Abstract

Methods by which the correlated color temperature and the distribution temperature of a light source may be calculated from a knowledge of the spectral power distribution of the source are described. Digital-computer programs have been written to perform the calculations; these programs are described, with the results of some tests for a number of sources. The two temperatures are significantly different for some sources. A new concept, “daylight distribution temperature” is also introduced and some examples are given.

© 1968 Optical Society of America

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References

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  1. The definition given in the current (May1968) draft of the 3rd edition of the International Lighting Vocabulary is: “Temperature of the full radiator for which the ordinates of the spectral distribution curve of its radiance are proportional (or approximately so), in the visible region, to those of the distribution curve of the radiation considered. Note: Both radiations will necessarily have the same, or nearly the same chromaticity.”
  2. K. L. Kelly, J. Opt. Soc. Am. 53, 999 (1963).
    [CrossRef]
  3. L. Mori, H. Sugiyama, and N. Kambe, Acta Chromatica 1, 93 (1964).
  4. I. G. Priest, J. Opt. Soc. Am. 23, 41 (1933); D. B. Judd, 23, 7 (1933).
    [CrossRef]
  5. D. Hahn and H. Hieke, Farbe 9, 247 (1960).
  6. C. L. Sanders and W. Gaw, Appl. Opt. 6, 1639 (1967).
    [CrossRef] [PubMed]
  7. G. Wyszecki and W. S. Stiles, Color Science (John Wiley& Sons, Inc., New York, 1967).
  8. D. Nickerson and C. W. Jerome, Illum. Eng. 60, 262 (1965).
  9. Commission Internationale de l’Eclairage, Compt. Rend. 1967[H. K. Hammond, Secy., Natl. Bur. Std. (U.S.)Washington, D. C., 1968]. Report of Committee E-1.3.1 (Colorimetry).
  10. D. B. Judd, D. L. MacAdam, and G. Wyszecki, J. Opt. Soc. Am. 54, 1031 (1964).
    [CrossRef]
  11. G. Wyszecki, J. Opt. Soc. Am. 58, 290 (1968).

1968 (1)

1967 (1)

1965 (1)

D. Nickerson and C. W. Jerome, Illum. Eng. 60, 262 (1965).

1964 (2)

D. B. Judd, D. L. MacAdam, and G. Wyszecki, J. Opt. Soc. Am. 54, 1031 (1964).
[CrossRef]

L. Mori, H. Sugiyama, and N. Kambe, Acta Chromatica 1, 93 (1964).

1963 (1)

1960 (1)

D. Hahn and H. Hieke, Farbe 9, 247 (1960).

1933 (1)

Gaw, W.

Hahn, D.

D. Hahn and H. Hieke, Farbe 9, 247 (1960).

Hieke, H.

D. Hahn and H. Hieke, Farbe 9, 247 (1960).

Jerome, C. W.

D. Nickerson and C. W. Jerome, Illum. Eng. 60, 262 (1965).

Judd, D. B.

Kambe, N.

L. Mori, H. Sugiyama, and N. Kambe, Acta Chromatica 1, 93 (1964).

Kelly, K. L.

MacAdam, D. L.

Mori, L.

L. Mori, H. Sugiyama, and N. Kambe, Acta Chromatica 1, 93 (1964).

Nickerson, D.

D. Nickerson and C. W. Jerome, Illum. Eng. 60, 262 (1965).

Priest, I. G.

Sanders, C. L.

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science (John Wiley& Sons, Inc., New York, 1967).

Sugiyama, H.

L. Mori, H. Sugiyama, and N. Kambe, Acta Chromatica 1, 93 (1964).

Wyszecki, G.

Acta Chromatica (1)

L. Mori, H. Sugiyama, and N. Kambe, Acta Chromatica 1, 93 (1964).

Appl. Opt. (1)

Farbe (1)

D. Hahn and H. Hieke, Farbe 9, 247 (1960).

Illum. Eng. (1)

D. Nickerson and C. W. Jerome, Illum. Eng. 60, 262 (1965).

J. Opt. Soc. Am. (4)

Other (3)

Commission Internationale de l’Eclairage, Compt. Rend. 1967[H. K. Hammond, Secy., Natl. Bur. Std. (U.S.)Washington, D. C., 1968]. Report of Committee E-1.3.1 (Colorimetry).

G. Wyszecki and W. S. Stiles, Color Science (John Wiley& Sons, Inc., New York, 1967).

The definition given in the current (May1968) draft of the 3rd edition of the International Lighting Vocabulary is: “Temperature of the full radiator for which the ordinates of the spectral distribution curve of its radiance are proportional (or approximately so), in the visible region, to those of the distribution curve of the radiation considered. Note: Both radiations will necessarily have the same, or nearly the same chromaticity.”

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Figures (1)

Fig. 1
Fig. 1

Method of interpolation to find correlated color temperature.

Tables (9)

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Table I Maximum errors (in μrd) of computed values of correlated color temperature, resulting from use of various sets of isotemperature lines.

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Table II Thirty one isotemperature lines.

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Table III Maximum errors of computed values of correlated color temperature, based on use of the 31 isotemperature lines listed in Table II.

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Table IV Maximum errors of computed values of correlated color temperature, based on the use of only nine isotemperature lines (0, 25, 50, 100, 200, 300, 400, 500, 600 μrd).

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Table V Correlated color temperatures and distribution temperatures (400–700 nm) of 16 sources.

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Table VI Distribution temperatures (400–700 nm) of eight incandescent sources calculated by use of the indicated wavelength intervals. (The figures in parentheses are rms percentage deviations.)

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Table VII Distribution temperatures of eight incandescent sources in four wavelength ranges. (The figures in parentheses are rms percentage deviations.)

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Table VIII Distribution temperatures of two sources for the indicated wavelength ranges, between 230 and 800 nm. (The figures in parentheses are rms percentage deviations.)

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Table IX Daylight distribution temperatures (400–700 nm) of eight sources.

Equations (33)

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S ( λ ) = c 1 λ - 5 [ exp ( c 2 / λ T ) - 1 ] - 1 ,
u = 4 x / ( - 2 x + 12 y + 3 ) , v = 6 y / ( - 2 x + 12 y + 3 ) ,
λ 1 λ 2 [ 1 - S ( λ ) a S ( λ ) ] 2 d λ min
d i = [ ( v T - v i ) - m i ( u T - u i ) ] / ( 1 + m i 2 ) 1 2 .
T c = [ 1 T j + θ 1 θ 1 + θ 2 ( 1 T j + 1 + 1 T j ) ] - 1 ,
T c = [ 1 T j + d j d j - d j + 1 ( 1 T j + 1 - 1 T j ) ] - 1 .
U = S ( λ ) u ¯ ( λ ) d λ , V = S ( λ ) v ¯ ( λ ) d λ ,
W = S ( λ ) w ¯ ( λ ) d λ .
u ¯ ( λ ) = 2 3 x ¯ ( λ ) , v ¯ ( λ ) = y ¯ ( λ ) ,
w ¯ ( λ ) = - 1 2 x ¯ ( λ ) + 3 2 y ¯ ( λ ) + 1 2 z ¯ ( λ ) .
u i = U / R             and             v i = V / R ,
l ι = d v i / d u i = v i / u i = ( V R - V R ) / ( U R - U R ) ,
U = c 1 c 2 T - 2 λ - 6 u ¯ ( λ ) exp ( c 2 / λ T i ) × [ exp ( c 2 / λ T i ) - 1 ] - 2 d λ , V = c 1 c 2 T - 2 λ - 6 v ¯ ( λ ) exp ( c 2 / λ T i ) × [ exp ( c 2 / λ T i ) - 1 ] - 2 d λ , W = c 1 c 2 T - 2 λ - 6 w ¯ ( λ ) exp ( c 2 / λ T i ) × [ exp ( c 2 / λ T i ) - 1 ] - 2 d λ ,
R = U + V + W .
m i = - 1 / l i .
and             u i + = u i - 0.01 ( 1 + m i 2 ) - 1 2 v i + = v i - 0.01 m i ( 1 + m i 2 ) - 1 2 .
and             u i - = u i + 0.01 ( 1 + m i 2 ) - 1 2 v i - = v i + 0.01 m i ( 1 + m i 2 ) - 1 2 .
A ( a , T ) = λ [ 1 - S ( λ ) a S ( λ ) ] 2
{ 2 a 2 [ S ( λ ) S ( λ ) ] - 2 a 3 [ S ( λ ) S ( λ ) ] 2 } = 0
a = [ S ( λ ) / S ( λ ) ] 2 / [ S ( λ ) / S ( λ ) ] ,
A ( T ) = { 1 - S ( λ ) [ S ( λ ) / S ( λ ) ] S ( λ ) [ S ( λ ) / S ( λ ) ] 2 } 2 ,
A ( 2820.1 ) = 0.0471 , A ( 2720.1 ) = 0.4212 ,
A ( 2920.1 ) = 0.0907.
A ( 2830.1 ) = 0.0345 , A ( 2840.1 ) = 0.0259 , A ( 2850.1 ) = 0.0212 , A ( 2860.1 ) = 0.0204 ,
A ( 2870.1 ) = 0.0234.
σ = 100 · { 1 n [ 1 - r ( λ ) ] 2 } 1 2 ,
r ( λ ) = S ( λ ) / a S ( λ ) .
x D = - 4.5993 10 9 T c 3 + 2.9645 10 6 T c 2 + 0.09905 10 3 T c + 0.244063 ,             for             4000 K T c 7000 K
x D = - 2.0031 10 9 T c 3 + 1.8997 10 6 T c 2 + 0.24734 10 3 T c + 0.237040             for             7000 K T c 25 000 K .
y D = 2.870 x D - 3.000 x D 2 - 0.275.
M 1 = - 1.3515 - 1.7703 x D + 5.9114 y D 0.0241 + 0.2562 x D - 0.7341 y D ,
M 2 = 0.0300 - 31.4424 x D + 30.0717 y D 0.0241 + 0.2562 x D - 0.7341 y D .
S ( λ ) = S 0 ( λ ) + M 1 S 1 ( λ ) + M 2 S 2 ( λ ) ,