Abstract

Determinations at the same brightness by six normal observers have been made of the color-temperature difference corresponding to a chromaticity difference just doubtfully perceptible over the range of 1800 to 11,000°K. It has been found that this temperature difference corresponds closely to a constant difference in the spectral centroid of light (Priest’s empirical relation); it is also closely proportional to the square of the color temperature (Davis’ representation of Priest’s empirical relation); furthermore it corresponds with good approximation to a constant difference in the “red” trilinear coordinate (Judd’s empirical relation). These experimental results have therefore approximately checked three empirical relations previously derived from less complete data. Priest’s spectral-centroid relation and Davis’ representation of it both agree so closely with the experimental data that the discrepancies are not known to be real, but Judd’s empirical relation yields discrepancies about twice as large as the experimental uncertainty. The verification of Priest’s spectral-centroid relation confirms the tentative conclusion by Davis and Gibson that between 2000 and 3000°K a given color-temperature difference causes for the normal observer nearly the same size chromaticity difference regardless of whether the radiators be viewed directly or through a blue filter not more highly selective than a “daylight filter.” This result has a bearing on the phenomenon of “color constancy”; that is, it helps to explain why the colors of objects are approximately constant for illuminants differing as widely as incandescent-lamplight and natural daylight.

© 1933 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. G. Priest, The Colorimetry and Photometry of Daylight and Incandescent Illuminants by the Method of Rotatory Dispersion, J. Opt. Soc. Am. and Rev. Sci. Inst. 7, 1190–1191 (1923).
  2. R. Davis, A Correlated Color Temperature for Illuminants, Bureau Standards J. Research 7, 659–681 (1931). This simpler statement of the spectral-centroid relation might have been deduced by combining two previous findings, one by Gibson (see footnote 10, p. 12) concerning a spectral-centroid relation between incident and transmitted light for daylight filters, the other by Langmuir and Orange (Trans. A.I.E.E.,  32, 1944–1946 (1913)) concerning a similar relation involving reciprocal temperature. The mathematical analysis on which this latter finding is based was given later by Foote, Mohler, and Fairchild, J. Wash. Acad. Sci. 7, 545–549 (1917), and Gage, Trans. I.E.S. 16, 428–429 (1921) also called attention to this relation.
    [Crossref]
  3. D. B. Judd, Chromaticity Sensibility to Stimulus Differences, J. Opt. Soc. Am. 22, 72–108 (1932).
    [Crossref]
  4. D. B. Judd, Precision of Color Temperature Measurements under Various Observing Conditions; A New Color Comparator for Incandescent Lamps, Bureau Standards J. Research 5, 1161–1177 (1930). (In Fig. 2, p. 1169 of this paper, a decimal point should be placed before each of the numbers on the ordinate scale.)
    [Crossref]
  5. F. F. Martens, Über ein neues Polarisationsphotometer, Phys. Zeits. 1, 299–303 (1900).
  6. R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub., Bur. Stds., No.  114, 68–69; January21 (1931).
  7. Later analysis showed that order of presentation of stimuli did not affect sensibility importantly.
  8. Analysis shows that variation from day to day accounts for a large part of this scatter.
  9. E for “Empfindung,” a fairly common usage among European writers; see also footnote 3, p. 8, for reference to a paper in which this symbol is used extensively.
  10. K. S. Gibson, Spectral Centroid Relations for Artificial Daylight Filters, J. Opt. Soc. Am. and Rev. Sci. Inst.,  11, 473–478 (1925).
    [Crossref]
  11. R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stds., No.  114, 79, January, (1931).
  12. See footnote 6, p. 8. This paper gives data for finding dθ/dθs.
  13. E. Hering, Grundzüge der Lehre vom Lichtsinn, aus Graefe-Sämisch Handb. d. ges. Augenheilk., XII, 1905 and 1907. H. v. Helmholtz, Handb. d. Physiol. Optik, 3d Ed., 2, 233, 243 (1911). D. Katz, Die Erscheinungsweisen der Farben und ihre Beeinflussung durch die individuelle Erfahrung, Ergänzungsband VII, Zeits. f. Psychol., 1911. E. R. Jaensch, Über Farbenkontrast und die sog. Berücksichtigung farbigen Beleuchtung, Zeits. f. Sinnesphysiol. 52, 165–180 (1921). O. Kroh, Über Farbenkonstanz und Farbentransformation, Zeits. f. Sinnesphysiol. 52, 181–216, 235–273 (1921). A. Gelb, Die “Farbenkonstanz” der Sehdinge, in Handb. d. normalen u. pathologischen Physiol.12, 1st half, Receptionsorgane II, 594–678; Berlin, Springer; 1929.
    [Crossref]
  14. A. Kohlrausch, Tagessehen, Dämmersehen, Adaptation, I. Allgemeines über Umstimmung und “Farbenkonstanz der Sehdinge,” in Handb. d. normalen u. pathologischen Physiol.12, 2d half, Receptionsorgane II, 1499–1506; Berlin, Springer (1931).

1932 (1)

1931 (3)

R. Davis, A Correlated Color Temperature for Illuminants, Bureau Standards J. Research 7, 659–681 (1931). This simpler statement of the spectral-centroid relation might have been deduced by combining two previous findings, one by Gibson (see footnote 10, p. 12) concerning a spectral-centroid relation between incident and transmitted light for daylight filters, the other by Langmuir and Orange (Trans. A.I.E.E.,  32, 1944–1946 (1913)) concerning a similar relation involving reciprocal temperature. The mathematical analysis on which this latter finding is based was given later by Foote, Mohler, and Fairchild, J. Wash. Acad. Sci. 7, 545–549 (1917), and Gage, Trans. I.E.S. 16, 428–429 (1921) also called attention to this relation.
[Crossref]

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub., Bur. Stds., No.  114, 68–69; January21 (1931).

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stds., No.  114, 79, January, (1931).

1930 (1)

D. B. Judd, Precision of Color Temperature Measurements under Various Observing Conditions; A New Color Comparator for Incandescent Lamps, Bureau Standards J. Research 5, 1161–1177 (1930). (In Fig. 2, p. 1169 of this paper, a decimal point should be placed before each of the numbers on the ordinate scale.)
[Crossref]

1925 (1)

K. S. Gibson, Spectral Centroid Relations for Artificial Daylight Filters, J. Opt. Soc. Am. and Rev. Sci. Inst.,  11, 473–478 (1925).
[Crossref]

1923 (1)

I. G. Priest, The Colorimetry and Photometry of Daylight and Incandescent Illuminants by the Method of Rotatory Dispersion, J. Opt. Soc. Am. and Rev. Sci. Inst. 7, 1190–1191 (1923).

1900 (1)

F. F. Martens, Über ein neues Polarisationsphotometer, Phys. Zeits. 1, 299–303 (1900).

Davis, R.

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub., Bur. Stds., No.  114, 68–69; January21 (1931).

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stds., No.  114, 79, January, (1931).

R. Davis, A Correlated Color Temperature for Illuminants, Bureau Standards J. Research 7, 659–681 (1931). This simpler statement of the spectral-centroid relation might have been deduced by combining two previous findings, one by Gibson (see footnote 10, p. 12) concerning a spectral-centroid relation between incident and transmitted light for daylight filters, the other by Langmuir and Orange (Trans. A.I.E.E.,  32, 1944–1946 (1913)) concerning a similar relation involving reciprocal temperature. The mathematical analysis on which this latter finding is based was given later by Foote, Mohler, and Fairchild, J. Wash. Acad. Sci. 7, 545–549 (1917), and Gage, Trans. I.E.S. 16, 428–429 (1921) also called attention to this relation.
[Crossref]

Gibson, K. S.

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stds., No.  114, 79, January, (1931).

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub., Bur. Stds., No.  114, 68–69; January21 (1931).

K. S. Gibson, Spectral Centroid Relations for Artificial Daylight Filters, J. Opt. Soc. Am. and Rev. Sci. Inst.,  11, 473–478 (1925).
[Crossref]

Hering, E.

E. Hering, Grundzüge der Lehre vom Lichtsinn, aus Graefe-Sämisch Handb. d. ges. Augenheilk., XII, 1905 and 1907. H. v. Helmholtz, Handb. d. Physiol. Optik, 3d Ed., 2, 233, 243 (1911). D. Katz, Die Erscheinungsweisen der Farben und ihre Beeinflussung durch die individuelle Erfahrung, Ergänzungsband VII, Zeits. f. Psychol., 1911. E. R. Jaensch, Über Farbenkontrast und die sog. Berücksichtigung farbigen Beleuchtung, Zeits. f. Sinnesphysiol. 52, 165–180 (1921). O. Kroh, Über Farbenkonstanz und Farbentransformation, Zeits. f. Sinnesphysiol. 52, 181–216, 235–273 (1921). A. Gelb, Die “Farbenkonstanz” der Sehdinge, in Handb. d. normalen u. pathologischen Physiol.12, 1st half, Receptionsorgane II, 594–678; Berlin, Springer; 1929.
[Crossref]

Judd, D. B.

D. B. Judd, Chromaticity Sensibility to Stimulus Differences, J. Opt. Soc. Am. 22, 72–108 (1932).
[Crossref]

D. B. Judd, Precision of Color Temperature Measurements under Various Observing Conditions; A New Color Comparator for Incandescent Lamps, Bureau Standards J. Research 5, 1161–1177 (1930). (In Fig. 2, p. 1169 of this paper, a decimal point should be placed before each of the numbers on the ordinate scale.)
[Crossref]

Kohlrausch, A.

A. Kohlrausch, Tagessehen, Dämmersehen, Adaptation, I. Allgemeines über Umstimmung und “Farbenkonstanz der Sehdinge,” in Handb. d. normalen u. pathologischen Physiol.12, 2d half, Receptionsorgane II, 1499–1506; Berlin, Springer (1931).

Martens, F. F.

F. F. Martens, Über ein neues Polarisationsphotometer, Phys. Zeits. 1, 299–303 (1900).

Priest, I. G.

I. G. Priest, The Colorimetry and Photometry of Daylight and Incandescent Illuminants by the Method of Rotatory Dispersion, J. Opt. Soc. Am. and Rev. Sci. Inst. 7, 1190–1191 (1923).

Bureau Standards J. Research (2)

R. Davis, A Correlated Color Temperature for Illuminants, Bureau Standards J. Research 7, 659–681 (1931). This simpler statement of the spectral-centroid relation might have been deduced by combining two previous findings, one by Gibson (see footnote 10, p. 12) concerning a spectral-centroid relation between incident and transmitted light for daylight filters, the other by Langmuir and Orange (Trans. A.I.E.E.,  32, 1944–1946 (1913)) concerning a similar relation involving reciprocal temperature. The mathematical analysis on which this latter finding is based was given later by Foote, Mohler, and Fairchild, J. Wash. Acad. Sci. 7, 545–549 (1917), and Gage, Trans. I.E.S. 16, 428–429 (1921) also called attention to this relation.
[Crossref]

D. B. Judd, Precision of Color Temperature Measurements under Various Observing Conditions; A New Color Comparator for Incandescent Lamps, Bureau Standards J. Research 5, 1161–1177 (1930). (In Fig. 2, p. 1169 of this paper, a decimal point should be placed before each of the numbers on the ordinate scale.)
[Crossref]

Grundzüge der Lehre vom Lichtsinn, aus Graefe-Sämisch Handb. d. ges. Augenheilk., XII (1)

E. Hering, Grundzüge der Lehre vom Lichtsinn, aus Graefe-Sämisch Handb. d. ges. Augenheilk., XII, 1905 and 1907. H. v. Helmholtz, Handb. d. Physiol. Optik, 3d Ed., 2, 233, 243 (1911). D. Katz, Die Erscheinungsweisen der Farben und ihre Beeinflussung durch die individuelle Erfahrung, Ergänzungsband VII, Zeits. f. Psychol., 1911. E. R. Jaensch, Über Farbenkontrast und die sog. Berücksichtigung farbigen Beleuchtung, Zeits. f. Sinnesphysiol. 52, 165–180 (1921). O. Kroh, Über Farbenkonstanz und Farbentransformation, Zeits. f. Sinnesphysiol. 52, 181–216, 235–273 (1921). A. Gelb, Die “Farbenkonstanz” der Sehdinge, in Handb. d. normalen u. pathologischen Physiol.12, 1st half, Receptionsorgane II, 594–678; Berlin, Springer; 1929.
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. and Rev. Sci. Inst. (2)

K. S. Gibson, Spectral Centroid Relations for Artificial Daylight Filters, J. Opt. Soc. Am. and Rev. Sci. Inst.,  11, 473–478 (1925).
[Crossref]

I. G. Priest, The Colorimetry and Photometry of Daylight and Incandescent Illuminants by the Method of Rotatory Dispersion, J. Opt. Soc. Am. and Rev. Sci. Inst. 7, 1190–1191 (1923).

Misc. Pub. Bur. Stds. (1)

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stds., No.  114, 79, January, (1931).

Misc. Pub., Bur. Stds. (1)

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub., Bur. Stds., No.  114, 68–69; January21 (1931).

Phys. Zeits. (1)

F. F. Martens, Über ein neues Polarisationsphotometer, Phys. Zeits. 1, 299–303 (1900).

Other (5)

Later analysis showed that order of presentation of stimuli did not affect sensibility importantly.

Analysis shows that variation from day to day accounts for a large part of this scatter.

E for “Empfindung,” a fairly common usage among European writers; see also footnote 3, p. 8, for reference to a paper in which this symbol is used extensively.

See footnote 6, p. 8. This paper gives data for finding dθ/dθs.

A. Kohlrausch, Tagessehen, Dämmersehen, Adaptation, I. Allgemeines über Umstimmung und “Farbenkonstanz der Sehdinge,” in Handb. d. normalen u. pathologischen Physiol.12, 2d half, Receptionsorgane II, 1499–1506; Berlin, Springer (1931).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Individual experimental values of the doubtful difference expressed according to the three parameters suggested by the three empirical relations. If one of the empirical relations represented the experimental results perfectly the corresponding plotted points would not deviate significantly from a horizontal line. Approach to the horizontal indicates, therefore, the degree of approximation. The scales are adjusted so as to afford a fair comparison of the three relations.

Fig. 2
Fig. 2

Mean experimental values of the doubtful difference in color temperature as a function of color temperature compared to the three empirical relations. The rapid variation of the doubtful difference expressed in terms of color temperature compared to its slow variation in the other parameters (see Fig. 1) indicates the relative inconvenience of color temperature for the specification of illuminants. Reciprocal color temperature is suggested as a substitute parameter.

Fig. 3
Fig. 3

Comparison of the doubtful difference in color temperature according to relation (2a) with that obtained by the assumption that the interposition of a daylight filter leaves the size of the chromaticity difference between two light sources unchanged. It is seen that this assumption is justified for the Davis-Gibson 2450-to-3500° filter, but not quite for the 2450-to-6500° filter which increases the chromaticity difference slightly.

Tables (2)

Tables Icon

Table I Individual variations of the doubtful difference.

Tables Icon

Table II Check of the three empirical relations against average experimental results.

Equations (8)

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

3.3 PE single = 0.5 ( GID + LPD ) .
Δ λ c = K 1 ,
Δ ( 1 / θ ) = K 2 ,
Δ r = K 3 ,
d θ / d E = - K 1 d θ / d λ c ,
d θ / d E = - K 2 d θ / d ( 1 / θ ) = K 2 θ 2 ,
d θ / d E = - K 3 d θ / d r ,
d θ / d E = - 5.5 d θ / d ( 1 / θ ) × 10 - 6 = 5.5 θ 2 × 10 - 6