Abstract

Optimization of solid-state lighting spectra is performed to achieve beneficial and tunable circadian effects. First, the minimum spectral circadian action factor (CAF) of 2700 K white light-emitting diodes (LEDs) is studied for applications where biologically active illumination is undesirable. It is found that white-LEDs based on (i) RGB chips, (ii) blue & red chips plus green phosphor, and (iii) blue chip plus green & red phosphors are the corresponding minimum-CAF solutions at color-rendering index (CRI) requirements of 80, 90, and 95, respectively. Second, maximum CAF tunability of LED clusters is studied for dynamic daylighting applications. A dichromatic phosphor-converted blue-centered LED, a dichromatic phosphor-converted green-centered LED, and a monochromatic red LED are grouped to obtain white spectra between 2700 K and 6500 K. A maximum CAF tunability of 3.25 times is achieved with CRI above 90 and luminous efficacy of radiation of 313 - 373 lm/W. We show that our approaches have advantages over previously reported solutions on system simplicity, minimum achievable CAF value, CAF tunability range, and light source efficacy.

© 2016 Optical Society of America

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2016 (1)

Q. Dai, L. Hao, Y. Lin, and Z. Cui, “Spectral optimization simulation of white light based on the photopic eye-sensitivity curve,” J. Appl. Phys. 119(5), 053103 (2016).
[Crossref]

2015 (3)

A. Liu, A. Khanna, P. S. Dutta, and M. Shur, “Red-blue-green solid state light sources using a narrow line-width green phosphor,” Opt. Express 23(7), A309–A315 (2015).
[Crossref] [PubMed]

P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref] [PubMed]

A. Žukauskas and R. Vaicekauskas, “Tunability of the circadian action of tetrachromatic solid-state light sources,” Appl. Phys. Lett. 106(4), 041107 (2015).
[Crossref]

2014 (4)

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

J. H. Oh, S. J. Yang, and Y. R. Do, “Healthy, natural, efficient and tunable lighting: four-package white LEDs for optimizing the circadian effect, color quality and vision performance,” Light Sci. Appl. 3(2), e141 (2014).
[Crossref]

A. Zabiliūtė, R. Vaicekauskas, P. Vitta, and A. Žukauskas, “Phosphor-converted LEDs with low circadian action for outdoor lighting,” Opt. Lett. 39(3), 563–566 (2014).
[Crossref] [PubMed]

G. He and J. Tang, “Spectral optimization of color temperature tunable white LEDs with excellent color rendering and luminous efficacy,” Opt. Lett. 39(19), 5570–5573 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (1)

2011 (3)

G. He and H. Yan, “Optimal spectra of the phosphor-coated white LEDs with excellent color rendering property and high luminous efficacy of radiation,” Opt. Express 19(3), 2519–2529 (2011).
[Crossref] [PubMed]

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

L. Bellia, F. Bisegna, and G. Spada, “Lighting in indoor environments: visual and non-visual effects of light sources with different spectral power distributions,” Build. Environ. 46(10), 1984–1992 (2011).
[Crossref]

2010 (2)

R. Kozakov, H. Schopp, St. Franke, C. Stoll, and D. Kunz, “Modification of light sources for appropriate biological action,” J. Phys. D Appl. Phys. 43(23), 234007 (2010).
[Crossref]

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

2008 (2)

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, and M. S. Shur, “Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering,” Appl. Phys. Lett. 93(5), 051115 (2008).
[Crossref]

R. Kozakov, S. Franke, and H. Schopp, “Approach to an effective biological spectrum of a light source,” Leukos 4, 255–263 (2008).

2006 (1)

R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “An interior algorithm for nonlinear optimization that combines line search and trust region steps,” Math. Program. 107(3), 391–408 (2006).
[Crossref]

2005 (3)

I. Y. Kim and O. L. de Weck, “Adaptive weighted-sum method for bi-objective optimization: Pareto front generation,” Struct. Multidiscipl. Optim. 29(2), 149–158 (2005).
[Crossref]

M. S. Rea, M. G. Figueiro, J. D. Bullough, and A. Bierman, “A model of phototransduction by the human circadian system,” Brain Res. Brain Res. Rev. 50(2), 213–228 (2005).
[Crossref] [PubMed]

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

2002 (4)

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]

D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295(5557), 1070–1073 (2002).
[Crossref] [PubMed]

D. Gall, “Circadiane Lichtgrößen und deren messtechnische ermittlung,” Licht 54, 1292–1297 (2002).

M. S. Rea, M. G. Figueiro, and J. D. Bullough, “Circadian photobiology: an emerging framework for lighting practice and research,” Light. Res. Technol. 34(3), 177–190 (2002).
[Crossref]

2001 (2)

G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001).
[PubMed]

K. Thapan, J. Arendt, and D. J. Skene, “An action spectrum for melatonin suppression: evidence for a novel non-rod, non-cone photoreceptor system in humans,” J. Physiol. 535(1), 261–267 (2001).
[Crossref] [PubMed]

2000 (1)

R. H. Byrd, J. C. Gilbert, and J. Nocedal, “A trust region method based on interior point techniques for nonlinear programming,” Math. Program. 89(1), 149–185 (2000).
[Crossref]

1998 (1)

C. I. Eastman, M. A. Young, L. F. Fogg, L. Liu, and P. M. Meaden, “Bright light treatment of winter depression: a placebo-controlled trial,” Arch. Gen. Psychiatry 55(10), 883–889 (1998).
[Crossref] [PubMed]

1994 (1)

T. Partonen, “Effects of morning light treatment on subjective sleepiness and mood in winter depression,” J. Affect. Disord. 30(2), 99–108 (1994).
[Crossref] [PubMed]

1979 (1)

W. Stadler, “A survey of multicriteria optimization, or the vector maximum problem,” J. Optim. Theory Appl. 29(1), 1–52 (1979).
[Crossref]

1963 (1)

L. A. Zadeh, “Optimality and non-scalar-valued performance criteria,” IEEE Trans. Automat. Contr. 8(1), 59–60 (1963).
[Crossref]

Arendt, J.

K. Thapan, J. Arendt, and D. J. Skene, “An action spectrum for melatonin suppression: evidence for a novel non-rod, non-cone photoreceptor system in humans,” J. Physiol. 535(1), 261–267 (2001).
[Crossref] [PubMed]

Ayers, M. A.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

Bellia, L.

L. Bellia, F. Bisegna, and G. Spada, “Lighting in indoor environments: visual and non-visual effects of light sources with different spectral power distributions,” Build. Environ. 46(10), 1984–1992 (2011).
[Crossref]

Berson, D. M.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295(5557), 1070–1073 (2002).
[Crossref] [PubMed]

Bierman, A.

M. S. Rea, M. G. Figueiro, J. D. Bullough, and A. Bierman, “A model of phototransduction by the human circadian system,” Brain Res. Brain Res. Rev. 50(2), 213–228 (2005).
[Crossref] [PubMed]

Bisegna, F.

L. Bellia, F. Bisegna, and G. Spada, “Lighting in indoor environments: visual and non-visual effects of light sources with different spectral power distributions,” Build. Environ. 46(10), 1984–1992 (2011).
[Crossref]

Bowen, C.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

Brainard, G. C.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001).
[PubMed]

Brown, T. M.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

Bullough, J. D.

M. S. Rea, M. G. Figueiro, J. D. Bullough, and A. Bierman, “A model of phototransduction by the human circadian system,” Brain Res. Brain Res. Rev. 50(2), 213–228 (2005).
[Crossref] [PubMed]

M. S. Rea, M. G. Figueiro, and J. D. Bullough, “Circadian photobiology: an emerging framework for lighting practice and research,” Light. Res. Technol. 34(3), 177–190 (2002).
[Crossref]

Byrd, R. H.

R. H. Byrd, J. C. Gilbert, and J. Nocedal, “A trust region method based on interior point techniques for nonlinear programming,” Math. Program. 89(1), 149–185 (2000).
[Crossref]

Byrne, B.

G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001).
[PubMed]

Cecil, K. S.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

Cooper, H. M.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

Cui, Z.

Q. Dai, L. Hao, Y. Lin, and Z. Cui, “Spectral optimization simulation of white light based on the photopic eye-sensitivity curve,” J. Appl. Phys. 119(5), 053103 (2016).
[Crossref]

Czeisler, C. A.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

C. A. Czeisler, “Perspective: casting light on sleep deficiency,” Nature 497(7450), S13 (2013).
[Crossref] [PubMed]

Dai, Q.

Q. Dai, L. Hao, Y. Lin, and Z. Cui, “Spectral optimization simulation of white light based on the photopic eye-sensitivity curve,” J. Appl. Phys. 119(5), 053103 (2016).
[Crossref]

Davis, W.

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

de Weck, O. L.

I. Y. Kim and O. L. de Weck, “Adaptive weighted-sum method for bi-objective optimization: Pareto front generation,” Struct. Multidiscipl. Optim. 29(2), 149–158 (2005).
[Crossref]

Do, Y. R.

J. H. Oh, S. J. Yang, and Y. R. Do, “Healthy, natural, efficient and tunable lighting: four-package white LEDs for optimizing the circadian effect, color quality and vision performance,” Light Sci. Appl. 3(2), e141 (2014).
[Crossref]

Dunn, F. A.

D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295(5557), 1070–1073 (2002).
[Crossref] [PubMed]

Dutta, P. S.

Eastman, C. I.

C. I. Eastman, M. A. Young, L. F. Fogg, L. Liu, and P. M. Meaden, “Bright light treatment of winter depression: a placebo-controlled trial,” Arch. Gen. Psychiatry 55(10), 883–889 (1998).
[Crossref] [PubMed]

Figueiro, M. G.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

M. S. Rea, M. G. Figueiro, J. D. Bullough, and A. Bierman, “A model of phototransduction by the human circadian system,” Brain Res. Brain Res. Rev. 50(2), 213–228 (2005).
[Crossref] [PubMed]

M. S. Rea, M. G. Figueiro, and J. D. Bullough, “Circadian photobiology: an emerging framework for lighting practice and research,” Light. Res. Technol. 34(3), 177–190 (2002).
[Crossref]

Fogg, L. F.

C. I. Eastman, M. A. Young, L. F. Fogg, L. Liu, and P. M. Meaden, “Bright light treatment of winter depression: a placebo-controlled trial,” Arch. Gen. Psychiatry 55(10), 883–889 (1998).
[Crossref] [PubMed]

Franke, S.

R. Kozakov, S. Franke, and H. Schopp, “Approach to an effective biological spectrum of a light source,” Leukos 4, 255–263 (2008).

Franke, St.

R. Kozakov, H. Schopp, St. Franke, C. Stoll, and D. Kunz, “Modification of light sources for appropriate biological action,” J. Phys. D Appl. Phys. 43(23), 234007 (2010).
[Crossref]

Gall, D.

D. Gall, “Circadiane Lichtgrößen und deren messtechnische ermittlung,” Licht 54, 1292–1297 (2002).

Gamlin, P. D.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

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]

Gerner, E.

G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001).
[PubMed]

Gilbert, J. C.

R. H. Byrd, J. C. Gilbert, and J. Nocedal, “A trust region method based on interior point techniques for nonlinear programming,” Math. Program. 89(1), 149–185 (2000).
[Crossref]

Glickman, G.

G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001).
[PubMed]

Greeson, J. M.

G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001).
[PubMed]

Hanifin, J. P.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001).
[PubMed]

Hao, L.

Q. Dai, L. Hao, Y. Lin, and Z. Cui, “Spectral optimization simulation of white light based on the photopic eye-sensitivity curve,” J. Appl. Phys. 119(5), 053103 (2016).
[Crossref]

He, G.

Ivanauskas, F.

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, and M. S. Shur, “Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering,” Appl. Phys. Lett. 93(5), 051115 (2008).
[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]

Jablonski, M. R.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

James, M.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

Khanna, A.

Kim, I. Y.

I. Y. Kim and O. L. de Weck, “Adaptive weighted-sum method for bi-objective optimization: Pareto front generation,” Struct. Multidiscipl. Optim. 29(2), 149–158 (2005).
[Crossref]

Kim, J. K.

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

Kozakov, R.

R. Kozakov, H. Schopp, St. Franke, C. Stoll, and D. Kunz, “Modification of light sources for appropriate biological action,” J. Phys. D Appl. Phys. 43(23), 234007 (2010).
[Crossref]

R. Kozakov, S. Franke, and H. Schopp, “Approach to an effective biological spectrum of a light source,” Leukos 4, 255–263 (2008).

Kunz, D.

R. Kozakov, H. Schopp, St. Franke, C. Stoll, and D. Kunz, “Modification of light sources for appropriate biological action,” J. Phys. D Appl. Phys. 43(23), 234007 (2010).
[Crossref]

Lin, Y.

Q. Dai, L. Hao, Y. Lin, and Z. Cui, “Spectral optimization simulation of white light based on the photopic eye-sensitivity curve,” J. Appl. Phys. 119(5), 053103 (2016).
[Crossref]

Liu, A.

Liu, L.

C. I. Eastman, M. A. Young, L. F. Fogg, L. Liu, and P. M. Meaden, “Bright light treatment of winter depression: a placebo-controlled trial,” Arch. Gen. Psychiatry 55(10), 883–889 (1998).
[Crossref] [PubMed]

Lockley, S. W.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

Lucas, R. J.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

Maida, J.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

Meaden, P. M.

C. I. Eastman, M. A. Young, L. F. Fogg, L. Liu, and P. M. Meaden, “Bright light treatment of winter depression: a placebo-controlled trial,” Arch. Gen. Psychiatry 55(10), 883–889 (1998).
[Crossref] [PubMed]

Morales, J. L.

R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “An interior algorithm for nonlinear optimization that combines line search and trust region steps,” Math. Program. 107(3), 391–408 (2006).
[Crossref]

Nocedal, J.

R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “An interior algorithm for nonlinear optimization that combines line search and trust region steps,” Math. Program. 107(3), 391–408 (2006).
[Crossref]

R. H. Byrd, J. C. Gilbert, and J. Nocedal, “A trust region method based on interior point techniques for nonlinear programming,” Math. Program. 89(1), 149–185 (2000).
[Crossref]

O’Hagan, J. B.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

Oh, J. H.

J. H. Oh, S. J. Yang, and Y. R. Do, “Healthy, natural, efficient and tunable lighting: four-package white LEDs for optimizing the circadian effect, color quality and vision performance,” Light Sci. Appl. 3(2), e141 (2014).
[Crossref]

Ohno, Y.

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

Orban, D.

R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “An interior algorithm for nonlinear optimization that combines line search and trust region steps,” Math. Program. 107(3), 391–408 (2006).
[Crossref]

Partonen, T.

T. Partonen, “Effects of morning light treatment on subjective sleepiness and mood in winter depression,” J. Affect. Disord. 30(2), 99–108 (1994).
[Crossref] [PubMed]

Peirson, S. N.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

Petrulis, A.

Price, L. L. A.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

Provencio, I.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

Pust, P.

P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref] [PubMed]

Rea, M. S.

M. S. Rea, M. G. Figueiro, J. D. Bullough, and A. Bierman, “A model of phototransduction by the human circadian system,” Brain Res. Brain Res. Rev. 50(2), 213–228 (2005).
[Crossref] [PubMed]

M. S. Rea, M. G. Figueiro, and J. D. Bullough, “Circadian photobiology: an emerging framework for lighting practice and research,” Light. Res. Technol. 34(3), 177–190 (2002).
[Crossref]

Rollag, M. D.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

G. C. Brainard, J. P. Hanifin, J. M. Greeson, B. Byrne, G. Glickman, E. Gerner, and M. D. Rollag, “Action spectrum for melatonin regulation in humans: evidence for a novel circadian photoreceptor,” J. Neurosci. 21(16), 6405–6412 (2001).
[PubMed]

Schmidt, P. J.

P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref] [PubMed]

Schnick, W.

P. Pust, P. J. Schmidt, and W. Schnick, “A revolution in lighting,” Nat. Mater. 14(5), 454–458 (2015).
[Crossref] [PubMed]

Schopp, H.

R. Kozakov, H. Schopp, St. Franke, C. Stoll, and D. Kunz, “Modification of light sources for appropriate biological action,” J. Phys. D Appl. Phys. 43(23), 234007 (2010).
[Crossref]

R. Kozakov, S. Franke, and H. Schopp, “Approach to an effective biological spectrum of a light source,” Leukos 4, 255–263 (2008).

Schubert, E. F.

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

Shur, M.

Shur, M. S.

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, and M. S. Shur, “Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering,” Appl. Phys. Lett. 93(5), 051115 (2008).
[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]

Skene, D. J.

R. J. Lucas, S. N. Peirson, D. M. Berson, T. M. Brown, H. M. Cooper, C. A. Czeisler, M. G. Figueiro, P. D. Gamlin, S. W. Lockley, J. B. O’Hagan, L. L. A. Price, I. Provencio, D. J. Skene, and G. C. Brainard, “Measuring and using light in the melanopsin age,” Trends Neurosci. 37(1), 1–9 (2014).
[Crossref] [PubMed]

K. Thapan, J. Arendt, and D. J. Skene, “An action spectrum for melatonin suppression: evidence for a novel non-rod, non-cone photoreceptor system in humans,” J. Physiol. 535(1), 261–267 (2001).
[Crossref] [PubMed]

Sliney, D. H.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

Spada, G.

L. Bellia, F. Bisegna, and G. Spada, “Lighting in indoor environments: visual and non-visual effects of light sources with different spectral power distributions,” Build. Environ. 46(10), 1984–1992 (2011).
[Crossref]

Stadler, W.

W. Stadler, “A survey of multicriteria optimization, or the vector maximum problem,” J. Optim. Theory Appl. 29(1), 1–52 (1979).
[Crossref]

Stoll, C.

R. Kozakov, H. Schopp, St. Franke, C. Stoll, and D. Kunz, “Modification of light sources for appropriate biological action,” J. Phys. D Appl. Phys. 43(23), 234007 (2010).
[Crossref]

Takao, M.

D. M. Berson, F. A. Dunn, and M. Takao, “Phototransduction by retinal ganglion cells that set the circadian clock,” Science 295(5557), 1070–1073 (2002).
[Crossref] [PubMed]

Tang, J.

Thapan, K.

K. Thapan, J. Arendt, and D. J. Skene, “An action spectrum for melatonin suppression: evidence for a novel non-rod, non-cone photoreceptor system in humans,” J. Physiol. 535(1), 261–267 (2001).
[Crossref] [PubMed]

Vaicekauskas, R.

A. Žukauskas and R. Vaicekauskas, “Tunability of the circadian action of tetrachromatic solid-state light sources,” Appl. Phys. Lett. 106(4), 041107 (2015).
[Crossref]

A. Zabiliūtė, R. Vaicekauskas, P. Vitta, and A. Žukauskas, “Phosphor-converted LEDs with low circadian action for outdoor lighting,” Opt. Lett. 39(3), 563–566 (2014).
[Crossref] [PubMed]

A. Žukauskas, R. Vaicekauskas, P. Vitta, A. Zabiliūtė, A. Petrulis, and M. Shur, “Color rendition engineering of phosphor-converted light-emitting diodes,” Opt. Express 21(22), 26642–26656 (2013).
[Crossref] [PubMed]

A. Žukauskas, R. Vaicekauskas, and P. Vitta, “Optimization of solid-state lamps for photobiologically friendly mesopic lighting,” Appl. Opt. 51(35), 8423–8432 (2012).
[Crossref] [PubMed]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, and M. S. Shur, “Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering,” Appl. Phys. Lett. 93(5), 051115 (2008).
[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, and M. S. Shur, “Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering,” Appl. Phys. Lett. 93(5), 051115 (2008).
[Crossref]

Vitta, P.

Waltz, R. A.

R. A. Waltz, J. L. Morales, J. Nocedal, and D. Orban, “An interior algorithm for nonlinear optimization that combines line search and trust region steps,” Math. Program. 107(3), 391–408 (2006).
[Crossref]

Warfield, B.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

West, K. E.

K. E. West, M. R. Jablonski, B. Warfield, K. S. Cecil, M. James, M. A. Ayers, J. Maida, C. Bowen, D. H. Sliney, M. D. Rollag, J. P. Hanifin, and G. C. Brainard, “Blue light from light-emitting diodes elicits a dose-dependent suppression of melatonin in humans,” J. Appl. Physiol. 110(3), 619–626 (2011).
[Crossref] [PubMed]

Yan, H.

Yang, S. J.

J. H. Oh, S. J. Yang, and Y. R. Do, “Healthy, natural, efficient and tunable lighting: four-package white LEDs for optimizing the circadian effect, color quality and vision performance,” Light Sci. Appl. 3(2), e141 (2014).
[Crossref]

Young, M. A.

C. I. Eastman, M. A. Young, L. F. Fogg, L. Liu, and P. M. Meaden, “Bright light treatment of winter depression: a placebo-controlled trial,” Arch. Gen. Psychiatry 55(10), 883–889 (1998).
[Crossref] [PubMed]

Zabiliute, A.

Zadeh, L. A.

L. A. Zadeh, “Optimality and non-scalar-valued performance criteria,” IEEE Trans. Automat. Contr. 8(1), 59–60 (1963).
[Crossref]

Žukauskas, A.

A. Žukauskas and R. Vaicekauskas, “Tunability of the circadian action of tetrachromatic solid-state light sources,” Appl. Phys. Lett. 106(4), 041107 (2015).
[Crossref]

A. Zabiliūtė, R. Vaicekauskas, P. Vitta, and A. Žukauskas, “Phosphor-converted LEDs with low circadian action for outdoor lighting,” Opt. Lett. 39(3), 563–566 (2014).
[Crossref] [PubMed]

A. Žukauskas, R. Vaicekauskas, P. Vitta, A. Zabiliūtė, A. Petrulis, and M. Shur, “Color rendition engineering of phosphor-converted light-emitting diodes,” Opt. Express 21(22), 26642–26656 (2013).
[Crossref] [PubMed]

A. Žukauskas, R. Vaicekauskas, and P. Vitta, “Optimization of solid-state lamps for photobiologically friendly mesopic lighting,” Appl. Opt. 51(35), 8423–8432 (2012).
[Crossref] [PubMed]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, and M. S. Shur, “Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering,” Appl. Phys. Lett. 93(5), 051115 (2008).
[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. (1)

Appl. Phys. Lett. (3)

A. Žukauskas and R. Vaicekauskas, “Tunability of the circadian action of tetrachromatic solid-state light sources,” Appl. Phys. Lett. 106(4), 041107 (2015).
[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]

A. Žukauskas, R. Vaicekauskas, F. Ivanauskas, H. Vaitkevičius, and M. S. Shur, “Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering,” Appl. Phys. Lett. 93(5), 051115 (2008).
[Crossref]

Arch. Gen. Psychiatry (1)

C. I. Eastman, M. A. Young, L. F. Fogg, L. Liu, and P. M. Meaden, “Bright light treatment of winter depression: a placebo-controlled trial,” Arch. Gen. Psychiatry 55(10), 883–889 (1998).
[Crossref] [PubMed]

Brain Res. Brain Res. Rev. (1)

M. S. Rea, M. G. Figueiro, J. D. Bullough, and A. Bierman, “A model of phototransduction by the human circadian system,” Brain Res. Brain Res. Rev. 50(2), 213–228 (2005).
[Crossref] [PubMed]

Build. Environ. (1)

L. Bellia, F. Bisegna, and G. Spada, “Lighting in indoor environments: visual and non-visual effects of light sources with different spectral power distributions,” Build. Environ. 46(10), 1984–1992 (2011).
[Crossref]

IEEE Trans. Automat. Contr. (1)

L. A. Zadeh, “Optimality and non-scalar-valued performance criteria,” IEEE Trans. Automat. Contr. 8(1), 59–60 (1963).
[Crossref]

J. Affect. Disord. (1)

T. Partonen, “Effects of morning light treatment on subjective sleepiness and mood in winter depression,” J. Affect. Disord. 30(2), 99–108 (1994).
[Crossref] [PubMed]

J. Appl. Phys. (1)

Q. Dai, L. Hao, Y. Lin, and Z. Cui, “Spectral optimization simulation of white light based on the photopic eye-sensitivity curve,” J. Appl. Phys. 119(5), 053103 (2016).
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Figures (6)

Fig. 1
Fig. 1 Comparison of photopic eye-sensitivity function V (λ) [23], circadian spectral efficiency function C (λ) [19], and CIE standard color matching function z ¯ (λ) [3].

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Fig. 2
Fig. 2 (a) CAF vs. CRI for 2700 K white sources based on the RGpB solution, and (b) the representative spectra with various CAFs.

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Fig. 3
Fig. 3 (a) Minimum CAF vs. CRI (Pareto frontiers) for 2700 K sources based on RGB, RGpB, and RpGpB white-LED solutions, (b) the corresponding LERs, and the corresponding spectra for lowest CAFs at CRI of (c) 80, (d) 90, and (e) 95.

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Fig. 4
Fig. 4 (a) CAF tunability between 2700 K and 6500 K, as a function of the common red LED wavelength. (b) The optimized spectra of three LEDs for maximum CAF tunability.

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Fig. 5
Fig. 5 (a) Color coordinates of three LEDs as well as white color points on the planckian locus. (b) Spectra of the tunable LED cluster at 2700 K, 3000 K, 4000 K, 4870 K, and 6500 K.

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Fig. 6
Fig. 6 CAF & LER as a function of CCT (at CRI ≥ 90) for the three-channel tunable LED cluster.

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Equations (5)

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a c =K ∫ 380 780 C(λ)P(λ)dλ / ∫ 380 780 V(λ)P(λ)dλ ,
a c =K  ∫ 380 780 C(λ)P(λ)dλ ∫ 380 780 z ¯ (λ)P(λ)dλ     ∫ 380 780 z ¯ (λ)P(λ)dλ ∫ 380 780 V(λ)P(λ)dλ =K  ∫ 380 780 C(λ)P(λ)dλ ∫ 380 780 z ¯ (λ)P(λ)dλ   1−x−y y ,
P phosphor (λ)= (λ/ λ 0 ) −2 exp[  −4ln(2) h 2 c 2 ( λ −1 − λ 0 −1 ) 2 / W 2 ],
F σ ( λ 1 , λ 2 , λ 3 , I 1 , I 2 , I 3 )=σ k CAF−( 1−σ ) CRI,
G σ ( λ BC-1 , λ BC-2 , I BC-1 , I BC-2 , I red )=CAF  | λ red CRI=90 ,

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