Abstract

Natural outdoor illumination daily undergoes large changes in its correlated color temperature (CCT), yet existing equations for calculating CCT from chromaticity coordinates span only part of this range. To improve both the gamut and accuracy of these CCT calculations, we use chromaticities calculated from our measurements of nearly 7000 daylight and skylight spectra to test an equation that accurately maps CIE 1931 chromaticities x and y into CCT. We extend the work of McCamy [Color Res. Appl. 12, 285–287(1992)] by using a chromaticity epicenter for CCT and the inverse slope of the line that connects it to x and y. With two epicenters for different CCT ranges, our simple equation is accurate across wide chromaticity and CCT ranges (3000–106 K) spanned by daylight and skylight.

© 1999 Optical Society of America

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References

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  1. D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964). Following convention, we distinguish between (1) hemispheric daylight that can include direct sunlight and (2) narrow field-of-view skylight that always excludes direct sunlight. Our observing sites have partially obstructed horizons, so our daylight measurements in fact sample somewhat <2π sr of the sky.
    [CrossRef]
  2. G. T. Winch, M. C. Boshoff, C. J. Kok, A. G. du Toit, “Spectroradiometric and colorimetric characteristics of daylight in the southern hemisphere: Pretoria, South Africa,” J. Opt. Soc. Am. 56, 456–464 (1966).
    [CrossRef]
  3. V. D. P. Sastri, S. R. Das, “Typical spectral distributions and color for tropical daylight,” J. Opt. Soc. Am. 58, 391–398 (1968).
    [CrossRef]
  4. A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).
  5. E. R. Dixon, “Spectral distribution of Australian daylight,” J. Opt. Soc. Am. 68, 437–450 (1978).
    [CrossRef]
  6. J. Romero, A. García-Beltrán, J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
    [CrossRef]
  7. J. Hernández-Andrés, J. Romero, A. García-Beltrán, J. L. Nieves, “Testing linear models on spectral daylight measurements,” Appl. Opt. 37, 971–977 (1998).
    [CrossRef]
  8. G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 144–146, 306–310.
  9. K. L. Kelly, “Lines of constant correlated color temperature based on MacAdam’s (u, v) uniform chromaticity transformation of the CIE diagram,” J. Opt. Soc. Am. 53, 999–1002 (1963).
    [CrossRef]
  10. A. R. Robertson, “Computation of correlated color temperature and distribution temperature,” J. Opt. Soc. Am. 58, 1528–1535 (1968).
    [CrossRef]
  11. J. Schanda, M. Mészáros, G. Czibula, “Calculating correlated color temperature with a desktop programmable calculator,” Color Res. Appl. 3, 65–68 (1978).
    [CrossRef]
  12. J. Schanda, M. Dányi, “Correlated color temperature calculations in the CIE 1976 UCS diagram,” Color Res. Appl. 2, 161–163 (1977).
    [CrossRef]
  13. M. Krystek, “An algorithm to calculate correlated colour temperature,” Color Res. Appl. 10, 38–40 (1985).
    [CrossRef]
  14. Q. Xingzhong, “Formulas for computing correlated color temperature,” Color Res. Appl. 12, 285–287 (1987).
    [CrossRef]
  15. C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. 17, 142–144 (1992).
    [CrossRef]
  16. C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates (Erratum),” Color Res. Appl. 18, 150 (1993).
  17. LI-1800 spectroradiometer from Li-Cor, Inc., 4421 Superior St., Lincoln, Neb. 68504-1327.
  18. PR-650 spectroradiometer from Photo Research, Inc., 9731 Topanga Canyon Place, Chatsworth, Calif. 91311.

1998 (1)

1997 (1)

1993 (1)

C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates (Erratum),” Color Res. Appl. 18, 150 (1993).

1992 (1)

C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. 17, 142–144 (1992).
[CrossRef]

1987 (1)

Q. Xingzhong, “Formulas for computing correlated color temperature,” Color Res. Appl. 12, 285–287 (1987).
[CrossRef]

1985 (1)

M. Krystek, “An algorithm to calculate correlated colour temperature,” Color Res. Appl. 10, 38–40 (1985).
[CrossRef]

1978 (2)

J. Schanda, M. Mészáros, G. Czibula, “Calculating correlated color temperature with a desktop programmable calculator,” Color Res. Appl. 3, 65–68 (1978).
[CrossRef]

E. R. Dixon, “Spectral distribution of Australian daylight,” J. Opt. Soc. Am. 68, 437–450 (1978).
[CrossRef]

1977 (1)

J. Schanda, M. Dányi, “Correlated color temperature calculations in the CIE 1976 UCS diagram,” Color Res. Appl. 2, 161–163 (1977).
[CrossRef]

1968 (3)

1966 (1)

1964 (1)

1963 (1)

Boshoff, M. C.

Czibula, G.

J. Schanda, M. Mészáros, G. Czibula, “Calculating correlated color temperature with a desktop programmable calculator,” Color Res. Appl. 3, 65–68 (1978).
[CrossRef]

Dányi, M.

J. Schanda, M. Dányi, “Correlated color temperature calculations in the CIE 1976 UCS diagram,” Color Res. Appl. 2, 161–163 (1977).
[CrossRef]

Das, S. R.

Dixon, E. R.

du Toit, A. G.

García-Beltrán, A.

Hernández-Andrés, J.

Judd, D. B.

Kelly, K. L.

Kok, C. J.

Krystek, M.

M. Krystek, “An algorithm to calculate correlated colour temperature,” Color Res. Appl. 10, 38–40 (1985).
[CrossRef]

MacAdam, D. L.

McCamy, C. S.

C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates (Erratum),” Color Res. Appl. 18, 150 (1993).

C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. 17, 142–144 (1992).
[CrossRef]

Mészáros, M.

J. Schanda, M. Mészáros, G. Czibula, “Calculating correlated color temperature with a desktop programmable calculator,” Color Res. Appl. 3, 65–68 (1978).
[CrossRef]

Nieves, J. L.

Robertson, A. R.

Romero, J.

Sastri, V. D. P.

Schanda, J.

J. Schanda, M. Mészáros, G. Czibula, “Calculating correlated color temperature with a desktop programmable calculator,” Color Res. Appl. 3, 65–68 (1978).
[CrossRef]

J. Schanda, M. Dányi, “Correlated color temperature calculations in the CIE 1976 UCS diagram,” Color Res. Appl. 2, 161–163 (1977).
[CrossRef]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 144–146, 306–310.

Tarrant, A. W. S.

A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).

Winch, G. T.

Wyszecki, G.

Xingzhong, Q.

Q. Xingzhong, “Formulas for computing correlated color temperature,” Color Res. Appl. 12, 285–287 (1987).
[CrossRef]

Appl. Opt. (1)

Color Res. Appl. (6)

J. Schanda, M. Mészáros, G. Czibula, “Calculating correlated color temperature with a desktop programmable calculator,” Color Res. Appl. 3, 65–68 (1978).
[CrossRef]

J. Schanda, M. Dányi, “Correlated color temperature calculations in the CIE 1976 UCS diagram,” Color Res. Appl. 2, 161–163 (1977).
[CrossRef]

M. Krystek, “An algorithm to calculate correlated colour temperature,” Color Res. Appl. 10, 38–40 (1985).
[CrossRef]

Q. Xingzhong, “Formulas for computing correlated color temperature,” Color Res. Appl. 12, 285–287 (1987).
[CrossRef]

C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates,” Color Res. Appl. 17, 142–144 (1992).
[CrossRef]

C. S. McCamy, “Correlated color temperature as an explicit function of chromaticity coordinates (Erratum),” Color Res. Appl. 18, 150 (1993).

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (1)

Trans. Illum. Eng. Soc. (1)

A. W. S. Tarrant, “The spectral power distribution of daylight,” Trans. Illum. Eng. Soc. 33, 75–82 (1968).

Other (3)

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982), pp. 144–146, 306–310.

LI-1800 spectroradiometer from Li-Cor, Inc., 4421 Superior St., Lincoln, Neb. 68504-1327.

PR-650 spectroradiometer from Photo Research, Inc., 9731 Topanga Canyon Place, Chatsworth, Calif. 91311.

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Figures (6)

Fig. 1
Fig. 1

CIE 1931 x, y chromaticities of our Granada, Spain, natural-light spectra (open circles) overlaid with the CIE daylight locus (solid curve) and Planckian locus (curve with open squares). The inset shows the entire CIE 1931 diagram and Planckian locus.

Fig. 2
Fig. 2

Normalized spectral irradiances E λ measured for particular daylight (solid curve) and calculated for a 5700-K blackbody (dashed curve). Because the 5700-K spectrum yields the Planckian chromaticity closest to the measured daylight chromaticity, this particular daylight has a CCT of 5700 K.

Fig. 3
Fig. 3

Relative errors of the Robertson algorithm10 CCT’s calculated by our spectroradiometers compared with reference CCT’s from a binary search algorithm that is given the same CIE 1931 x, y chromaticities.

Fig. 4
Fig. 4

CIE 1931 x, y chromaticities of our U.S. natural-light spectra (open circles) overlaid with the CIE daylight locus (plain curve) and Planckian locus (curve with open squares).

Fig. 5
Fig. 5

Equation (3) CCT’s compared with reference CCT’s calculated for the same chromaticities. If Eq. (3) were exact, all points would lie exactly on the main diagonal (dashed line).

Fig. 6
Fig. 6

Relative CCT errors for Eq. (3) when it is given the CIE 1931 x, y chromaticities of 138 Planckian radiators of known temperatures. Note that the high-temperature Planckian chromaticities lie far from the locus of natural-light chromaticities used to develop Eq. (3) (see Figs. 1 and 4). Thus, when Eq. (3) is properly limited to calculating CCT’s for natural-light chromaticities, its errors will be much smaller (see Table 4) than those shown here.

Tables (4)

Tables Icon

Table 1 Temporal and Spatial Details of Our Seven Spanish and U.S. Observing Sites, Listed in Decreasing Order of the Number of Spectra Measured at Each Site

Tables Icon

Table 2 CIE 1931 Best-Fit Colorimetric Epicenters x e , y e and Constants for Eq. (3)

Tables Icon

Table 3 Percentile Distribution of Eq. (3) CCT Errors Compared with Reference CCT’s

Tables Icon

Table 4 Maximum and Mean Percentage CCT Errors from Eq. (3) and Its Maximum and Mean CIE 1931 Colorimetric Errors Compared with Reference CCT’s for Our Measured Daylight and Skylight Spectra

Equations (3)

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

CCT=an3+bn2+cn+d
n=x-xe/y-ye
CCT=A0+A1 exp-n/t1+A2 exp-n/t2+A3 exp-n/t3

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