Abstract

This paper presents a methodology analogous to a general lens design rule to optimize step-by-step the spectral power distribution of a white-light LED cluster with the highest possible color rendering and efficiency in a defined range of color temperatures. By examining a platform composed of four single-color LEDs and a phosphor-converted cool-white (CW) LED, we successfully validate the proposed algorithm and suggest the optimal operation range (correlated color temperature = 2600–8500 K) accompanied by a high color quality scale (CQS > 80 points) as well as high luminous efficiency (97% of cluster’s theoretical maximum value).

© 2011 OSA

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  1. J. K. Kim and E. F. Schubert, “Transcending the replacement paradigm of solid-state lighting,” Opt. Express 16(26), 21835–21842 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-26-21835 .
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010).
    [CrossRef]
  9. M. S. Rea and J. P. Freyssinier-Nova, “Color rendering: a tale of two metrics,” Color Res. Appl. 33(3), 192–202 (2008).
    [CrossRef]
  10. A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, P. Vitta, and M. S. Shur, “Statistical approach to color quality of solid-state lamps,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1753–1762 (2009).
    [CrossRef]
  11. E. F. Schubert, J. K. Kim, H. Luo, and J.-Q. Xi, “Solid-state lighting––a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099(2006).
    [CrossRef]
  12. Epistar Corporation, Taiwan, General LED product catalog (2010).
  13. Toyoda Gosei Corporation, Japan, LED product catalog (2010).
  14. R. Kingslake, Lens Design Fundamentals (Academic Press, 1978).
  15. A. Žukauskas, R. Vaicekauskas, and M. S. Shur, “Solid-state lamps with optimized color saturation ability,” Opt. Express 18(3), 2287–2295 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-18-3-2287 .
    [CrossRef] [PubMed]
  16. R. Mirhosseini, M. F. Schubert, S. Chhajed, J. Cho, J. K. Kim, and E. F. Schubert, “Improved color rendering and luminous efficacy in phosphor-converted white light-emitting diodes by use of dual-blue emitting active regions,” Opt. Express 17(13), 10806–10813 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-13-10806 .
    [CrossRef] [PubMed]
  17. S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light-emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005).
    [CrossRef]
  18. G. Wyszecki, and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae (Wiley, 2000).
  19. J. S. R. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing (Prentice Hall, 1997).
  20. R. L. Haupt, and S. E. Haupt, Practical Genetic Algorithms, 2nd ed. (John Wiley, 2004).
  21. W. J. Smith, Modern Lens Design, 2nd ed. (McGraw-Hill, 2005).
  22. M. Laikin, Lens Design, 4th ed. (CRC Press, 2006).
  23. I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
    [CrossRef] [PubMed]
  24. R. S. Berns, “A genetic approach to color modeling,” Color Res. Appl. 22(5), 318–325 (1997).
    [CrossRef]

2010 (4)

2009 (2)

2008 (2)

2006 (2)

I. Moreno, M. Avendaño-Alejo, and R. I. Tzonchev, “Designing light-emitting diode arrays for uniform near-field irradiance,” Appl. Opt. 45(10), 2265–2272 (2006).
[CrossRef] [PubMed]

E. F. Schubert, J. K. Kim, H. Luo, and J.-Q. Xi, “Solid-state lighting––a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099(2006).
[CrossRef]

2005 (2)

S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light-emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005).
[CrossRef]

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005).
[CrossRef] [PubMed]

2004 (1)

Y. Ohno, “Color rendering and luminous efficacy of white LED spectra,” Proc. SPIE 5530, 88–98 (2004).
[CrossRef]

2002 (1)

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett. 80(2), 234–236 (2002).
[CrossRef]

1997 (1)

R. S. Berns, “A genetic approach to color modeling,” Color Res. Appl. 22(5), 318–325 (1997).
[CrossRef]

Avendaño-Alejo, M.

Berns, R. S.

R. S. Berns, “A genetic approach to color modeling,” Color Res. Appl. 22(5), 318–325 (1997).
[CrossRef]

Chhajed, S.

R. Mirhosseini, M. F. Schubert, S. Chhajed, J. Cho, J. K. Kim, and E. F. Schubert, “Improved color rendering and luminous efficacy in phosphor-converted white light-emitting diodes by use of dual-blue emitting active regions,” Opt. Express 17(13), 10806–10813 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-13-10806 .
[CrossRef] [PubMed]

S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light-emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005).
[CrossRef]

Cho, J.

Davis, W.

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010).
[CrossRef]

Freyssinier-Nova, J. P.

M. S. Rea and J. P. Freyssinier-Nova, “Color rendering: a tale of two metrics,” Color Res. Appl. 33(3), 192–202 (2008).
[CrossRef]

Gaska, R.

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett. 80(2), 234–236 (2002).
[CrossRef]

Gessmann, T.

S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light-emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005).
[CrossRef]

He, G.

Ivanauskas, F.

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, P. Vitta, and M. S. Shur, “Statistical approach to color quality of solid-state lamps,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1753–1762 (2009).
[CrossRef]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett. 80(2), 234–236 (2002).
[CrossRef]

Kim, J. K.

Li, Y. L.

S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light-emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005).
[CrossRef]

Luo, H.

E. F. Schubert, J. K. Kim, H. Luo, and J.-Q. Xi, “Solid-state lighting––a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099(2006).
[CrossRef]

Mirhosseini, R.

Moreno, I.

Ohno, Y.

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010).
[CrossRef]

Y. Ohno, “Color rendering and luminous efficacy of white LED spectra,” Proc. SPIE 5530, 88–98 (2004).
[CrossRef]

Rea, M. S.

M. S. Rea and J. P. Freyssinier-Nova, “Color rendering: a tale of two metrics,” Color Res. Appl. 33(3), 192–202 (2008).
[CrossRef]

Schubert, E. F.

R. Mirhosseini, M. F. Schubert, S. Chhajed, J. Cho, J. K. Kim, and E. F. Schubert, “Improved color rendering and luminous efficacy in phosphor-converted white light-emitting diodes by use of dual-blue emitting active regions,” Opt. Express 17(13), 10806–10813 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-13-10806 .
[CrossRef] [PubMed]

J. K. Kim and E. F. Schubert, “Transcending the replacement paradigm of solid-state lighting,” Opt. Express 16(26), 21835–21842 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-16-26-21835 .
[CrossRef] [PubMed]

E. F. Schubert, J. K. Kim, H. Luo, and J.-Q. Xi, “Solid-state lighting––a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099(2006).
[CrossRef]

S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light-emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005).
[CrossRef]

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005).
[CrossRef] [PubMed]

Schubert, M. F.

Shur, M. S.

A. Žukauskas, R. Vaicekauskas, and M. S. Shur, “Solid-state lamps with optimized color saturation ability,” Opt. Express 18(3), 2287–2295 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-18-3-2287 .
[CrossRef] [PubMed]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, P. Vitta, and M. S. Shur, “Statistical approach to color quality of solid-state lamps,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1753–1762 (2009).
[CrossRef]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett. 80(2), 234–236 (2002).
[CrossRef]

Tzonchev, R. I.

Vaicekauskas, R.

A. Žukauskas, R. Vaicekauskas, and M. S. Shur, “Solid-state lamps with optimized color saturation ability,” Opt. Express 18(3), 2287–2295 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-18-3-2287 .
[CrossRef] [PubMed]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, P. Vitta, and M. S. Shur, “Statistical approach to color quality of solid-state lamps,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1753–1762 (2009).
[CrossRef]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett. 80(2), 234–236 (2002).
[CrossRef]

Vaitkevicius, H.

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, P. Vitta, and M. S. Shur, “Statistical approach to color quality of solid-state lamps,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1753–1762 (2009).
[CrossRef]

Vitta, P.

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, P. Vitta, and M. S. Shur, “Statistical approach to color quality of solid-state lamps,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1753–1762 (2009).
[CrossRef]

Xi, J.-Q.

E. F. Schubert, J. K. Kim, H. Luo, and J.-Q. Xi, “Solid-state lighting––a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099(2006).
[CrossRef]

Xi, Y.

S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light-emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005).
[CrossRef]

Zheng, L.

Žukauskas, A.

A. Žukauskas, R. Vaicekauskas, and M. S. Shur, “Solid-state lamps with optimized color saturation ability,” Opt. Express 18(3), 2287–2295 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-18-3-2287 .
[CrossRef] [PubMed]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, P. Vitta, and M. S. Shur, “Statistical approach to color quality of solid-state lamps,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1753–1762 (2009).
[CrossRef]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett. 80(2), 234–236 (2002).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, R. Gaska, and M. S. Shur, “Optimization of white polychromatic semiconductor lamps,” Appl. Phys. Lett. 80(2), 234–236 (2002).
[CrossRef]

Color Res. Appl. (2)

M. S. Rea and J. P. Freyssinier-Nova, “Color rendering: a tale of two metrics,” Color Res. Appl. 33(3), 192–202 (2008).
[CrossRef]

R. S. Berns, “A genetic approach to color modeling,” Color Res. Appl. 22(5), 318–325 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, P. Vitta, and M. S. Shur, “Statistical approach to color quality of solid-state lamps,” IEEE J. Sel. Top. Quantum Electron. 15(6), 1753–1762 (2009).
[CrossRef]

J. Appl. Phys. (1)

S. Chhajed, Y. Xi, Y. L. Li, T. Gessmann, and E. F. Schubert, “Influence of junction temperature on chromaticity and color rendering properties of trichromatic white light source based on light-emitting diodes,” J. Appl. Phys. 97(5), 054506 (2005).
[CrossRef]

Opt. Eng. (1)

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (1)

Y. Ohno, “Color rendering and luminous efficacy of white LED spectra,” Proc. SPIE 5530, 88–98 (2004).
[CrossRef]

Rep. Prog. Phys. (1)

E. F. Schubert, J. K. Kim, H. Luo, and J.-Q. Xi, “Solid-state lighting––a benevolent technology,” Rep. Prog. Phys. 69(12), 3069–3099(2006).
[CrossRef]

Science (1)

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005).
[CrossRef] [PubMed]

Other (9)

E. F. Schubert, Light-emitting Diodes, 2nd ed. (Cambridge University Press, 2006).

Epistar Corporation, Taiwan, General LED product catalog (2010).

Toyoda Gosei Corporation, Japan, LED product catalog (2010).

R. Kingslake, Lens Design Fundamentals (Academic Press, 1978).

G. Wyszecki, and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data, and Formulae (Wiley, 2000).

J. S. R. Jang, C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing (Prentice Hall, 1997).

R. L. Haupt, and S. E. Haupt, Practical Genetic Algorithms, 2nd ed. (John Wiley, 2004).

W. J. Smith, Modern Lens Design, 2nd ed. (McGraw-Hill, 2005).

M. Laikin, Lens Design, 4th ed. (CRC Press, 2006).

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Figures (11)

Fig. 1
Fig. 1

Conceptual analogy between the SPD synthesis and conventional lens design. An LED cluster composed of red/cool-white/cool-white/green (R/CW/CW/G) can be regarded as a double Gauss lens system with two singlet lenses and two cemented doublets, where the CW LED is caused by dichromatic mixing.

Fig. 2
Fig. 2

Design procedure of (a) lens design and (b) spectral synthesis of a LED cluster. Both flow charts include six steps: (2.1) initial system, (2.2) define boundary condition, (2.3) optimization, (2.4) aberration or merit analysis, (2.5) judgment, and (2.6) tolerance analysis.

Fig. 3
Fig. 3

Normalized LE of visible LED made from GaInN and AlGaInP series versus individual peak wavelength. The LED with high LE is analogous to a lens with high-refractive index.

Fig. 4
Fig. 4

Emission spectrum of a phosphor-converted CW LED under different Ta . The blue and fluorescence spectrum have individual temperature dependence of λ0 . i and Δλi that should be considered in SPD modeling of this kind of LED.

Fig. 5
Fig. 5

(a) Illustration of the Pareto fronts (PF) for different TCC on the CQS-LE plane. (b) The flowchart of SA1. Either end point P0 or P1 located within quadrant III will lead to an unacceptable performance as PF3. The curve with end points located within quadrant II and IV, like PF2, should be confirmed the operation portion (red curve).

Fig. 6
Fig. 6

Spectra of red (R), green (G), blue (B), amber (A), and CW LEDs at ambient temperature Ta of 300 K with all driving currents of 20 mA. The corresponding chromaticity points and specifications are also shown in the figure. The deriving currents were controlled by a pulse-width modulation (PWM) approach with a pulse width of 6.66 ms at differences of 0.04–0.06 ms for each gray level (a total of 128 gray levels).

Fig. 7
Fig. 7

Spectral comparisons of simulations and experiments for P 0 and P 1 at TCC of 6500 K and 3000 K. The simulated spectra closely matched the measurements in spite of baring a few peak deviations.

Fig. 8
Fig. 8

Illuminant environments at (a) CQS = 87 points for TCC = 6500 K and (b) CQS = 69 points for TCC = 3000 K show apparently different color rendering abilities.

Fig. 9
Fig. 9

SA2 results of (a) R/G/B (black curve), R/G/B/A, and (b) R/G/B/A/CW clusters aimed to P 1 and P 0 for full range of TCC from 1000 K to 10000 K.

Fig. 10
Fig. 10

Results of CQS1/0 and LE1/0 for R/G/B/A and R/G/B/A/CW clusters. By using SA2 analysis, R/G/B/A/CW can extend the operation window.

Fig. 11
Fig. 11

(a) Values of CQS and LE, and (b) the stacked emission power ratio versus correlated color temperature for an optimized R/G/B/A/CW design (CQSm = 80 points and LEm = 60 lm/W). The operation window has been extended to 2600 K < TCC < 8500 K with the selected weight using SA2 for each TCC . In fact, the operation window is restricted by the CQS rather than efficiency. The result shows that high efficiency CW LED is a good substitute for a blue LED.

Equations (15)

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

T _ i _ = t _ ,
T _ = [ X 1 X 2 ... Y 1 Y 2 ... Z 1 Z 2 ...      X i ... X M Y i ... Y M Z i ... Z M ] i = 1 ,   ... , M ,    i _ = [ I 1 I 2 I i I M ] i = 1 ,   ... , M ,    a n d    t _ = [ X Y Z ] ,
| | ( x ,   y ) ( x T ,   y T ) | | < 0.01.
0 <   I i   < max  I i ,
max   I i = min [ ( max   I i  in datasheet) ,  (max  I i  for  Y i = Y T   ) ] .
X i = 380 780 x ˜ ( λ ) S P D i ( λ ,   λ 0 , i ,   Δ λ i ) d λ ,
Y i = 380 780 y ˜ ( λ ) S P D i ( λ ,   λ 0 , i ,   Δ λ i ) d λ ,
Z i = 380 780 z ˜ ( λ ) S P D i ( λ ,   λ 0 , i ,   Δ λ i ) d λ .
ν = j = 1 n a j f j ( μ _ ) ,
F _ a _ = v _ ,
F _ = [ f 11 f 12 ... ... f m 1 f m 2 ...      f 1 j ... f 1 n ... f m k ... f m n ] k = 1 ,   ... , m j = 1 ,   ... , n ,    a _ = [ a 1 a 2 a j a n ] j = 1 ,   ... , n ,  and    v _ = [ ν 1 ν 2 ν k ν m ] k = 1 ,   ... , m .
E ( a _ ) = ( v _ F _ a _ ) T ( v _ F _ a _ ) .
           f = w × C Q S + ( 1 w ) × L E , subject to the constrain: weight  w [ 0 , 1 ] .
C Q S 1 / 0 = C Q S 1 C Q S 0 C Q S 0 ,  and    L E 1 / 0 = L E 1 L E 0 L E 0 .
c = ( C Q S c C Q S 0 ) / C Q S 0 C Q S 1 / 0 = ( L E c L E 0 ) / L E 0 L E 1 / 0 ,

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