Abstract

The spectral power distributions of tri- and tetrachromatic clusters of Light-Emitting-Diodes, composed of simulated and commercially available LEDs, were optimized with a genetic algorithm to maximize the luminous efficacy of radiation and the colour quality as assessed by the memory colour quality metric developed by the authors. The trade-off of the colour quality as assessed by the memory colour metric and the luminous efficacy of radiation was investigated by calculating the Pareto optimal front using the NSGA-II genetic algorithm. Optimal peak wavelengths and spectral widths of the LEDs were derived, and over half of them were found to be close to Thornton’s prime colours. The Pareto optimal fronts of real LED clusters were always found to be smaller than those of the simulated clusters. The effect of binning on designing a real LED cluster was investigated and was found to be quite large. Finally, a real LED cluster of commercially available AlGaInP, InGaN and phosphor white LEDs was optimized to obtain a higher score on memory colour quality scale than its corresponding CIE reference illuminant.

© 2011 OSA

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  1. E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005).
    [CrossRef] [PubMed]
  2. 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]
  3. M. S. Shur, and R. Zukauskas, “Solid-State Lighting: Toward Superior Illumination,” in Proceedings of the IEEE (2005), pp. 1691 - 1703.
  4. A. Žukauskas, R. Vaicekauskas, and M. Shur, “Solid-state lamps with optimized color saturation ability,” Opt. Express 18(3), 2287–2295 (2010).
    [CrossRef] [PubMed]
  5. P. Bodrogi, P. Csuti, P. Hotváth, and J. Schanda, “Why does the CIE Colour Rendering Index fail for White RGB LED Light Sources?” in CIE Expert Symposium on LED Light Sources: Physical Measurement and Visual and Photobiological Assessment(Tokyo, Japan, 2004).
  6. W. Davis and Y. Ohno, “Toward an Improved Color Rendering Metric,” SPIE 59411–59418 (2005).
  7. F. Szabó, J. Schanda, P. Bodrogi, and E. Radkov, “A Comparative Study of New Solid State Light Sources,” in CIE Session 2007(2007).
  8. N. Narendran, and L. Deng, “Color Rendering Properties of LED Light Sources,” in Solid State Lighting II: Proceedings of SPIE(2002).
  9. T. Tarczali, P. Bodrogi, and J. Schanda, “Colour Rendering Properties of LED Sources,” in CIE 2nd LED Measurement Symposium(Gaithersburg, 2001).
  10. CIE, “TC 1-62: Colour Rendering of White LED Light Sources,” in CIE 177:2007(CIE, Vienna, Austria, 2007).
  11. J. D. Bullough, “Research matters: Color rendering - a CRIing game?” Lighting Design and Application 35, 16–18 (2005).
  12. D. B. Judd, “A flattery index for artificial illuminants,” Illum. Eng. 62, 593–598 (1967).
  13. W. A. Thornton, “A validation of the color preference index,” Illum. Eng. 62, 191–194 (1972).
  14. W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602–033616 (2010).
    [CrossRef]
  15. A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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]
  16. M. S. Rea and J. P. Freyssinier-Nova, “Color rendering: A tale of two metrics,” Color Res. Appl. 33(3), 192–202 (2008).
    [CrossRef]
  17. F. Szabó, P. Bodrogi, and J. Schanda, “A colour harmony rendering index based on predictions of colour harmony impression,” Lighting Res. Tech. 41(2), 165–182 (2009).
    [CrossRef]
  18. K. Hashimoto, T. Yano, M. Shimizu, and Y. Nayatani, “New method for specifying color-rendering properties of light sources based on feeling of contrast,” Color Res. Appl. 32(5), 361–371 (2007).
    [CrossRef]
  19. K. Smet, W. R. Ryckaert, M. R. Pointer, G. Deconinck, and P. Hanselaer, “Colour Appearance Rating of Familiar Real Objects,” Colour Research and Application DOI: 10.1002/col.20620 (2010).
  20. K. A. G. Smet, W. R. Ryckaert, M. R. Pointer, G. Deconinck, and P. Hanselaer, “Memory colours and colour quality evaluation of conventional and solid-state lamps,” Opt. Express 18(25), 26229–26244 (2010).
    [CrossRef] [PubMed]
  21. Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44(11), 111302 (2005).
    [CrossRef]
  22. K. Smet, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Colour rendering of white light sources: visual experiments on preference, fidelity, vividness, naturalness & attractiveness.,” in 2nd CIE Expert Symposium: When Appearance meets lighting ...(Ghent, 2010).
  23. K. Smet, S. Jost-Boissard, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Validation of a colour rendering index based on memory colours,” in CIE Lighting Quality & Energy Efficiency(CIE, Vienna, 2010), pp. 136–142.
  24. F. Ebner, and M. D. Fairchild, “Development and testing of a color space (IPT) with improved hue uniformity,” in IS&T 6th Color Imaging Conference(Scottsdale, Arizona, USA, 1998), pp. 8–13.
  25. A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation withjunction temperature,” J. Appl. Phys. 108(4), 043104 (2010).
    [CrossRef]
  26. A. Keppens, “Modelling and evaluation of high-power light-emitting diodes for general lighting,” K.U.Leuven University Press, Leuven, pp. 154–155, 2010.,” in Faculty of Engineering, ESAT/ELECTA(K.U.Leuven, Leuven, 2010), p. 234.
  27. C. A. C. Coello, and G. B. Lamont, “Chapter 1: An Introduction to Multi-Objective Evolutionary Algorithms and Their Applications ” in Applications of Multi-Objective Evolutionary Algorithms, C. A. C. Coello, and G. B. Lamont, eds. (World Scientific, Singapore, 2004).
  28. A. Konak, D. Coit, and A. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Special. Issue. – Genetic. Algorithms and Reliability 91, 992–1007 (2006).
  29. E. Hamidreza and D. G. Christopher, “A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems,” J. Heuristics 14(3), 203–241 (2008).
    [CrossRef]
  30. K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002).
    [CrossRef]
  31. W. A. Thornton, “Spectral sensitivities of the normal human visual system, color-matching functions and their principles, and how and why the two sets should coincide,” Color Res. Appl. 24(2), 139–156 (1999).
    [CrossRef]

2010

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602–033616 (2010).
[CrossRef]

A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation withjunction temperature,” J. Appl. Phys. 108(4), 043104 (2010).
[CrossRef]

A. Žukauskas, R. Vaicekauskas, and M. Shur, “Solid-state lamps with optimized color saturation ability,” Opt. Express 18(3), 2287–2295 (2010).
[CrossRef] [PubMed]

K. A. G. Smet, W. R. Ryckaert, M. R. Pointer, G. Deconinck, and P. Hanselaer, “Memory colours and colour quality evaluation of conventional and solid-state lamps,” Opt. Express 18(25), 26229–26244 (2010).
[CrossRef] [PubMed]

2009

F. Szabó, P. Bodrogi, and J. Schanda, “A colour harmony rendering index based on predictions of colour harmony impression,” Lighting Res. Tech. 41(2), 165–182 (2009).
[CrossRef]

A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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]

2008

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

E. Hamidreza and D. G. Christopher, “A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems,” J. Heuristics 14(3), 203–241 (2008).
[CrossRef]

2007

K. Hashimoto, T. Yano, M. Shimizu, and Y. Nayatani, “New method for specifying color-rendering properties of light sources based on feeling of contrast,” Color Res. Appl. 32(5), 361–371 (2007).
[CrossRef]

2006

A. Konak, D. Coit, and A. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Special. Issue. – Genetic. Algorithms and Reliability 91, 992–1007 (2006).

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

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

Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44(11), 111302 (2005).
[CrossRef]

W. Davis and Y. Ohno, “Toward an Improved Color Rendering Metric,” SPIE 59411–59418 (2005).

J. D. Bullough, “Research matters: Color rendering - a CRIing game?” Lighting Design and Application 35, 16–18 (2005).

2002

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002).
[CrossRef]

1999

W. A. Thornton, “Spectral sensitivities of the normal human visual system, color-matching functions and their principles, and how and why the two sets should coincide,” Color Res. Appl. 24(2), 139–156 (1999).
[CrossRef]

1972

W. A. Thornton, “A validation of the color preference index,” Illum. Eng. 62, 191–194 (1972).

1967

D. B. Judd, “A flattery index for artificial illuminants,” Illum. Eng. 62, 593–598 (1967).

Agarwal, S.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002).
[CrossRef]

Bodrogi, P.

F. Szabó, P. Bodrogi, and J. Schanda, “A colour harmony rendering index based on predictions of colour harmony impression,” Lighting Res. Tech. 41(2), 165–182 (2009).
[CrossRef]

Bullough, J. D.

J. D. Bullough, “Research matters: Color rendering - a CRIing game?” Lighting Design and Application 35, 16–18 (2005).

Christopher, D. G.

E. Hamidreza and D. G. Christopher, “A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems,” J. Heuristics 14(3), 203–241 (2008).
[CrossRef]

Coit, D.

A. Konak, D. Coit, and A. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Special. Issue. – Genetic. Algorithms and Reliability 91, 992–1007 (2006).

Davis, W.

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602–033616 (2010).
[CrossRef]

W. Davis and Y. Ohno, “Toward an Improved Color Rendering Metric,” SPIE 59411–59418 (2005).

Deb, K.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002).
[CrossRef]

Deconinck, G.

K. A. G. Smet, W. R. Ryckaert, M. R. Pointer, G. Deconinck, and P. Hanselaer, “Memory colours and colour quality evaluation of conventional and solid-state lamps,” Opt. Express 18(25), 26229–26244 (2010).
[CrossRef] [PubMed]

A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation withjunction temperature,” J. Appl. Phys. 108(4), 043104 (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]

Hamidreza, E.

E. Hamidreza and D. G. Christopher, “A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems,” J. Heuristics 14(3), 203–241 (2008).
[CrossRef]

Hanselaer, P.

A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation withjunction temperature,” J. Appl. Phys. 108(4), 043104 (2010).
[CrossRef]

K. A. G. Smet, W. R. Ryckaert, M. R. Pointer, G. Deconinck, and P. Hanselaer, “Memory colours and colour quality evaluation of conventional and solid-state lamps,” Opt. Express 18(25), 26229–26244 (2010).
[CrossRef] [PubMed]

Hashimoto, K.

K. Hashimoto, T. Yano, M. Shimizu, and Y. Nayatani, “New method for specifying color-rendering properties of light sources based on feeling of contrast,” Color Res. Appl. 32(5), 361–371 (2007).
[CrossRef]

Ivanauskas, F.

A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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]

Judd, D. B.

D. B. Judd, “A flattery index for artificial illuminants,” Illum. Eng. 62, 593–598 (1967).

Keppens, A.

A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation withjunction temperature,” J. Appl. Phys. 108(4), 043104 (2010).
[CrossRef]

Kim, J. K.

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]

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

Konak, A.

A. Konak, D. Coit, and A. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Special. Issue. – Genetic. Algorithms and Reliability 91, 992–1007 (2006).

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]

Meyarivan, T.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002).
[CrossRef]

Nayatani, Y.

K. Hashimoto, T. Yano, M. Shimizu, and Y. Nayatani, “New method for specifying color-rendering properties of light sources based on feeling of contrast,” Color Res. Appl. 32(5), 361–371 (2007).
[CrossRef]

Ohno, Y.

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602–033616 (2010).
[CrossRef]

Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44(11), 111302 (2005).
[CrossRef]

W. Davis and Y. Ohno, “Toward an Improved Color Rendering Metric,” SPIE 59411–59418 (2005).

Pointer, M. R.

Pratap, A.

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002).
[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]

Ryckaert, W. R.

A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation withjunction temperature,” J. Appl. Phys. 108(4), 043104 (2010).
[CrossRef]

K. A. G. Smet, W. R. Ryckaert, M. R. Pointer, G. Deconinck, and P. Hanselaer, “Memory colours and colour quality evaluation of conventional and solid-state lamps,” Opt. Express 18(25), 26229–26244 (2010).
[CrossRef] [PubMed]

Schanda, J.

F. Szabó, P. Bodrogi, and J. Schanda, “A colour harmony rendering index based on predictions of colour harmony impression,” Lighting Res. Tech. 41(2), 165–182 (2009).
[CrossRef]

Schubert, E. F.

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]

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

Shimizu, M.

K. Hashimoto, T. Yano, M. Shimizu, and Y. Nayatani, “New method for specifying color-rendering properties of light sources based on feeling of contrast,” Color Res. Appl. 32(5), 361–371 (2007).
[CrossRef]

Shur, M.

Shur, M. S.

A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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]

Smet, K. A. G.

Smith, A.

A. Konak, D. Coit, and A. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Special. Issue. – Genetic. Algorithms and Reliability 91, 992–1007 (2006).

Szabó, F.

F. Szabó, P. Bodrogi, and J. Schanda, “A colour harmony rendering index based on predictions of colour harmony impression,” Lighting Res. Tech. 41(2), 165–182 (2009).
[CrossRef]

Thornton, W. A.

W. A. Thornton, “Spectral sensitivities of the normal human visual system, color-matching functions and their principles, and how and why the two sets should coincide,” Color Res. Appl. 24(2), 139–156 (1999).
[CrossRef]

W. A. Thornton, “A validation of the color preference index,” Illum. Eng. 62, 191–194 (1972).

Vaicekauskas, R.

A. Žukauskas, R. Vaicekauskas, and M. Shur, “Solid-state lamps with optimized color saturation ability,” Opt. Express 18(3), 2287–2295 (2010).
[CrossRef] [PubMed]

A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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]

Vaitkevicius, H.

A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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]

Yano, T.

K. Hashimoto, T. Yano, M. Shimizu, and Y. Nayatani, “New method for specifying color-rendering properties of light sources based on feeling of contrast,” Color Res. Appl. 32(5), 361–371 (2007).
[CrossRef]

Zukauskas, A.

A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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]

Žukauskas, A.

Color Res. Appl.

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

K. Hashimoto, T. Yano, M. Shimizu, and Y. Nayatani, “New method for specifying color-rendering properties of light sources based on feeling of contrast,” Color Res. Appl. 32(5), 361–371 (2007).
[CrossRef]

W. A. Thornton, “Spectral sensitivities of the normal human visual system, color-matching functions and their principles, and how and why the two sets should coincide,” Color Res. Appl. 24(2), 139–156 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Zukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevicius, 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]

IEEE Trans. Evolutionary Computation

K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation 6(2), 182–197 (2002).
[CrossRef]

Illum. Eng.

D. B. Judd, “A flattery index for artificial illuminants,” Illum. Eng. 62, 593–598 (1967).

W. A. Thornton, “A validation of the color preference index,” Illum. Eng. 62, 191–194 (1972).

J. Appl. Phys.

A. Keppens, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Modeling high-power light-emitting diode spectra and their variation withjunction temperature,” J. Appl. Phys. 108(4), 043104 (2010).
[CrossRef]

J. Heuristics

E. Hamidreza and D. G. Christopher, “A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems,” J. Heuristics 14(3), 203–241 (2008).
[CrossRef]

Lighting Design and Application

J. D. Bullough, “Research matters: Color rendering - a CRIing game?” Lighting Design and Application 35, 16–18 (2005).

Lighting Res. Tech.

F. Szabó, P. Bodrogi, and J. Schanda, “A colour harmony rendering index based on predictions of colour harmony impression,” Lighting Res. Tech. 41(2), 165–182 (2009).
[CrossRef]

Opt. Eng.

Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44(11), 111302 (2005).
[CrossRef]

W. Davis and Y. Ohno, “Color quality scale,” Opt. Eng. 49(3), 033602–033616 (2010).
[CrossRef]

Opt. Express

Rep. Prog. Phys.

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

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

Special. Issue. – Genetic. Algorithms and Reliability

A. Konak, D. Coit, and A. Smith, “Multi-objective optimization using genetic algorithms: A tutorial,” Special. Issue. – Genetic. Algorithms and Reliability 91, 992–1007 (2006).

Other

A. Keppens, “Modelling and evaluation of high-power light-emitting diodes for general lighting,” K.U.Leuven University Press, Leuven, pp. 154–155, 2010.,” in Faculty of Engineering, ESAT/ELECTA(K.U.Leuven, Leuven, 2010), p. 234.

C. A. C. Coello, and G. B. Lamont, “Chapter 1: An Introduction to Multi-Objective Evolutionary Algorithms and Their Applications ” in Applications of Multi-Objective Evolutionary Algorithms, C. A. C. Coello, and G. B. Lamont, eds. (World Scientific, Singapore, 2004).

M. S. Shur, and R. Zukauskas, “Solid-State Lighting: Toward Superior Illumination,” in Proceedings of the IEEE (2005), pp. 1691 - 1703.

P. Bodrogi, P. Csuti, P. Hotváth, and J. Schanda, “Why does the CIE Colour Rendering Index fail for White RGB LED Light Sources?” in CIE Expert Symposium on LED Light Sources: Physical Measurement and Visual and Photobiological Assessment(Tokyo, Japan, 2004).

W. Davis and Y. Ohno, “Toward an Improved Color Rendering Metric,” SPIE 59411–59418 (2005).

F. Szabó, J. Schanda, P. Bodrogi, and E. Radkov, “A Comparative Study of New Solid State Light Sources,” in CIE Session 2007(2007).

N. Narendran, and L. Deng, “Color Rendering Properties of LED Light Sources,” in Solid State Lighting II: Proceedings of SPIE(2002).

T. Tarczali, P. Bodrogi, and J. Schanda, “Colour Rendering Properties of LED Sources,” in CIE 2nd LED Measurement Symposium(Gaithersburg, 2001).

CIE, “TC 1-62: Colour Rendering of White LED Light Sources,” in CIE 177:2007(CIE, Vienna, Austria, 2007).

K. Smet, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Colour rendering of white light sources: visual experiments on preference, fidelity, vividness, naturalness & attractiveness.,” in 2nd CIE Expert Symposium: When Appearance meets lighting ...(Ghent, 2010).

K. Smet, S. Jost-Boissard, W. R. Ryckaert, G. Deconinck, and P. Hanselaer, “Validation of a colour rendering index based on memory colours,” in CIE Lighting Quality & Energy Efficiency(CIE, Vienna, 2010), pp. 136–142.

F. Ebner, and M. D. Fairchild, “Development and testing of a color space (IPT) with improved hue uniformity,” in IS&T 6th Color Imaging Conference(Scottsdale, Arizona, USA, 1998), pp. 8–13.

K. Smet, W. R. Ryckaert, M. R. Pointer, G. Deconinck, and P. Hanselaer, “Colour Appearance Rating of Familiar Real Objects,” Colour Research and Application DOI: 10.1002/col.20620 (2010).

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Fig. 1
Fig. 1

S a and LER Pareto optimal fronts for tri- and tetrachromatic LED clusters. Left: trichromatic clusters (blue: R/G/B; red: R/B/phLED). Right: tetrachromatic clusters (blue: R/G/B/Y-A; red: R/G/B/phLED).

Fig. 2
Fig. 2

Histogram of the individual LED peak wavelengths in the subset of Pareto optimal solutions with S a ≥ 0.775. Legend: blue LED (blue); green LED (green); red LED (red); yellow-to-amber LED (yellow) and phosphor type LED (cyan+black).

Fig. 3
Fig. 3

(a) S a and LER Pareto optimal fronts for simulated and real LED clusters. Black: simulated tetrachromatic LED clusters; green: two real R/G/B clusters; red: two real R/G/B/phLED type clusters; blue: two real R/G/B/A clusters. Dots and circles represent LED clusters composed of LEDs from two different suppliers A and B. (b) Spectral power distributions of the commercially high power LEDs: supplier A (solid line) and supplier B (dashed line).

Tables (1)

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Table 1 Optimal Full-Width-Half-Maxima of the Individual LEDs in the Subset of Pareto Optimal Solutions with S a ≥ 0.775.

Equations (4)

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S i   ( X i ) =   e   1 2   [ ( X i a i,1 ) T ( a i,3 a i,5 a i,5 a i,4 )   ( X i a i,2 ) ]       ( i = 1..10 )
P h ( λ , λ 0 , Δ λ 0.5 ) = g ( λ , λ 0 , Δ λ 0.5 ) + 1 g 5 ( λ , λ 0 , Δ λ 0.5 ) 2     ;     g ( λ , λ 0 , Δ λ 0.5 ) =   e ( λ λ 0 / Δ λ 0.5 ) 2 Φ e , λ , P h ' ( λ 0 , Δ λ 0.5 , α , β ) = Φ e , λ , c ( λ 0 , c , Δ λ 0.5 , c ) + α [ β P h ( λ , λ 0 , p h 1 , Δ λ 0.5 , p h 1 ) + ( 1 β ) P h ( λ , λ 0 , p h 2 , Δ λ 0.5 , p h 2 ) ] ( 1 + α ) Φ e , λ , P h ( λ 0 , Δ λ 0.5 ) =    Φ e , λ , P h ' ( λ 0 , Δ λ 0.5 )   f c ' ( λ , λ 0 , c , Δ λ 0.5 , c ) w i t h f c ' ( λ , λ 0 , c , Δ λ 0.5 , c ) = { Φ e , λ , c ( λ 0 , c , Δ λ 0.5 , c )     λ <     λ 0 , c 1                                                               λ     λ 0 , c
Φ e , λ c l u s t e r ( λ ) = { λ 0 , c=i ; Δ λ 0.5 , c=i ; φ c=i ; λ 0 , c=j ; Δ λ 0.5 , c=j ; λ 0 , ph (1,2) =j ; Δ λ 0.5 , ph (1,2) =j ; α ; β ; φ ph=j }
L E R = 683 × λ Φ e , λ V ( λ ) d λ / λ Φ e , λ d λ ( lmW -1 )

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