Abstract

The optimal spectral parameters and photometric performances of white LEDs with red LEDs instead of phosphor (pc/R-WLEDs) for the color fidelity index (Rf) above 97 at correlated color temperatures (CCTs) of 2700 K to 6500 K have been obtained based on the luminous efficacy (LE) model. We have first reported four real pc/R-WLEDs with Rfs of 96–97 and LEs of 120–124 lm/W at CCTs of 2969 K, 4468 K, 5682 K, and 6558 K by using blue (448 nm) and red (650 nm) LEDs, as well as green (507 nm) and yellow (586 nm) phosphors. As compared with phosphor-converted white LEDs (pc-WLEDs) as well as quantum dots white LEDs (QD-WLED), it was found that the pc/R-WLEDs, not the QD-WLED as widely expected, make strong candidates for excellent color rendition, especially in the low color temperature range, for replacing current pc-WLEDs in the future.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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  7. W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
    [Crossref]
  8. W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
    [Crossref]
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    [Crossref]
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    [Crossref]
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  17. Y. Ohno, “Spectral design considerations for white LED color rendering,” Opt. Eng. 44(11), 111302 (2005).
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    [Crossref]
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    [Crossref]
  23. G. X. He and L. H. Zheng, “White-light LED clusters with high color rendering,” Opt. Lett. 35(17), 2955–2957 (2010).
    [Crossref]

2018 (1)

2017 (4)

F. Zhang, H. Xu, and Z. Wang, “Optimizing spectral compositions of multichannel LED light sources by IES color fidelity index and luminous efficacy of radiation,” Appl. Opt. 56(7), 1962–1971 (2017).
[Crossref]

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. L. Zhang, W. Yang, P. Zhong, S. L. Mei, G. L. Zhang, G. P. Chen, G. X. He, and R. Q. Guo, “Spectral optimization of color temperature tunable white LEDs based on perovskite quantum dots for ultrahigh color rendition,” Opt. Mater. Express 7(9), 3065–3067 (2017).
[Crossref]

D. Y. Lin, P. Zhong, and G. X. He, “Color temperature tunable white LED cluster with color rendering index above 98,” IEEE Photon. Technol. Lett. 29(12), 1050–1053 (2017).
[Crossref]

2016 (1)

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

2014 (2)

G. X. 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]

G. X. He and J. Tang, “Spectral optimization of phosphor-coated white LEDs for color rendering and luminous efficacy,” IEEE Photon. Technol. Lett. 26(14), 1450–1453 (2014).
[Crossref]

2012 (2)

P. Zhong, G. X. He, and M. H. Zhang, “Optimal spectra of white light-emitting diodes using quantum dot nanophosphors,” Opt. Express 20(8), 9122–9134 (2012).
[Crossref]

Y. Lin, Y. L. Gao, Y. J. Lu, L. H. Zhu, Y. Zhang, and Z. Chen, “Study of temperature sensitive optical parameters and junction temperature determination of light-emitting diodes,” Appl. Phys. Lett. 100(20), 202108 (2012).
[Crossref]

2011 (1)

2010 (1)

2008 (1)

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 (1)

2006 (1)

N. Sándor and J. Schanda, “Visual colour rendering based on colour difference evaluations,” Light. Res. Technol. 38(3), 225–239 (2006).
[Crossref]

2005 (1)

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

2002 (1)

N. Narendran and L. Deng, “Color rendering properties of LED light sources,” Proc. SPIE 4776, 61–67 (2002).
[Crossref]

2001 (1)

S. J. Rosenthal, “Bar-coding biomolecules with fluorescent nanocrystals,” Nat. Biotechnol. 19(7), 621–622 (2001).
[Crossref]

Chen, G. P.

Chen, Q. H.

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

Chen, Z.

Y. Lin, Y. L. Gao, Y. J. Lu, L. H. Zhu, Y. Zhang, and Z. Chen, “Study of temperature sensitive optical parameters and junction temperature determination of light-emitting diodes,” Appl. Phys. Lett. 100(20), 202108 (2012).
[Crossref]

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]

Contreras, U.

Deng, L.

N. Narendran and L. Deng, “Color rendering properties of LED light sources,” Proc. SPIE 4776, 61–67 (2002).
[Crossref]

Ding, K.

Gao, W. J.

Gao, Y. L.

Y. Lin, Y. L. Gao, Y. J. Lu, L. H. Zhu, Y. Zhang, and Z. Chen, “Study of temperature sensitive optical parameters and junction temperature determination of light-emitting diodes,” Appl. Phys. Lett. 100(20), 202108 (2012).
[Crossref]

Guo, R. Q.

W. L. Zhang, W. Yang, P. Zhong, S. L. Mei, G. L. Zhang, G. P. Chen, G. X. He, and R. Q. Guo, “Spectral optimization of color temperature tunable white LEDs based on perovskite quantum dots for ultrahigh color rendition,” Opt. Mater. Express 7(9), 3065–3067 (2017).
[Crossref]

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[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]

He, G. X.

W. J. Gao, K. Ding, G. X. He, and P. Zhong, “Color temperature tunable phosphor-coated white LEDs with excellent photometric and colorimetric performances,” Appl. Opt. 57(31), 9322–9327 (2018).
[Crossref]

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. L. Zhang, W. Yang, P. Zhong, S. L. Mei, G. L. Zhang, G. P. Chen, G. X. He, and R. Q. Guo, “Spectral optimization of color temperature tunable white LEDs based on perovskite quantum dots for ultrahigh color rendition,” Opt. Mater. Express 7(9), 3065–3067 (2017).
[Crossref]

D. Y. Lin, P. Zhong, and G. X. He, “Color temperature tunable white LED cluster with color rendering index above 98,” IEEE Photon. Technol. Lett. 29(12), 1050–1053 (2017).
[Crossref]

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

G. X. He and J. Tang, “Spectral optimization of phosphor-coated white LEDs for color rendering and luminous efficacy,” IEEE Photon. Technol. Lett. 26(14), 1450–1453 (2014).
[Crossref]

G. X. 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]

P. Zhong, G. X. He, and M. H. Zhang, “Optimal spectra of white light-emitting diodes using quantum dot nanophosphors,” Opt. Express 20(8), 9122–9134 (2012).
[Crossref]

G. X. He and H. F. 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]

G. X. He and L. H. Zheng, “White-light LED clusters with high color rendering,” Opt. Lett. 35(17), 2955–2957 (2010).
[Crossref]

Lin, D. Y.

D. Y. Lin, P. Zhong, and G. X. He, “Color temperature tunable white LED cluster with color rendering index above 98,” IEEE Photon. Technol. Lett. 29(12), 1050–1053 (2017).
[Crossref]

Lin, Y.

Y. Lin, Y. L. Gao, Y. J. Lu, L. H. Zhu, Y. Zhang, and Z. Chen, “Study of temperature sensitive optical parameters and junction temperature determination of light-emitting diodes,” Appl. Phys. Lett. 100(20), 202108 (2012).
[Crossref]

Lu, Y. J.

Y. Lin, Y. L. Gao, Y. J. Lu, L. H. Zhu, Y. Zhang, and Z. Chen, “Study of temperature sensitive optical parameters and junction temperature determination of light-emitting diodes,” Appl. Phys. Lett. 100(20), 202108 (2012).
[Crossref]

Mei, S. L.

W. L. Zhang, W. Yang, P. Zhong, S. L. Mei, G. L. Zhang, G. P. Chen, G. X. He, and R. Q. Guo, “Spectral optimization of color temperature tunable white LEDs based on perovskite quantum dots for ultrahigh color rendition,” Opt. Mater. Express 7(9), 3065–3067 (2017).
[Crossref]

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

Mereno, I.

Narendran, N.

N. Narendran and L. Deng, “Color rendering properties of LED light sources,” Proc. SPIE 4776, 61–67 (2002).
[Crossref]

Ohno, Y.

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

Rosenthal, S. J.

S. J. Rosenthal, “Bar-coding biomolecules with fluorescent nanocrystals,” Nat. Biotechnol. 19(7), 621–622 (2001).
[Crossref]

Sándor, N.

N. Sándor and J. Schanda, “Visual colour rendering based on colour difference evaluations,” Light. Res. Technol. 38(3), 225–239 (2006).
[Crossref]

Schanda, J.

N. Sándor and J. Schanda, “Visual colour rendering based on colour difference evaluations,” Light. Res. Technol. 38(3), 225–239 (2006).
[Crossref]

Tang, J.

G. X. 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]

G. X. He and J. Tang, “Spectral optimization of phosphor-coated white LEDs for color rendering and luminous efficacy,” IEEE Photon. Technol. Lett. 26(14), 1450–1453 (2014).
[Crossref]

Wang, Z.

Xu, H.

Yan, H. F.

Yang, W.

W. L. Zhang, W. Yang, P. Zhong, S. L. Mei, G. L. Zhang, G. P. Chen, G. X. He, and R. Q. Guo, “Spectral optimization of color temperature tunable white LEDs based on perovskite quantum dots for ultrahigh color rendition,” Opt. Mater. Express 7(9), 3065–3067 (2017).
[Crossref]

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

Zhang, F.

Zhang, G. L.

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. L. Zhang, W. Yang, P. Zhong, S. L. Mei, G. L. Zhang, G. P. Chen, G. X. He, and R. Q. Guo, “Spectral optimization of color temperature tunable white LEDs based on perovskite quantum dots for ultrahigh color rendition,” Opt. Mater. Express 7(9), 3065–3067 (2017).
[Crossref]

Zhang, M. H.

Zhang, W. L.

W. L. Zhang, W. Yang, P. Zhong, S. L. Mei, G. L. Zhang, G. P. Chen, G. X. He, and R. Q. Guo, “Spectral optimization of color temperature tunable white LEDs based on perovskite quantum dots for ultrahigh color rendition,” Opt. Mater. Express 7(9), 3065–3067 (2017).
[Crossref]

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

Zhang, Y.

Y. Lin, Y. L. Gao, Y. J. Lu, L. H. Zhu, Y. Zhang, and Z. Chen, “Study of temperature sensitive optical parameters and junction temperature determination of light-emitting diodes,” Appl. Phys. Lett. 100(20), 202108 (2012).
[Crossref]

Zheng, L. H.

Zhong, P.

Zhu, J. T.

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

Zhu, L. H.

Y. Lin, Y. L. Gao, Y. J. Lu, L. H. Zhu, Y. Zhang, and Z. Chen, “Study of temperature sensitive optical parameters and junction temperature determination of light-emitting diodes,” Appl. Phys. Lett. 100(20), 202108 (2012).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

Y. Lin, Y. L. Gao, Y. J. Lu, L. H. Zhu, Y. Zhang, and Z. Chen, “Study of temperature sensitive optical parameters and junction temperature determination of light-emitting diodes,” Appl. Phys. Lett. 100(20), 202108 (2012).
[Crossref]

Appl. Surf. Sci. (1)

W. Yang, G. X. He, S. L. Mei, J. T. Zhu, W. L. Zhang, Q. H. Chen, G. L. Zhang, and R. Q. Guo, “Controllable synthesis of dual emissive Ag:InP/ZnS quantum dots with high fluorescence quantum yield,” Appl. Surf. Sci. 423, 686–694 (2017).
[Crossref]

IEEE Photon. J. (1)

W. Yang, P. Zhong, S. L. Mei, Q. H. Chen, W. L. Zhang, J. T. Zhu, R. Q. Guo, and G. X. He, “Photometric optimization of color temperature tunable quantum dots converted white LEDs for excellent color rendition,” IEEE Photon. J. 8(5), 1–11 (2016).
[Crossref]

IEEE Photon. Technol. Lett. (2)

G. X. He and J. Tang, “Spectral optimization of phosphor-coated white LEDs for color rendering and luminous efficacy,” IEEE Photon. Technol. Lett. 26(14), 1450–1453 (2014).
[Crossref]

D. Y. Lin, P. Zhong, and G. X. He, “Color temperature tunable white LED cluster with color rendering index above 98,” IEEE Photon. Technol. Lett. 29(12), 1050–1053 (2017).
[Crossref]

J. Heuristics (1)

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]

Light. Res. Technol. (1)

N. Sándor and J. Schanda, “Visual colour rendering based on colour difference evaluations,” Light. Res. Technol. 38(3), 225–239 (2006).
[Crossref]

Nat. Biotechnol. (1)

S. J. Rosenthal, “Bar-coding biomolecules with fluorescent nanocrystals,” Nat. Biotechnol. 19(7), 621–622 (2001).
[Crossref]

Opt. Eng. (1)

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

Opt. Express (3)

Opt. Lett. (2)

Opt. Mater. Express (1)

Proc. SPIE (1)

N. Narendran and L. Deng, “Color rendering properties of LED light sources,” Proc. SPIE 4776, 61–67 (2002).
[Crossref]

Other (5)

Illuminating Engineering Society of North America, IES method for evaluating light source color rendition, IES TM-30-15, (IESNA, 2015).

Commission Internationale de l’Eclairage, CIE 224:2017 CIE 2017 Colour Fidelity Index for accurate scientific use, January 4, 2017 (CIE Central Bureau, Vienna, 2017).

Commission Internationale de l’Eclairage, “Method of measuring and specifying colour rendering properties of light sources,” CIE 13.3-1995 (CIE Central Bureau, Vienna, 1995).

Commission Internationale de l’Eclairage, “ILV: International Lighting Vocabulary,” CIE S 017/E: 2011, (CIECentral Bureau, Vienna, 2011).

American National Standard, American National Standard for Electric Lamps, ANSIC78.377 (American National Standards Institute, 2008).

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Figures (4)

Fig. 1.
Fig. 1. SPDs of the optimal CCT tunable pc/R-WLEDs with Rf ≥ 97 at CCTs of 2700 – 6500 K (Duv = 0).
Fig. 2.
Fig. 2. Rf, hues for 16 hue bins of the optimal CCT tunable pc/R-WLEDs with Rf ≥ 97 at CCTs of 2700- 6500 K (Duv = 0).
Fig. 3.
Fig. 3. Rf, hues for 16 hue bins of four real pc/R-WLEDs at CCTs of 2969 K, 3955 K, 5034 K, and 6558 K, respectively.
Fig. 4.
Fig. 4. SPDs of four real pc/R-WLEDs consisting of different pc-LEDs under IF,pcs of 117 mA, 178 mA, 238 mA, and 316 mA, as well as a AlGaInP red LED under the forward current of 50 mA at CCTs of 2969 K, 3955 K, 5034 K, and 6558 K, respectively. The inset shows photographs of white light of the real pc/R WLED from the integrating sphere with a increase in the CCT from top to bottom.

Tables (3)

Tables Icon

Table 1. qs, ks, Φes of each color component, Ras, Rfs, Rgs, Rf, skins, LERs, and Les of the optimal CCT tunable pc/R-WLEDs at CCTs of 2700 K to 6500 K for Re,b = Re,r = 60% and Qe = 90%.

Tables Icon

Table 2. Luminous efficacy ratios of the pc/R-WLEDs with the pc-WLEDs and QD-WLEDs [16], LEpc/R/LEpc and LEpc/R/LEQD, for Qe = 90% at CCTs of 2700 K to 6500 K under Rf ≥ 97.

Tables Icon

Table 3. Photometric and colorimetric performances of four real pc/R-WLEDs consisting of different pc-LED and an AlGaInP red LED under the forward current of 50 mA at CCTs of 2969 K, 3955 K, 5034 K, and 6558 K, respectively.

Equations (9)

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

S pc/R ( λ ) = k pc S pc ( λ ) + k r S ( λ , λ r , Δ λ r )
S pc ( λ ) = q b S ( λ , λ b , Δ λ b ) + q g S ( λ , λ g , Δ λ g ) + q y S ( λ , λ y , Δ λ y )
N p = k pc q g hc λ S ( λ , λ g , Δ λ g ) λ d λ + k pc q y hc λ S ( λ , λ y , Δ λ y ) λ d λ
N ab = q ab hc λ S ( λ , λ b , Δ λ b ) λ d λ
q ab = k pc q g λ S ( λ , λ g , Δ λ g ) λ d λ + k pc q y λ S ( λ , λ y , Δ λ y ) λ d λ Q e λ S ( λ , λ b , Δ λ b ) λ d λ
R e,b = 1 P in,b λ ( k pc q b + q ab ) S ( λ , λ b , Δ λ b ) d λ
R e,r = 1 P in,r λ k r S ( λ , λ r , Δ λ r ) d λ
LE = 683 ( P inb + P inR ) λ V ( λ ) S pc / R ( λ ) d λ = 683 λ V ( λ ) S pc / R ( λ ) d λ 1 R e , b λ ( k pc q b + q ab ) S ( λ , λ b , Δ λ b ) d λ + 1 R e , r λ k r S ( λ , λ r , Δ λ r ) d λ
F = j = 1 8 LE j ( k r , j , λ b , λ g , λ y , λ r , Δ λ b , Δ λ g , Δ λ y , Δ λ r ) ( for R f 97 , D uv = 0 )

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