Abstract

Recently, a color appearance model, CAM18sl, has been published. The model can predict the color perception (hue, colorfulness, brightness) of self-luminous stimuli seen against neutral backgrounds varying in luminance. In this paper, the applicability of CAM18sl to situations different from the one for which it was originally developed is explored. The brightness perception predicted by this model (expressed in “bright”) is compared with the outcome of the CIE Unified Glare Rating (UGR) for luminaires, the limiting luminance values for Variable Message Signs as indicated in the European standard for outdoor situations, the visual gloss (VG) formula to characterize the gloss of objects, the CIE grey-scale calculation for self-luminous devices, and the predicted brightness value of illuminated objects according to CIECAM02. Although the application domains mentioned above are very distinct, it appears that the predicted brightness perception of the CAM18sl model correlates well with the outcome of the particular and dedicated metrics. It seems that, for brightness perception, CAM18sl can be considered as a general model applicable for a wide range of applications. This could lead to a reduction of a number of application-specific metrics.

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

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References

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  27. H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).
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2018 (3)

G. H. Scheir, M. Donners, L. Geerdinck, M. Vissenberg, P. Hanselaer, and W. R. Ryckaert, “A psychophysical model for visual discomfort based on receptive fields,” Light. Res. Technol. 50(2), 205–217 (2018).
[Crossref]

Y. Yang, R. M. Luo, and W. J. Huang, “Assessing glare, Part 3: Glare sources having different colours,” Light. Res. Technol. 50(4), 596–615 (2018).
[Crossref]

S. Hermans, K. A. G. Smet, and P. Hanselaer, “Color appearance model for self-luminous stimuli,” J. Opt. Soc. Am. A 35(12), 2000–2009 (2018).
[Crossref] [PubMed]

2017 (7)

K. A. G. Smet, Q. Zhai, M. R. Luo, and P. Hanselaer, “Study of chromatic adaptation using memory color matches, Part I: neutral illuminants,” Opt. Express 25(7), 7732–7748 (2017).
[Crossref] [PubMed]

K. A. G. Smet, Q. Zhai, M. R. Luo, and P. Hanselaer, “Study of chromatic adaptation using memory color matches, Part II: colored illuminants,” Opt. Express 25(7), 8350–8365 (2017).
[Crossref] [PubMed]

G. H. Scheir, P. Hanselaer, and W. Rita Ryckaert, “Defining the Actual Luminous Surface in the Unified Glare Rating,” Leukos 13(4), 201–210 (2017).
[Crossref]

Y. Yang, M. R. Luo, and S. N. Ma, “Assessing glare. Part 2: Modifying Unified Glare Rating for uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(6), 727–742 (2017).
[Crossref]

Y. Yang, R. M. Luo, S. N. Ma, and X. Y. Liu, “Assessing glare. Part 1: Comparing uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(2), 195–210 (2017).
[Crossref]

P.-L. Sun, H.-C. Li, and M. Ronnier Luo, “Background luminance and subtense affects color appearance,” Color Res. Appl. 42(4), 440–449 (2017).
[Crossref]

W. J. Huang, Y. Yang, and M. R. Luo, “Verification of the CAM15u colour appearance model and the QUGR glare model,” Light. Res. Technol. 51, 1–13 (2017).

2016 (1)

K. A. G. Smet, A. David, and L. Whitehead, “Why Color Space Uniformity and Sample Set Spectral Uniformity Are Essential for Color Rendering Measures,” Leukos 12(1-2), 39–50 (2016).
[Crossref]

2015 (1)

2011 (1)

2004 (1)

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77(2), 137–157 (2004).
[Crossref]

1992 (1)

P. Whittle, “Brightness, discriminability and the “crispening effect”,” Vision Res. 32(8), 1493–1507 (1992).
[Crossref] [PubMed]

1913 (1)

V. L. Michaelis, M. L. Maud Menten, R. S. Goody, and K. A. Johnson, “Die Kinetik der Invertinwirkung The Kinetics of Invertase Action,” Biochem. Z. 49, 333–369 (1913).

Cui, G.

C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, and M. Pointer, “A Revision of CIECAM02 and its CAT and UCS,” Color Imaging Conf.1, 208–212 (2016).
[Crossref]

David, A.

K. A. G. Smet, A. David, and L. Whitehead, “Why Color Space Uniformity and Sample Set Spectral Uniformity Are Essential for Color Rendering Measures,” Leukos 12(1-2), 39–50 (2016).
[Crossref]

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Donners, M.

G. H. Scheir, M. Donners, L. Geerdinck, M. Vissenberg, P. Hanselaer, and W. R. Ryckaert, “A psychophysical model for visual discomfort based on receptive fields,” Light. Res. Technol. 50(2), 205–217 (2018).
[Crossref]

Dutré, P.

Fairchild, M. D.

N. Moroney, M. D. Fairchild, R. W. G. Hunt, C. Li, M. R. Luo, and T. Newman, “The CIECAM02 color appearance model,” IS&T/SID Tenth Color Imaging Conference 23 (Society for Imaging Science and Technology, 2002).

Fuchida, T.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Geerdinck, L.

G. H. Scheir, M. Donners, L. Geerdinck, M. Vissenberg, P. Hanselaer, and W. R. Ryckaert, “A psychophysical model for visual discomfort based on receptive fields,” Light. Res. Technol. 50(2), 205–217 (2018).
[Crossref]

Goody, R. S.

V. L. Michaelis, M. L. Maud Menten, R. S. Goody, and K. A. Johnson, “Die Kinetik der Invertinwirkung The Kinetics of Invertase Action,” Biochem. Z. 49, 333–369 (1913).

Hanselaer, P.

Hashimoto, K.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Heidel, G.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Hermans, S.

Huang, W. J.

Y. Yang, R. M. Luo, and W. J. Huang, “Assessing glare, Part 3: Glare sources having different colours,” Light. Res. Technol. 50(4), 596–615 (2018).
[Crossref]

W. J. Huang, Y. Yang, and M. R. Luo, “Verification of the CAM15u colour appearance model and the QUGR glare model,” Light. Res. Technol. 51, 1–13 (2017).

Hunt, R. W. G.

N. Moroney, M. D. Fairchild, R. W. G. Hunt, C. Li, M. R. Luo, and T. Newman, “The CIECAM02 color appearance model,” IS&T/SID Tenth Color Imaging Conference 23 (Society for Imaging Science and Technology, 2002).

Igawa, N.

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77(2), 137–157 (2004).
[Crossref]

Johnson, K. A.

V. L. Michaelis, M. L. Maud Menten, R. S. Goody, and K. A. Johnson, “Die Kinetik der Invertinwirkung The Kinetics of Invertase Action,” Biochem. Z. 49, 333–369 (1913).

Jordan, W.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Jost-Boissard, S.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Kobayashi, S.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Koga, Y.

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77(2), 137–157 (2004).
[Crossref]

Kotani, T.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Leloup, F. B.

Li, C.

N. Moroney, M. D. Fairchild, R. W. G. Hunt, C. Li, M. R. Luo, and T. Newman, “The CIECAM02 color appearance model,” IS&T/SID Tenth Color Imaging Conference 23 (Society for Imaging Science and Technology, 2002).

C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, and M. Pointer, “A Revision of CIECAM02 and its CAT and UCS,” Color Imaging Conf.1, 208–212 (2016).
[Crossref]

Li, H.-C.

P.-L. Sun, H.-C. Li, and M. Ronnier Luo, “Background luminance and subtense affects color appearance,” Color Res. Appl. 42(4), 440–449 (2017).
[Crossref]

Li, Z.

C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, and M. Pointer, “A Revision of CIECAM02 and its CAT and UCS,” Color Imaging Conf.1, 208–212 (2016).
[Crossref]

Liu, X. Y.

Y. Yang, R. M. Luo, S. N. Ma, and X. Y. Liu, “Assessing glare. Part 1: Comparing uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(2), 195–210 (2017).
[Crossref]

Luo, M. R.

Y. Yang, M. R. Luo, and S. N. Ma, “Assessing glare. Part 2: Modifying Unified Glare Rating for uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(6), 727–742 (2017).
[Crossref]

W. J. Huang, Y. Yang, and M. R. Luo, “Verification of the CAM15u colour appearance model and the QUGR glare model,” Light. Res. Technol. 51, 1–13 (2017).

K. A. G. Smet, Q. Zhai, M. R. Luo, and P. Hanselaer, “Study of chromatic adaptation using memory color matches, Part II: colored illuminants,” Opt. Express 25(7), 8350–8365 (2017).
[Crossref] [PubMed]

K. A. G. Smet, Q. Zhai, M. R. Luo, and P. Hanselaer, “Study of chromatic adaptation using memory color matches, Part I: neutral illuminants,” Opt. Express 25(7), 7732–7748 (2017).
[Crossref] [PubMed]

C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, and M. Pointer, “A Revision of CIECAM02 and its CAT and UCS,” Color Imaging Conf.1, 208–212 (2016).
[Crossref]

N. Moroney, M. D. Fairchild, R. W. G. Hunt, C. Li, M. R. Luo, and T. Newman, “The CIECAM02 color appearance model,” IS&T/SID Tenth Color Imaging Conference 23 (Society for Imaging Science and Technology, 2002).

Luo, R.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Luo, R. M.

Y. Yang, R. M. Luo, and W. J. Huang, “Assessing glare, Part 3: Glare sources having different colours,” Light. Res. Technol. 50(4), 596–615 (2018).
[Crossref]

Y. Yang, R. M. Luo, S. N. Ma, and X. Y. Liu, “Assessing glare. Part 1: Comparing uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(2), 195–210 (2017).
[Crossref]

Ma, S. N.

Y. Yang, R. M. Luo, S. N. Ma, and X. Y. Liu, “Assessing glare. Part 1: Comparing uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(2), 195–210 (2017).
[Crossref]

Y. Yang, M. R. Luo, and S. N. Ma, “Assessing glare. Part 2: Modifying Unified Glare Rating for uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(6), 727–742 (2017).
[Crossref]

Matsuzawa, T.

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77(2), 137–157 (2004).
[Crossref]

Maud Menten, M. L.

V. L. Michaelis, M. L. Maud Menten, R. S. Goody, and K. A. Johnson, “Die Kinetik der Invertinwirkung The Kinetics of Invertase Action,” Biochem. Z. 49, 333–369 (1913).

Melgosa, M.

C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, and M. Pointer, “A Revision of CIECAM02 and its CAT and UCS,” Color Imaging Conf.1, 208–212 (2016).
[Crossref]

Michaelis, V. L.

V. L. Michaelis, M. L. Maud Menten, R. S. Goody, and K. A. Johnson, “Die Kinetik der Invertinwirkung The Kinetics of Invertase Action,” Biochem. Z. 49, 333–369 (1913).

Mizokami, Y.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Moroney, N.

N. Moroney, M. D. Fairchild, R. W. G. Hunt, C. Li, M. R. Luo, and T. Newman, “The CIECAM02 color appearance model,” IS&T/SID Tenth Color Imaging Conference 23 (Society for Imaging Science and Technology, 2002).

Nakamura, H.

N. Igawa, Y. Koga, T. Matsuzawa, and H. Nakamura, “Models of sky radiance distribution and sky luminance distribution,” Sol. Energy 77(2), 137–157 (2004).
[Crossref]

Newman, T.

N. Moroney, M. D. Fairchild, R. W. G. Hunt, C. Li, M. R. Luo, and T. Newman, “The CIECAM02 color appearance model,” IS&T/SID Tenth Color Imaging Conference 23 (Society for Imaging Science and Technology, 2002).

Pointer, M.

C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, and M. Pointer, “A Revision of CIECAM02 and its CAT and UCS,” Color Imaging Conf.1, 208–212 (2016).
[Crossref]

Pointer, M. R.

Rita Ryckaert, W.

G. H. Scheir, P. Hanselaer, and W. Rita Ryckaert, “Defining the Actual Luminous Surface in the Unified Glare Rating,” Leukos 13(4), 201–210 (2017).
[Crossref]

Ronnier Luo, M.

P.-L. Sun, H.-C. Li, and M. Ronnier Luo, “Background luminance and subtense affects color appearance,” Color Res. Appl. 42(4), 440–449 (2017).
[Crossref]

Ryckaert, W. R.

G. H. Scheir, M. Donners, L. Geerdinck, M. Vissenberg, P. Hanselaer, and W. R. Ryckaert, “A psychophysical model for visual discomfort based on receptive fields,” Light. Res. Technol. 50(2), 205–217 (2018).
[Crossref]

M. Withouck, K. A. Smet, W. R. Ryckaert, and P. Hanselaer, “Experimental driven modelling of the color appearance of unrelated self-luminous stimuli: CAM15u,” Opt. Express 23(9), 12045–12064 (2015).
[Crossref] [PubMed]

Scheir, G. H.

G. H. Scheir, M. Donners, L. Geerdinck, M. Vissenberg, P. Hanselaer, and W. R. Ryckaert, “A psychophysical model for visual discomfort based on receptive fields,” Light. Res. Technol. 50(2), 205–217 (2018).
[Crossref]

G. H. Scheir, P. Hanselaer, and W. Rita Ryckaert, “Defining the Actual Luminous Surface in the Unified Glare Rating,” Leukos 13(4), 201–210 (2017).
[Crossref]

Smet, K. A.

Smet, K. A. G.

Steffy, G. R.

G. R. Steffy, Architectural Lighting Design (John Wiley, 2002).

Sun, P.-L.

P.-L. Sun, H.-C. Li, and M. Ronnier Luo, “Background luminance and subtense affects color appearance,” Color Res. Appl. 42(4), 440–449 (2017).
[Crossref]

Vissenberg, M.

G. H. Scheir, M. Donners, L. Geerdinck, M. Vissenberg, P. Hanselaer, and W. R. Ryckaert, “A psychophysical model for visual discomfort based on receptive fields,” Light. Res. Technol. 50(2), 205–217 (2018).
[Crossref]

Wang, Z.

C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, and M. Pointer, “A Revision of CIECAM02 and its CAT and UCS,” Color Imaging Conf.1, 208–212 (2016).
[Crossref]

Whitehead, L.

K. A. G. Smet, A. David, and L. Whitehead, “Why Color Space Uniformity and Sample Set Spectral Uniformity Are Essential for Color Rendering Measures,” Leukos 12(1-2), 39–50 (2016).
[Crossref]

Whittle, P.

P. Whittle, “Brightness, discriminability and the “crispening effect”,” Vision Res. 32(8), 1493–1507 (1992).
[Crossref] [PubMed]

Withouck, M.

Xu, Y.

C. Li, Z. Li, Z. Wang, Y. Xu, M. R. Luo, G. Cui, M. Melgosa, and M. Pointer, “A Revision of CIECAM02 and its CAT and UCS,” Color Imaging Conf.1, 208–212 (2016).
[Crossref]

Yaguchi, H.

H. Yaguchi, A. David, T. Fuchida, K. Hashimoto, G. Heidel, W. Jordan, S. Jost-Boissard, S. Kobayashi, T. Kotani, R. Luo, and Y. Mizokami, CIE 2017 Colour Fidelity Index for Accurate Scientific Use (CIE Central Bureau, 2017).

Yang, Y.

Y. Yang, R. M. Luo, and W. J. Huang, “Assessing glare, Part 3: Glare sources having different colours,” Light. Res. Technol. 50(4), 596–615 (2018).
[Crossref]

Y. Yang, R. M. Luo, S. N. Ma, and X. Y. Liu, “Assessing glare. Part 1: Comparing uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(2), 195–210 (2017).
[Crossref]

Y. Yang, M. R. Luo, and S. N. Ma, “Assessing glare. Part 2: Modifying Unified Glare Rating for uniform and non-uniform LED luminaires,” Light. Res. Technol. 49(6), 727–742 (2017).
[Crossref]

W. J. Huang, Y. Yang, and M. R. Luo, “Verification of the CAM15u colour appearance model and the QUGR glare model,” Light. Res. Technol. 51, 1–13 (2017).

Zhai, Q.

Biochem. Z. (1)

V. L. Michaelis, M. L. Maud Menten, R. S. Goody, and K. A. Johnson, “Die Kinetik der Invertinwirkung The Kinetics of Invertase Action,” Biochem. Z. 49, 333–369 (1913).

Color Res. Appl. (1)

P.-L. Sun, H.-C. Li, and M. Ronnier Luo, “Background luminance and subtense affects color appearance,” Color Res. Appl. 42(4), 440–449 (2017).
[Crossref]

J. Opt. Soc. Am. A (2)

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Figures (10)

Fig. 1
Fig. 1 The luminance grid used for the comparison between CAM18sl and the UGR formula. L10,B refers to the to the luminance value of the background; L10,S refers to the luminance value of the stimulus. Red stars indicate the range in which both models have been developed; black circles are scenes outside of the range for which CAM18sl was originally developed.
Fig. 2
Fig. 2 The CIE UGR formula (left) and the brightness prediction of CAM18sl in bright (right), applied for different luminance levels of stimulus and background.
Fig. 3
Fig. 3 CIE UGR formula and the predicted brightness values of CAM18sl in bright, for the luminance levels of stimulus and background shown in Fig. 1. Red stars indicate the range in which both models have been developed; black circles are scenes outside of the range for which CAM18sl was originally developed.
Fig. 4
Fig. 4 Brightness perception (in bright) as predicted by CAM18sl for color class C2 (red, orange, yellow, white, green and blue) as a function of the background luminance. Error bars are the minimum and maximum brightness values of those obtained when selecting the corners of the allowed color coordinate regions (C2).
Fig. 5
Fig. 5 Brightness perception (in bright) as predicted by CAM18sl for color class C2 (red, orange, yellow, white, green and blue) as a function of the average sky luminance. Error bars are the minimum and maximum brightness values of those obtained when selecting the corners of the allowed color coordinate regions (C2).
Fig. 6
Fig. 6 The luminance grid used for the comparison between CAM18sl and the VG formula. Red stars indicate the scenes for which both models were developed; black circles are scenes outside of the range for which VG was originally developed.
Fig. 7
Fig. 7 VG and the brightness prediction of CAM18sl in bright, applied for different luminance levels of stimulus and background (red stars: common scenes; black circles: scenes outside of the range for which VG was originally developed).
Fig. 8
Fig. 8 Brightness prediction of CAM18sl against the NEPD. Black, blue and red stars indicate stimuli with a 500, 75 and 10 cd/m2 luminance level seen against backgrounds with luminance levels varying between 10 and 500 cd/m2.
Fig. 9
Fig. 9 Luminance values as a function of the CIE 1976 saturation values of the central self-luminous stimuli used to develop the CAM18sl model (red stars) and of the 99 reflective test-colors (black stars) illuminated with equal energy white (10 to 2000 lux).
Fig. 10
Fig. 10 Brightness prediction of CAM18sl in bright as a function of the brightness prediction by CIECAM02. Red circles: achromatic neutral stimuli; red/blue/green stars: saturated red/blue/green stimuli.

Tables (1)

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Table 1 Minimum luminance levels (Le(min)) in cd/m2 of luminance class L3 of each specific color (C2)

Equations (11)

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ρ=676.7 390 830 L e,λ ( λ ) l ¯ 10 ( λ )dλ γ=794.0 390 830 L e,λ ( λ ) m ¯ 10 ( λ )dλ β=1461.5 390 830 L e,λ ( λ ) s ¯ 10 ( λ )dλ
[ ρ c γ c β c ]=[ ρ wr ρ B 0 0 0 γ wr γ B 0 0 0 β wr β B ][ ρ γ β ]
ρ c,a = ρ c 0.58 ρ c 0.58 + (291.20+71.8 α wr 0.78 ) 0.58 γ c,a = γ c 0.58 γ c 0.58 + (291.20+71.8 α wr 0.78 ) 0.58 β c,a = β c 0.58 β c 0.58 + (291.20+71.8 α wr 0.78 ) 0.58
a=0.63( ρ c,a 12 11 γ c,a + β c,a 11 ) b=0.12( ρ c,a + γ c,a 2 β c,a )
M=3260 ( a 2 + b 2 )
Q=0.937( ( 2 ρ c,a + γ c,a + 1 20 β c,a )+0.0024 M 1.09 )
UGR=8log[ 0.25 L b i L i 2 ω i p i 2 ]
L= ρ π E
VG=28 L im 1/3 21 L b 1/3
NEPD=8.22log(1+(0.26+0.3095 L B )(1k)(L L b )/(0,39+ L b )) (forL> L b )
NEPD=7.07log(1+6.58(1k)( L b L)/(0,39+L+k( L b L))) ( forL L b )

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