig. 18 The simulated scene of the illumination on the volleyball court: (a) top view and (b) 3D view.
The average illuminace is about 400 lux for section A and the uniformity is 75%.

4.3 Indoor natatorium

Fig. 19 The simulated cinestrip: (a) top view and (b) 3D view.
The dimension of the natatorium shown in Fig. 19 is 29 × 63 m2. The red-line area represents the swimming pool. For entertainment purposes, the range of illuminance is in the range of 75 to 150 lux. To meet the regulation, two arrays should be set in each side and the amount of the luminaire for each array is 59 pcs. The average illuminace is 140 lux and the uniformity is 50%.

5. Summary

We have proposed a novel method to shape the illumination light pattern from a side-illuminating luminaire to a certain shape on the ground by trimming a circular projection lens. The side-illuminating luminaire with cutting-edge lens shape efficiently adjusts the illumination pattern on the ground with high uniformity and high optical utilization factor because the illumination pattern fits well the shape of the target. The luminaire is composed of only two parts: one is a freeform lens array, which has a specific cutting-edge design for each segment; the other is a mirror.

To get an accurate design, the precise LED model based on the mid-field concept has been established and the NCCs are all as high as 99.5% at different distances in the mid-field region. Then, the optical efficiency of the whole luminaire is 80% and the optical utilization factor is higher than 70%. Therefore, it has positive effect on energy saving because the optical flux is efficiently used. For the experimental analysis, the illuminance distribution of the simulation and experiment is similar. Moreover, the virtual reality for real playground has been discussed and analyzed. For the badminton court, 59 pcs luminaires should be set in the array in each side. The optimal height of the array is 12 m. The average illuminance higher than 420 lux and the uniformity higher than 78% in each racing area have been calculated.

The proposed design has many potential applications, such as sport courts. In the volleyball court, the number of luminaire in each array is about 59 pcs and the optimal height is 9.5 m. The average illuminance is higher than 400 lux and the uniformity is higher than 75% in each racing area. For these two playgrounds, the optical performance can meet the normal racing request in the Taiwanese regulation named CNS-12112. For the indoor natatorium, the average illuminance is higher than 140lux so it can meet the amusement request from CNS-12112. The proposed side-illumination design with combination of a freeform lens array and a mirror is proven very useful in lighting a larger-area court with rectangle shape, and benefits energy saving with high optical utilization factor with accurate projection.

Acknowledgments

References and links

1.

D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron. 8(2), 310–320 (2002). [CrossRef]

2.

A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-state Lighting, (John Wiley & Sons, 2002).

3.

F. Nguyen, B. Terao, and J. Laski, “Realizing LED illumination lighting applications,” Proc. SPIE 5941, 594105 (2005). [CrossRef]

4.

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]

5.

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

6.

X. H. Lee, C. S. Wu, K. H. Lee, T. H. Yang, and C. C. Sun, “An optical-adjustable illumination pattern with a surface-structured diffuser compensated by index-matching liquid,” Opt. Laser Technol. 49, 153–155 (2013). [CrossRef]

7.

Y. C. Lo, K. T. Huang, X. H. Lee, and C. C. Sun, “Optical design of a Butterfly lens for a street light based on a double-cluster LED,” Microelectron. Reliab. 52(5), 889–893 (2012). [CrossRef]

8.

Y. Luo, Z. Feng, Y. Han, and H. 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]

9.

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008). [CrossRef] [PubMed]

10.

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

11.

R. Winston, J. C. Miñano, and P. Benítez, NonimagingOptics, (Elsevier, 2005).

12.

P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004). [CrossRef]

13.

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]

14.

CREE,http://www.cree.com/led-components-and-modules/products/xlamp/discrete-directional/xlamp-xml.

15.

C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M. Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett. 31(14), 2193–2195 (2006). [CrossRef] [PubMed]

16.

W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express 15(12), 7572–7577 (2007). [CrossRef] [PubMed]

17.

C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express 17(16), 13918–13927 (2009). [CrossRef] [PubMed]

18.

ASAP, http://www.bro.com/.

19.

DIALux, http://www.dial.de/DIAL/.

20.

CNS 12112 standard, http://www.pws.stu.edu.tw/paul/lecture/e207-1.pdf.

OCIS Codes
(150.2950) Machine vision : Illumination
(220.0220) Optical design and fabrication : Optical design and fabrication
(230.3670) Optical devices : Light-emitting diodes
(150.2945) Machine vision : Illumination design
(080.4295) Geometric optics : Nonimaging optical systems

ToC Category:
Illumination Design

History
Original Manuscript: December 20, 2013
Revised Manuscript: February 5, 2014
Manuscript Accepted: February 5, 2014
Published: February 18, 2014

Citation
Yi-Chien Lo, Jhih-You Cai, Ming-Shiou Tasi, Zheng-Yu Tasi, and Ching-Cherng Sun, "Side-illuminating LED luminaires with accurate projection in high uniformity and high optical utilization factor for large-area field illumination," Opt. Express 22, A365-A375 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-S2-A365


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References

  1. D. A. Steigerwald, J. C. Bhat, D. Collins, R. M. Fletcher, M. O. Holcomb, M. J. Ludowise, P. S. Martin, and S. L. Rudaz, “Illumination with solid state lighting technology,” IEEE J. Sel. Top. Quantum Electron.8(2), 310–320 (2002). [CrossRef]
  2. A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-state Lighting, (John Wiley & Sons, 2002).
  3. F. Nguyen, B. Terao, and J. Laski, “Realizing LED illumination lighting applications,” Proc. SPIE5941, 594105 (2005). [CrossRef]
  4. X. H. Lee, I. Moreno, and C. C. Sun, “High-performance LED street lighting using microlens arrays,” Opt. Express21(9), 10612–10621 (2013). [CrossRef] [PubMed]
  5. H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A19(3), 590–595 (2002). [CrossRef] [PubMed]
  6. X. H. Lee, C. S. Wu, K. H. Lee, T. H. Yang, and C. C. Sun, “An optical-adjustable illumination pattern with a surface-structured diffuser compensated by index-matching liquid,” Opt. Laser Technol.49, 153–155 (2013). [CrossRef]
  7. Y. C. Lo, K. T. Huang, X. H. Lee, and C. C. Sun, “Optical design of a Butterfly lens for a street light based on a double-cluster LED,” Microelectron. Reliab.52(5), 889–893 (2012). [CrossRef]
  8. Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express18(9), 9055–9063 (2010). [CrossRef] [PubMed]
  9. Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express16(17), 12958–12966 (2008). [CrossRef] [PubMed]
  10. L. Wang, K. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt.46(18), 3716–3723 (2007). [CrossRef] [PubMed]
  11. R. Winston, J. C. Miñano, and P. Benítez, NonimagingOptics, (Elsevier, 2005).
  12. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004). [CrossRef]
  13. X. H. Lee, I. Moreno, and C. C. Sun, “High-performance LED street lighting using microlens arrays,” Opt. Express21(9), 10612–10621 (2013). [CrossRef] [PubMed]
  14. CREE, http://www.cree.com/led-components-and-modules/products/xlamp/discrete-directional/xlamp-xml .
  15. C. C. Sun, T. X. Lee, S. H. Ma, Y. L. Lee, and S. M. Huang, “Precise optical modeling for LED lighting verified by cross correlation in the midfield region,” Opt. Lett.31(14), 2193–2195 (2006). [CrossRef] [PubMed]
  16. W. T. Chien, C. C. Sun, and I. Moreno, “Precise optical model of multi-chip white LEDs,” Opt. Express15(12), 7572–7577 (2007). [CrossRef] [PubMed]
  17. C. C. Sun, W. T. Chien, I. Moreno, C. C. Hsieh, and Y. C. Lo, “Analysis of the far-field region of LEDs,” Opt. Express17(16), 13918–13927 (2009). [CrossRef] [PubMed]
  18. ASAP, http://www.bro.com/ .
  19. DIALux, http://www.dial.de/DIAL/ .
  20. CNS 12112 standard, http://www.pws.stu.edu.tw/paul/lecture/e207-1.pdf .

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