Abstract

A novel freeform lens structure made up of two surfaces is proposed and optimized to enhance the color spatial uniformity (CSU) of white light-emitting diodes (LEDs). Compared with our previous method, an improved design method by optimizing the light energy mapping relationship is proposed to eliminate the dark area, which appears in the illumination pattern due to a deep batwing luminous intensity distribution. Moreover, experiments with a significant evaluation function are performed and demonstrate that the CSU in terms of color difference (Δu'v') can be enhanced as high as 92%. In addition, this novel lens can further improve the CSU of white LEDs with conformal coating. High-quality illumination pattern without yellow rings and dark areas can be realized based on this novel freeform lens with little light loss.

© 2012 OSA

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References

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  1. M. G. Craford, “LEDs for solid state lighting and other emerging applications: status, trends, and challenges,” Proc. SPIE594101, (2005).
    [CrossRef]
  2. E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2006).
  3. S. Liu and X. B. Luo, LED Packaging for Lighting Applications: Design, Manufacturing and Testing (John Wiley and Son, 2011).
  4. ENERGY STAR, Program Requirements for Solid State Lighting Luminaires (U.S. Environmental Protection Agency and U.S. Department of Energy, 2007).
  5. I. Ashdown, “Chromaticity and color temperature for architectural lighting,” Proc. SPIE4776, 51–60 (2002).
    [CrossRef]
  6. Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett.20(24), 2027–2029 (2008).
    [CrossRef]
  7. C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
    [CrossRef]
  8. R. C. Jordan, J. Bauer, and H. Oppermann, “Optimized heat transfer and homogeneous color converting for ultra high brightness LED package,” Proc. SPIE6198, 61980B, 61980B-12 (2006).
    [CrossRef]
  9. W. D. Collins, M. R. Krames, G. J. Verhoeckx, and N. J. M. Leth, “Using electrophoresis to produce a conformally coated phosphor-converted light emitting semiconductor,” U. S. Patent 6 576 488 B2 (2003).
  10. L. Zhu, X. H. Wang, P. T. Lai, and H. W. Choi, “Angular uniform white light-emitting diodes using an integrated reflector cup,” IEEE Photon. Technol. Lett.22(7), 513–515 (2010).
    [CrossRef]
  11. H. Wu, N. Narendran, Y. Gu, and A. Bierman, “Improving the performance of mixed-color white LED systems by using scattered photon extraction technique,” Proc. SPIE6669, 666905, 666905-12 (2007).
    [CrossRef]
  12. K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett.35(11), 1860–1862 (2010).
    [CrossRef] [PubMed]
  13. C. C. Sun, C. Y. Chen, C. C. Chen, C. Y. Chiu, Y. N. Peng, Y. H. Wang, T. H. Yang, T. Y. Chung, and C. Y. Chung, “High uniformity in angular correlated-color-temperature distribution of white LEDs from 2800K to 6500K,” Opt. Express20(6), 6622–6630 (2012).
    [CrossRef] [PubMed]
  14. A. Borbély, A. Sámson, and J. Schanda, “The concept of correlated colour temperature revisited,” Color Res. Appl.26(6), 450–457 (2001).
    [CrossRef]
  15. D. Malacara, Color Vision and Colorimetry: Theory and Application (SPIE Press, 2002).
  16. T. X. Lee, K. F. Gao, W. T. Chien, and C. C. Sun, “Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate,” Opt. Express15(11), 6670–6676 (2007).
    [CrossRef] [PubMed]
  17. Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Studies on optical consistency of white LEDs affected by phosphor thickness and concentration using optical simulation,” IEEE Trans. Compon. Packag. Tech.33(4), 680–687 (2010).
    [CrossRef]
  18. F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illumination quality lighting-emitting diode MR16 lamps,” Opt. Eng.48(12), 123002 (2009).
    [CrossRef]
  19. K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express18(2), 413–425 (2010).
    [CrossRef] [PubMed]

2012 (1)

2010 (4)

L. Zhu, X. H. Wang, P. T. Lai, and H. W. Choi, “Angular uniform white light-emitting diodes using an integrated reflector cup,” IEEE Photon. Technol. Lett.22(7), 513–515 (2010).
[CrossRef]

K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett.35(11), 1860–1862 (2010).
[CrossRef] [PubMed]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Studies on optical consistency of white LEDs affected by phosphor thickness and concentration using optical simulation,” IEEE Trans. Compon. Packag. Tech.33(4), 680–687 (2010).
[CrossRef]

K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express18(2), 413–425 (2010).
[CrossRef] [PubMed]

2009 (1)

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illumination quality lighting-emitting diode MR16 lamps,” Opt. Eng.48(12), 123002 (2009).
[CrossRef]

2008 (2)

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett.20(24), 2027–2029 (2008).
[CrossRef]

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

2007 (2)

H. Wu, N. Narendran, Y. Gu, and A. Bierman, “Improving the performance of mixed-color white LED systems by using scattered photon extraction technique,” Proc. SPIE6669, 666905, 666905-12 (2007).
[CrossRef]

T. X. Lee, K. F. Gao, W. T. Chien, and C. C. Sun, “Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate,” Opt. Express15(11), 6670–6676 (2007).
[CrossRef] [PubMed]

2006 (1)

R. C. Jordan, J. Bauer, and H. Oppermann, “Optimized heat transfer and homogeneous color converting for ultra high brightness LED package,” Proc. SPIE6198, 61980B, 61980B-12 (2006).
[CrossRef]

2005 (1)

M. G. Craford, “LEDs for solid state lighting and other emerging applications: status, trends, and challenges,” Proc. SPIE594101, (2005).
[CrossRef]

2002 (1)

I. Ashdown, “Chromaticity and color temperature for architectural lighting,” Proc. SPIE4776, 51–60 (2002).
[CrossRef]

2001 (1)

A. Borbély, A. Sámson, and J. Schanda, “The concept of correlated colour temperature revisited,” Color Res. Appl.26(6), 450–457 (2001).
[CrossRef]

Ashdown, I.

I. Ashdown, “Chromaticity and color temperature for architectural lighting,” Proc. SPIE4776, 51–60 (2002).
[CrossRef]

Bauer, J.

R. C. Jordan, J. Bauer, and H. Oppermann, “Optimized heat transfer and homogeneous color converting for ultra high brightness LED package,” Proc. SPIE6198, 61980B, 61980B-12 (2006).
[CrossRef]

Bierman, A.

H. Wu, N. Narendran, Y. Gu, and A. Bierman, “Improving the performance of mixed-color white LED systems by using scattered photon extraction technique,” Proc. SPIE6669, 666905, 666905-12 (2007).
[CrossRef]

Borbély, A.

A. Borbély, A. Sámson, and J. Schanda, “The concept of correlated colour temperature revisited,” Color Res. Appl.26(6), 450–457 (2001).
[CrossRef]

Chen, C. C.

Chen, C. Y.

Chen, F.

Chien, W. T.

Chiu, C. Y.

Choi, H. W.

L. Zhu, X. H. Wang, P. T. Lai, and H. W. Choi, “Angular uniform white light-emitting diodes using an integrated reflector cup,” IEEE Photon. Technol. Lett.22(7), 513–515 (2010).
[CrossRef]

Chung, C. Y.

Chung, T. Y.

Craford, M. G.

M. G. Craford, “LEDs for solid state lighting and other emerging applications: status, trends, and challenges,” Proc. SPIE594101, (2005).
[CrossRef]

Gao, K. F.

Gu, Y.

H. Wu, N. Narendran, Y. Gu, and A. Bierman, “Improving the performance of mixed-color white LED systems by using scattered photon extraction technique,” Proc. SPIE6669, 666905, 666905-12 (2007).
[CrossRef]

Hartmann, P.

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

Jordan, R. C.

R. C. Jordan, J. Bauer, and H. Oppermann, “Optimized heat transfer and homogeneous color converting for ultra high brightness LED package,” Proc. SPIE6198, 61980B, 61980B-12 (2006).
[CrossRef]

Lai, P. T.

L. Zhu, X. H. Wang, P. T. Lai, and H. W. Choi, “Angular uniform white light-emitting diodes using an integrated reflector cup,” IEEE Photon. Technol. Lett.22(7), 513–515 (2010).
[CrossRef]

Lee, T. X.

Leising, G. Ü.

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

Liu, S.

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Studies on optical consistency of white LEDs affected by phosphor thickness and concentration using optical simulation,” IEEE Trans. Compon. Packag. Tech.33(4), 680–687 (2010).
[CrossRef]

K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express18(2), 413–425 (2010).
[CrossRef] [PubMed]

K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett.35(11), 1860–1862 (2010).
[CrossRef] [PubMed]

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illumination quality lighting-emitting diode MR16 lamps,” Opt. Eng.48(12), 123002 (2009).
[CrossRef]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett.20(24), 2027–2029 (2008).
[CrossRef]

Liu, Z. Y.

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Studies on optical consistency of white LEDs affected by phosphor thickness and concentration using optical simulation,” IEEE Trans. Compon. Packag. Tech.33(4), 680–687 (2010).
[CrossRef]

K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett.35(11), 1860–1862 (2010).
[CrossRef] [PubMed]

K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express18(2), 413–425 (2010).
[CrossRef] [PubMed]

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illumination quality lighting-emitting diode MR16 lamps,” Opt. Eng.48(12), 123002 (2009).
[CrossRef]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett.20(24), 2027–2029 (2008).
[CrossRef]

Luo, X. B.

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Studies on optical consistency of white LEDs affected by phosphor thickness and concentration using optical simulation,” IEEE Trans. Compon. Packag. Tech.33(4), 680–687 (2010).
[CrossRef]

K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express18(2), 413–425 (2010).
[CrossRef] [PubMed]

K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett.35(11), 1860–1862 (2010).
[CrossRef] [PubMed]

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illumination quality lighting-emitting diode MR16 lamps,” Opt. Eng.48(12), 123002 (2009).
[CrossRef]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett.20(24), 2027–2029 (2008).
[CrossRef]

Narendran, N.

H. Wu, N. Narendran, Y. Gu, and A. Bierman, “Improving the performance of mixed-color white LED systems by using scattered photon extraction technique,” Proc. SPIE6669, 666905, 666905-12 (2007).
[CrossRef]

Oppermann, H.

R. C. Jordan, J. Bauer, and H. Oppermann, “Optimized heat transfer and homogeneous color converting for ultra high brightness LED package,” Proc. SPIE6198, 61980B, 61980B-12 (2006).
[CrossRef]

Pachler, P.

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

Peng, Y. N.

Sámson, A.

A. Borbély, A. Sámson, and J. Schanda, “The concept of correlated colour temperature revisited,” Color Res. Appl.26(6), 450–457 (2001).
[CrossRef]

Schanda, J.

A. Borbély, A. Sámson, and J. Schanda, “The concept of correlated colour temperature revisited,” Color Res. Appl.26(6), 450–457 (2001).
[CrossRef]

Schweighart, M.

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

Sommer, C.

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

Sun, C. C.

Tasch, S.

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

Wang, K.

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Studies on optical consistency of white LEDs affected by phosphor thickness and concentration using optical simulation,” IEEE Trans. Compon. Packag. Tech.33(4), 680–687 (2010).
[CrossRef]

K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express18(2), 413–425 (2010).
[CrossRef] [PubMed]

K. Wang, D. Wu, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Angular color uniformity enhancement of white light-emitting diodes integrated with freeform lenses,” Opt. Lett.35(11), 1860–1862 (2010).
[CrossRef] [PubMed]

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illumination quality lighting-emitting diode MR16 lamps,” Opt. Eng.48(12), 123002 (2009).
[CrossRef]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett.20(24), 2027–2029 (2008).
[CrossRef]

Wang, X. H.

L. Zhu, X. H. Wang, P. T. Lai, and H. W. Choi, “Angular uniform white light-emitting diodes using an integrated reflector cup,” IEEE Photon. Technol. Lett.22(7), 513–515 (2010).
[CrossRef]

Wang, Y. H.

Wenzl, F.-P.

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

Wu, D.

Wu, H.

H. Wu, N. Narendran, Y. Gu, and A. Bierman, “Improving the performance of mixed-color white LED systems by using scattered photon extraction technique,” Proc. SPIE6669, 666905, 666905-12 (2007).
[CrossRef]

Yang, T. H.

Zhu, L.

L. Zhu, X. H. Wang, P. T. Lai, and H. W. Choi, “Angular uniform white light-emitting diodes using an integrated reflector cup,” IEEE Photon. Technol. Lett.22(7), 513–515 (2010).
[CrossRef]

Color Res. Appl. (1)

A. Borbély, A. Sámson, and J. Schanda, “The concept of correlated colour temperature revisited,” Color Res. Appl.26(6), 450–457 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

L. Zhu, X. H. Wang, P. T. Lai, and H. W. Choi, “Angular uniform white light-emitting diodes using an integrated reflector cup,” IEEE Photon. Technol. Lett.22(7), 513–515 (2010).
[CrossRef]

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Optical analysis of color distribution in white LEDs with various packaging methods,” IEEE Photon. Technol. Lett.20(24), 2027–2029 (2008).
[CrossRef]

C. Sommer, F.-P. Wenzl, P. Hartmann, P. Pachler, M. Schweighart, S. Tasch, and G. Ü. Leising, “Tailoring of the color conversion elements in phosphor-converted high-power LEDs by optical simulations,” IEEE Photon. Technol. Lett.20(9), 739–741 (2008).
[CrossRef]

IEEE Trans. Compon. Packag. Tech. (1)

Z. Y. Liu, S. Liu, K. Wang, and X. B. Luo, “Studies on optical consistency of white LEDs affected by phosphor thickness and concentration using optical simulation,” IEEE Trans. Compon. Packag. Tech.33(4), 680–687 (2010).
[CrossRef]

Opt. Eng. (1)

F. Chen, S. Liu, K. Wang, Z. Y. Liu, and X. B. Luo, “Free-form lenses for high illumination quality lighting-emitting diode MR16 lamps,” Opt. Eng.48(12), 123002 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (4)

I. Ashdown, “Chromaticity and color temperature for architectural lighting,” Proc. SPIE4776, 51–60 (2002).
[CrossRef]

H. Wu, N. Narendran, Y. Gu, and A. Bierman, “Improving the performance of mixed-color white LED systems by using scattered photon extraction technique,” Proc. SPIE6669, 666905, 666905-12 (2007).
[CrossRef]

R. C. Jordan, J. Bauer, and H. Oppermann, “Optimized heat transfer and homogeneous color converting for ultra high brightness LED package,” Proc. SPIE6198, 61980B, 61980B-12 (2006).
[CrossRef]

M. G. Craford, “LEDs for solid state lighting and other emerging applications: status, trends, and challenges,” Proc. SPIE594101, (2005).
[CrossRef]

Other (5)

E. F. Schubert, Light-Emitting Diodes (Cambridge University Press, 2006).

S. Liu and X. B. Luo, LED Packaging for Lighting Applications: Design, Manufacturing and Testing (John Wiley and Son, 2011).

ENERGY STAR, Program Requirements for Solid State Lighting Luminaires (U.S. Environmental Protection Agency and U.S. Department of Energy, 2007).

W. D. Collins, M. R. Krames, G. J. Verhoeckx, and N. J. M. Leth, “Using electrophoresis to produce a conformally coated phosphor-converted light emitting semiconductor,” U. S. Patent 6 576 488 B2 (2003).

D. Malacara, Color Vision and Colorimetry: Theory and Application (SPIE Press, 2002).

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Figures (11)

Fig. 1
Fig. 1

(a) Actual illumination pattern taken by a CCD camera and (b) the measured LICR of a white LED integrated a designed freeform lens.

Fig. 2
Fig. 2

(a) Blue chip adopted for (b) a traditional white LED model. (c) YBR distribution of the traditional white LED.

Fig. 3
Fig. 3

Lenses designed with different light energy mapping relationships. (a) Uniform and (b) non-uniform illumination design methods.

Fig. 4
Fig. 4

Sketch map of the light outputs of (a) the traditional LED and (b) the modified LED.

Fig. 5
Fig. 5

(a). YBR distributions of the traditional LED and modified LED. (b). Simulated CSUs and LICRs of white modified LEDs based on the uniform illumination design method.

Fig. 6
Fig. 6

(a). Sketch map of the light output of a modified LED. (b). Simulated CSUs and LICRs of white modified LEDs based on the non-uniform illumination design method.

Fig. 7
Fig. 7

(a). Four manufactured freeform lenses. (b). Bare LED integrated with the lenses.

Fig. 8
Fig. 8

(a). Schematic diagram of (b) the test system. (c). Heat sink. (d). Angle regulator. (e). User interface of the software.

Fig. 9
Fig. 9

(a). Color difference ( Δu'v' ) distributions of the bare LED and Lens IV in −90°-90°. (b). Quantities of qualified points of different LEDs.

Fig. 10
Fig. 10

Comparison of (b) measured luminous intensity distributions and illumination patterns of (a) the bare LED, (c) Lens I, (d) Lens II, (e) Lens III, and (f) Lens IV. The actual LICRs of Lens I, Lens II, Lens III, and Lens IV are 32.6%, 61.4%, 64.4%, and 71.8%, respectively.

Fig. 11
Fig. 11

(a) CCT distributions and (b) the CSUs of K2 and modified LEDs.

Tables (3)

Tables Icon

Table 1 Results of Freeform Lenses at θ = 40°

Tables Icon

Table 2 Lenses Chosen for Manufacturing

Tables Icon

Table 3 Light Output Efficiencies of Freeform Lenses

Equations (4)

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

LICR= I 0 max(I(γ)) ×100%
u n = i=1 n ( E i ×u ' i ) i=1 n E i
v n = i=1 n ( E i ×v ' i ) i=1 n E i
Δu'v ' i = ( u ' i u n ) 2 + ( v ' i v n ) 2

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