Abstract

The spectral power distribution of white light required to maximize luminous efficiency and the color-rendering index is approximated by additive combination of three spectral lines near 450, 540, and 610 nm. The two wavelength regions near 500 and 580 nm are disadvantageous. These results are related to the color-mixture functions of human color vision. Three functions that indicate the effectiveness of red, green, and blue light for composing high-performance white light are shown.

© 1971 Optical Society of America

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References

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  1. “IES Subcommittee on Color Rendering,” Illum. Engr. 57, 471 (1962); Comm. Intern. de l’Eclairage (CIE), Publ. CIE No. 13 (E-1.3.2.), Bur. Central de la CIE, 57, rue Cuvier, Paris, France (1965).
  2. D. L. MacAdam, J. Opt. Soc. Am. 40, 120 (1950).
    [Crossref]
  3. H. W. Leverenz, J. Opt. Soc. Am. 30, 309 (1940).
    [Crossref]
  4. H. F. Ivey, J. Opt. Soc. Am. 53, 1185 (1963).
    [Crossref]
  5. W. D. Wright, Trans. Opt. Soc. (London) 30, 141 (1928).
    [Crossref]
  6. W. D. Wright, Researches on Normal and Defective Color Vision(Kimpton, London, 1946).
  7. J. M. Enoch and W. S. Stiles, Opt. Acta 8, 329 (1961).
    [Crossref]
  8. W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
    [Crossref]
  9. L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 45, 602 (1955).
    [Crossref] [PubMed]
  10. E. Q. Adams, J. Opt. Soc. Am. 32, 168 (1942).
    [Crossref]
  11. J. L. Ouweltjes, Die Farbe 9, 207 (1960).
  12. B. T. Barnes, J. Opt. Soc. Am. 47, 1124 (1957).
    [Crossref]
  13. B. H. Crawford, J. Opt. Soc. Am. 49, 1147 (1959).
    [Crossref]
  14. D. B. Judd, in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951), p. 831.
  15. Handbook of Colorimetry (Technology Press, Cambridge, Mass., 1936), p. 35.
  16. A. Wachtel (private communication).

1963 (1)

1962 (1)

“IES Subcommittee on Color Rendering,” Illum. Engr. 57, 471 (1962); Comm. Intern. de l’Eclairage (CIE), Publ. CIE No. 13 (E-1.3.2.), Bur. Central de la CIE, 57, rue Cuvier, Paris, France (1965).

1961 (1)

J. M. Enoch and W. S. Stiles, Opt. Acta 8, 329 (1961).
[Crossref]

1960 (1)

J. L. Ouweltjes, Die Farbe 9, 207 (1960).

1959 (1)

1957 (1)

1955 (1)

1950 (1)

1942 (1)

1940 (1)

1934 (1)

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
[Crossref]

1928 (1)

W. D. Wright, Trans. Opt. Soc. (London) 30, 141 (1928).
[Crossref]

Adams, E. Q.

Barnes, B. T.

Crawford, B. H.

Enoch, J. M.

J. M. Enoch and W. S. Stiles, Opt. Acta 8, 329 (1961).
[Crossref]

Hurvich, L. M.

Ivey, H. F.

Jameson, D.

Judd, D. B.

D. B. Judd, in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951), p. 831.

Leverenz, H. W.

MacAdam, D. L.

Ouweltjes, J. L.

J. L. Ouweltjes, Die Farbe 9, 207 (1960).

Pitt, F. H. G.

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
[Crossref]

Stiles, W. S.

J. M. Enoch and W. S. Stiles, Opt. Acta 8, 329 (1961).
[Crossref]

Wachtel, A.

A. Wachtel (private communication).

Wright, W. D.

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
[Crossref]

W. D. Wright, Trans. Opt. Soc. (London) 30, 141 (1928).
[Crossref]

W. D. Wright, Researches on Normal and Defective Color Vision(Kimpton, London, 1946).

Die Farbe (1)

J. L. Ouweltjes, Die Farbe 9, 207 (1960).

Illum. Engr. (1)

“IES Subcommittee on Color Rendering,” Illum. Engr. 57, 471 (1962); Comm. Intern. de l’Eclairage (CIE), Publ. CIE No. 13 (E-1.3.2.), Bur. Central de la CIE, 57, rue Cuvier, Paris, France (1965).

J. Opt. Soc. Am. (7)

Opt. Acta (1)

J. M. Enoch and W. S. Stiles, Opt. Acta 8, 329 (1961).
[Crossref]

Proc. Phys. Soc. (London) (1)

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 46, 459 (1934).
[Crossref]

Trans. Opt. Soc. (London) (1)

W. D. Wright, Trans. Opt. Soc. (London) 30, 141 (1928).
[Crossref]

Other (4)

W. D. Wright, Researches on Normal and Defective Color Vision(Kimpton, London, 1946).

D. B. Judd, in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951), p. 831.

Handbook of Colorimetry (Technology Press, Cambridge, Mass., 1936), p. 35.

A. Wachtel (private communication).

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Figures (15)

Fig. 1
Fig. 1

Luminosity η vs CRI. Solid curves, two-component SPDs consisting of a blue and a yellow gaussian power distribution, of varying width at half-maximum in nanometers The two components combine to form white light of color temperature 3000 or 4200 K as indicated on the curves. One of the components is specified, for example, 450W50 for a gaussian distribution of peak wavelength 450 nm and 50-nm width at half-maximum. W0 signifies spectral color distributions of zero width. Triangles, commercial lamps designated warm white (3000 K), white (3500 K), cool white (4200 K), and cool white deluxe (4200 K) fluorescent, high-pressure sodium vapor (about 2000 K), and high-pressure mercury vapor (about 6000 K). ⋯· Series of pairs of complementary spectral colors composing white light at 4200 K. – – – – Series of pairs of components, one blue-green near 500 nm and one red, of varying width at half-maximum W in nanometers, composing white light at 4200 K.

Fig. 2
Fig. 2

CRI of white light composed of three spectral colors. The wavelength λ of one spectral color is varied, while that of each of the other two is held at one of 450, 540, and 610 nm. Three color temperatures (chromaticities) of white light are represented and two reference illuminants. ——— 4200 K, Illumn. Engr. reference; ⋯ 4200 K, CIE reference; – – – – 6800 K, CIE reference; — · — · — 2850 K, CIE reference.

Fig. 3
Fig. 3

Luminosity η of white light composed of three spectral colors, varied as in Fig. 2. Two color temperatures of white light are represented.

Fig. 4
Fig. 4

Combined luminosity and CRI of the daylight (6800 K) color of white light of Figs. 2 and 3 composed of three spectral colors whose wavelengths were varied one at a time.

Fig. 5
Fig. 5

Contours of equal luminosity (———) and of equal CRI (– – – –) for white light of color temperature 4200 K composed of three components of gaussian shape in wavelength, each of which varies in peak (or average) wavelength and in width at half-maximum. Abscissa—peak wavelength λP in nanometers. Ordinate—width W at half-maximum in nanometers. The three standard components 450W46, 550W46, and 620W46 are shown as circles. Two of these are held constant (together with the chromaticity of the white light generated by the three components), while the λP and W of the third component are both varied.

Fig. 6
Fig. 6

Curve A, CRI and luminosity of white light of various color temperatures, composed of the spectral colors 450, 540, and 610 nm. – – – – Envelopes of two-component performance as in Fig. 1. ——— Contours of equal figure of merit. Direction of steepest ascent of performance is in a perpendicular direction toward the upper left. ⋯· Approximate envelopes of performance of white lights of indicated color temperature composed of three components obtained by broadening and/or shifting the three specified spectral colors.

Fig. 7
Fig. 7

Watts W of the complementary spectral color required per watt at wavelength λ to generate daylight chromaticity (illuminant C). Purples complementary to the green wavelengths (dashed curve) are synthesized by combinations of spectral colors at 450 and 610 nm.

Fig. 8
Fig. 8

Total watts W of two specified spectral colors of constant wavelengths required per watt at wavelength λ to generate daylight chromaticity (illuminant C). Two of the three wavelengths 450, 540, and 610 nm are constant while the third is varied.

Fig. 9
Fig. 9

Alterations of the chromaticity (x = 0.333, y = 0.333) of the equal-energy SPD by the addition of the same increment of power at successive wavelengths. Scale of the inset is four times that of the surrounding 1931 CIE x,y diagram. See text for discussion of vectors r and R.

Fig. 10
Fig. 10

The function R( x ¯ + y ¯ + z ¯), where R is the vector distance from the white point to the periphery of the color diagram.

Fig. 11
Fig. 11

Difference functions x ¯ - y ¯ - z ¯ , y ¯ - z ¯ - x ¯ , z ¯ - x ¯ - y ¯ from the tristimulus functions x ¯ , y ¯ , z ¯ of the 1931 CIE Standard Observer for a 2° field. Dashed curves, for a 10° field (1964 CIE Supplementary Standard Observer).

Fig. 12
Fig. 12

Comparison of the positive regions of the difference functions (solid) of Fig. 11 to the wavelength dependence data (dashed curves) on color rendition of white light from Fig. 2, 6800 K, vs CIE illuminant C reference light. The curves of CRI are shifted arbitrarily, vertically.

Fig. 13
Fig. 13

Correlation with ρ of CRI, of white light (4200 K) composed of emission from standard blue- and green-emitting phosphors combined with each of 40 red-emitting phosphors.

Fig. 14
Fig. 14

Correlation with ρ of figure of merit, defined as in Fig. 6, in arbitrary units.

Fig. 15
Fig. 15

CRI and luminosity of blue-emitting phosphors (crosses) and blue spectral colors (circles) in combination with standard green and red emissions combining to give white light at 4200 K. ——— Spectral colors of various wavelengths. – – – – Contours of equal bluminosity β.

Tables (1)

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Table I Criteria for high CRI and luminosity.

Equations (9)

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η = y ¯ ( λ ) P ( λ ) d λ / P ( λ ) d λ .
FM = 320 η + CRI .
R ( x ¯ λ + y ¯ λ + z ¯ λ ) ,
R = [ ( x λ - 1 3 ) 2 + ( y λ - 1 3 ) 2 ] 1 2 ,
x = x ¯ / ( x ¯ + y ¯ + z ¯ ) ,             etc . ,
x ¯ - y ¯ - z ¯ y ¯ - x ¯ - z ¯ z ¯ - x ¯ - y ¯
b ¯ = z ¯ = x ¯ - y ¯ , g ¯ = y ¯ - x ¯ - z ¯ , r ¯ = x ¯ - y ¯ - z ¯ ,
β = P b ¯ d λ / P d λ             ( bluminosity ) , γ = P g ¯ d λ / P d λ             ( verdinosity ) , ρ = P r ¯ d λ / P d λ             ( rubinosity ) ,
blumen = 680 β W , verden = 680 γ W , ruben = 680 ρ W ,