Abstract

A colorimetric coordinate system has been found by trial and error whose Maxwell triangle has the useful property that the length of any line on it is a close measure of the chromaticity difference between the stimuli represented at the extremes of the line. Such accurate chromaticity scales may be derived from this triangle merely by stepping off equal intervals on it that it has been called the “uniform-scale triangle.” The definition of the system is given, and also a comparison of experimental sensibility data with corresponding data derived from the triangle. An important application of this coordinate system is its use in finding from any series of colors the one most resembling a neighboring color of the same brilliance, for example, the finding of the nearest color temperature for a neighboring non-Planckian stimulus. The method is to draw the shortest line from the point representing the non-Planckian stimulus to the Planckian locus.

© 1935 Optical Society of America

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References

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  1. D. B. Judd, Chromaticity Sensibility to Stimulus Differences, J. Opt. Soc. Am. 22, 72 (1932).
    [Crossref]
  2. Judd, J. Opt. Soc. Am. 22, 87 (1932).
    [Crossref]
  3. Proc. 8th Session, International Commission on Illumination, Cambridge, pp. 19–29, September, 1931. D. B. Judd, The 1931 I. C. I. Standard Observer and Coordinate System for Colorimetry, J. Opt. Soc. Am. 23, 359 (1933). T. Smith and J. Guild, The C. I. E. Colorimetric Standards and Their Use, Trans. Opt. Soc. 33, 73 (1931–32).
    [Crossref]
  4. Judd, J. Opt. Soc. Am. 22, 102 (1932).
    [Crossref]
  5. I. G. Priest, A Precision Method for Producing Artificial Daylight, Phys. Rev. 11, 502 (1918); J. Opt. Soc. Am. and Rev. Sci. Inst. 12, 479 (1926). D. B. Judd, Reduction of Data on Mixture of Color Stimuli, Bur. Standards J. Research 4, 525 (1930); RP163.
  6. R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stand. 114, 16 (1931).
  7. Reference 6, Table I.
  8. D. B. Judd, J. Opt. Soc. Am. 22, 89 (1932).
    [Crossref]
  9. W. D. Wright and F. H. G. Pitt, Hue-Discrimination in Normal Colour-Vision, Proc. Phys. Soc. 46, 459 (1934).
    [Crossref]
  10. H. Laurens and W. F. Hamilton, The Sensibility of the Eye to Differences in Wave Length, Am. J. Physiol. 65, 547 (1923).
  11. Wright and Pitt, Proc. Phys. Soc. 46, 466 (1934).
  12. D. B. Judd, A General Formula for the Computation of Colorimetric Purity, J. Opt. Soc. Am. 21, 729 (1931); see Eq. (14).
    [Crossref]
  13. E. P. T. Tyndall, Chromaticity Sensibility to Wave Length Difference as a Function of Purity, J. Opt. Soc. Am. 23, 15 (1933).
    [Crossref]
  14. W. Watson, Note on the Sensibility of the Eye to Variations of Wave Length, Proc. Roy. Soc. B84, 118 (1911).
    [Crossref]
  15. F. Donath, Die funktionale Abhängigkeit zwischen Reiz und Empfindung bei der Farbensättigung, Neue Psych. Stud. 2, 143 (1926).
  16. J. Opt. Soc. Am. 22, 94 (1932).
  17. L. C. Martin, F. L. Warburton, and W. J. Morgan, Determination of the Sensitiveness of the Eye to Differences in the Saturation of Colours, , Special Report Series, No. 188, London, 1933.
  18. P. G. Nutting, The Retinal Sensibilities Related to Illuminating Engineering, Trans. Illum. Eng. Soc. 11, 16 (1916).
  19. L. A. Jones and E. M. Lowry, Retinal Sensibility to Saturation Differences, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 25 (1926).
    [Crossref]
  20. Judd, J. Opt. Soc. Am. 22, 95 (1932); see also footnote 17.
    [Crossref]
  21. D. B. Judd, Saturation Scale for Yellow Colors, J. Opt. Soc. Am. 23, 35 (1933).
    [Crossref]
  22. I. G. Priest and F. G. Brickwedde, The Minimum Perceptible Colorimetric Purity as a Function of Dominant Wave Length with Sunlight as Neutral Standard, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 306 (1926); see also footnote 1.
  23. D. McL. Purdy, On the Saturations and Chromatic Thresholds of the Spectral Colours, Brit. J. Psych. (Gen. Sec.) 21 (Part 3), 283 (1931).
  24. K. S. Gibson and E. P. T. Tyndall, Visibility of Radiant Energy, Bur. Stand. Sci. Pap. 19, 131 (1923–24); S475. See first column of their Table III, p. 174.
    [Crossref]
  25. D. B. Judd, Sensibility to Color-Temperature Change as a Function of Temperature, J. Opt. Soc. Am. 23, 7 (1933).
    [Crossref]
  26. I. G. Priest, A Proposed Scale for Use in Specifying the Chromaticity of Inandescent Illuminants and Various Phases of Daylight, J. Opt. Soc. Am. 23, 41 (1933).
    [Crossref]
  27. I. G. Priest and K. S. Gibson, Standardizing the Red and Yellow Lovibond Glasses, J. Opt. Soc. Am. and Rev. Sci. Inst. 16, 116 (1928).
  28. Judd, J. Opt. Soc. Am. 23, 35 (1933).
    [Crossref]
  29. K. S. Gibson and G. W. Haupt, Standardization of Lovibond Red Glasses in Combination with Lovibond 35 Yellow, Bur. Standards J. Research,  13, 433 (1934), RP718.
    [Crossref]
  30. Judd, J. Opt. Soc. Am. 22, 98 (1932).
    [Crossref]
  31. J. Opt. Soc. Am. 23, 35 (1933).
    [Crossref]
  32. E. Schrödinger, Grundlinien einer Theorie der Farbenmetrik im Tagessehen, Ann. d. Physik (4),  63, 481 (1920); Die Gesichtsempfindungen, Müller-Pouillets Lehrbuch der Physik, 2nd Ed. 2, 456 (1926).
  33. Selig Hecht, The Interrelation of Various Aspects of Color Vision, J. Opt. Soc. Am. 21, 615 (1931).
    [Crossref]
  34. G. E. Müller, Über die Farbenempfindungen, Leipzig: Barth, 1930.
  35. I. G. Priest, The Complete Scale of Color Temperature …, Phys. Rev. 20, 93 (1922); The Colorimetry and Photometry of Daylight and Incandescent Illuminants …, J. Opt. Soc. Am. and Rev. Sci. Inst. 7, 1175 (1923).
    [Crossref]
  36. Report of Color Committee of the American Oil Chemists’ Society, Year 1932–1933, Oil and Soap10, 114 (1933).
    [Crossref]
  37. In this instrument no provision at all is made for equalizing the brightnesses of the two fields; hence, the problem, strictly a tridimensional one, is reduced to a single specification by neglecting both small chromaticity and small brilliance differences.
  38. R. Davis, A Correlated Color Temperature for Illuminants, Bur. Standards J. Research 7, 659 (1931); RP365.
    [Crossref]
  39. Note distinction from x¯ and y¯ of relation (3).

1934 (3)

W. D. Wright and F. H. G. Pitt, Hue-Discrimination in Normal Colour-Vision, Proc. Phys. Soc. 46, 459 (1934).
[Crossref]

Wright and Pitt, Proc. Phys. Soc. 46, 466 (1934).

K. S. Gibson and G. W. Haupt, Standardization of Lovibond Red Glasses in Combination with Lovibond 35 Yellow, Bur. Standards J. Research,  13, 433 (1934), RP718.
[Crossref]

1933 (6)

1932 (7)

J. Opt. Soc. Am. 22, 94 (1932).

D. B. Judd, J. Opt. Soc. Am. 22, 89 (1932).
[Crossref]

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

Judd, J. Opt. Soc. Am. 22, 87 (1932).
[Crossref]

Judd, J. Opt. Soc. Am. 22, 102 (1932).
[Crossref]

Judd, J. Opt. Soc. Am. 22, 95 (1932); see also footnote 17.
[Crossref]

Judd, J. Opt. Soc. Am. 22, 98 (1932).
[Crossref]

1931 (5)

D. McL. Purdy, On the Saturations and Chromatic Thresholds of the Spectral Colours, Brit. J. Psych. (Gen. Sec.) 21 (Part 3), 283 (1931).

R. Davis, A Correlated Color Temperature for Illuminants, Bur. Standards J. Research 7, 659 (1931); RP365.
[Crossref]

Selig Hecht, The Interrelation of Various Aspects of Color Vision, J. Opt. Soc. Am. 21, 615 (1931).
[Crossref]

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stand. 114, 16 (1931).

D. B. Judd, A General Formula for the Computation of Colorimetric Purity, J. Opt. Soc. Am. 21, 729 (1931); see Eq. (14).
[Crossref]

1928 (1)

I. G. Priest and K. S. Gibson, Standardizing the Red and Yellow Lovibond Glasses, J. Opt. Soc. Am. and Rev. Sci. Inst. 16, 116 (1928).

1926 (3)

I. G. Priest and F. G. Brickwedde, The Minimum Perceptible Colorimetric Purity as a Function of Dominant Wave Length with Sunlight as Neutral Standard, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 306 (1926); see also footnote 1.

F. Donath, Die funktionale Abhängigkeit zwischen Reiz und Empfindung bei der Farbensättigung, Neue Psych. Stud. 2, 143 (1926).

L. A. Jones and E. M. Lowry, Retinal Sensibility to Saturation Differences, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 25 (1926).
[Crossref]

1923 (1)

H. Laurens and W. F. Hamilton, The Sensibility of the Eye to Differences in Wave Length, Am. J. Physiol. 65, 547 (1923).

1922 (1)

I. G. Priest, The Complete Scale of Color Temperature …, Phys. Rev. 20, 93 (1922); The Colorimetry and Photometry of Daylight and Incandescent Illuminants …, J. Opt. Soc. Am. and Rev. Sci. Inst. 7, 1175 (1923).
[Crossref]

1920 (1)

E. Schrödinger, Grundlinien einer Theorie der Farbenmetrik im Tagessehen, Ann. d. Physik (4),  63, 481 (1920); Die Gesichtsempfindungen, Müller-Pouillets Lehrbuch der Physik, 2nd Ed. 2, 456 (1926).

1918 (1)

I. G. Priest, A Precision Method for Producing Artificial Daylight, Phys. Rev. 11, 502 (1918); J. Opt. Soc. Am. and Rev. Sci. Inst. 12, 479 (1926). D. B. Judd, Reduction of Data on Mixture of Color Stimuli, Bur. Standards J. Research 4, 525 (1930); RP163.

1916 (1)

P. G. Nutting, The Retinal Sensibilities Related to Illuminating Engineering, Trans. Illum. Eng. Soc. 11, 16 (1916).

1911 (1)

W. Watson, Note on the Sensibility of the Eye to Variations of Wave Length, Proc. Roy. Soc. B84, 118 (1911).
[Crossref]

Brickwedde, F. G.

I. G. Priest and F. G. Brickwedde, The Minimum Perceptible Colorimetric Purity as a Function of Dominant Wave Length with Sunlight as Neutral Standard, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 306 (1926); see also footnote 1.

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. Stand. 114, 16 (1931).

R. Davis, A Correlated Color Temperature for Illuminants, Bur. Standards J. Research 7, 659 (1931); RP365.
[Crossref]

Donath, F.

F. Donath, Die funktionale Abhängigkeit zwischen Reiz und Empfindung bei der Farbensättigung, Neue Psych. Stud. 2, 143 (1926).

Gibson, K. S.

K. S. Gibson and G. W. Haupt, Standardization of Lovibond Red Glasses in Combination with Lovibond 35 Yellow, Bur. Standards J. Research,  13, 433 (1934), RP718.
[Crossref]

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stand. 114, 16 (1931).

I. G. Priest and K. S. Gibson, Standardizing the Red and Yellow Lovibond Glasses, J. Opt. Soc. Am. and Rev. Sci. Inst. 16, 116 (1928).

K. S. Gibson and E. P. T. Tyndall, Visibility of Radiant Energy, Bur. Stand. Sci. Pap. 19, 131 (1923–24); S475. See first column of their Table III, p. 174.
[Crossref]

Hamilton, W. F.

H. Laurens and W. F. Hamilton, The Sensibility of the Eye to Differences in Wave Length, Am. J. Physiol. 65, 547 (1923).

Haupt, G. W.

K. S. Gibson and G. W. Haupt, Standardization of Lovibond Red Glasses in Combination with Lovibond 35 Yellow, Bur. Standards J. Research,  13, 433 (1934), RP718.
[Crossref]

Hecht, Selig

Jones, L. A.

L. A. Jones and E. M. Lowry, Retinal Sensibility to Saturation Differences, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 25 (1926).
[Crossref]

Judd,

Judd, J. Opt. Soc. Am. 23, 35 (1933).
[Crossref]

Judd, J. Opt. Soc. Am. 22, 95 (1932); see also footnote 17.
[Crossref]

Judd, J. Opt. Soc. Am. 22, 98 (1932).
[Crossref]

Judd, J. Opt. Soc. Am. 22, 87 (1932).
[Crossref]

Judd, J. Opt. Soc. Am. 22, 102 (1932).
[Crossref]

Judd, D. B.

Laurens, H.

H. Laurens and W. F. Hamilton, The Sensibility of the Eye to Differences in Wave Length, Am. J. Physiol. 65, 547 (1923).

Lowry, E. M.

L. A. Jones and E. M. Lowry, Retinal Sensibility to Saturation Differences, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 25 (1926).
[Crossref]

Martin, L. C.

L. C. Martin, F. L. Warburton, and W. J. Morgan, Determination of the Sensitiveness of the Eye to Differences in the Saturation of Colours, , Special Report Series, No. 188, London, 1933.

Morgan, W. J.

L. C. Martin, F. L. Warburton, and W. J. Morgan, Determination of the Sensitiveness of the Eye to Differences in the Saturation of Colours, , Special Report Series, No. 188, London, 1933.

Müller, G. E.

G. E. Müller, Über die Farbenempfindungen, Leipzig: Barth, 1930.

Nutting, P. G.

P. G. Nutting, The Retinal Sensibilities Related to Illuminating Engineering, Trans. Illum. Eng. Soc. 11, 16 (1916).

Pitt,

Wright and Pitt, Proc. Phys. Soc. 46, 466 (1934).

Pitt, F. H. G.

W. D. Wright and F. H. G. Pitt, Hue-Discrimination in Normal Colour-Vision, Proc. Phys. Soc. 46, 459 (1934).
[Crossref]

Priest, I. G.

I. G. Priest, A Proposed Scale for Use in Specifying the Chromaticity of Inandescent Illuminants and Various Phases of Daylight, J. Opt. Soc. Am. 23, 41 (1933).
[Crossref]

I. G. Priest and K. S. Gibson, Standardizing the Red and Yellow Lovibond Glasses, J. Opt. Soc. Am. and Rev. Sci. Inst. 16, 116 (1928).

I. G. Priest and F. G. Brickwedde, The Minimum Perceptible Colorimetric Purity as a Function of Dominant Wave Length with Sunlight as Neutral Standard, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 306 (1926); see also footnote 1.

I. G. Priest, The Complete Scale of Color Temperature …, Phys. Rev. 20, 93 (1922); The Colorimetry and Photometry of Daylight and Incandescent Illuminants …, J. Opt. Soc. Am. and Rev. Sci. Inst. 7, 1175 (1923).
[Crossref]

I. G. Priest, A Precision Method for Producing Artificial Daylight, Phys. Rev. 11, 502 (1918); J. Opt. Soc. Am. and Rev. Sci. Inst. 12, 479 (1926). D. B. Judd, Reduction of Data on Mixture of Color Stimuli, Bur. Standards J. Research 4, 525 (1930); RP163.

Purdy, D. McL.

D. McL. Purdy, On the Saturations and Chromatic Thresholds of the Spectral Colours, Brit. J. Psych. (Gen. Sec.) 21 (Part 3), 283 (1931).

Schrödinger, E.

E. Schrödinger, Grundlinien einer Theorie der Farbenmetrik im Tagessehen, Ann. d. Physik (4),  63, 481 (1920); Die Gesichtsempfindungen, Müller-Pouillets Lehrbuch der Physik, 2nd Ed. 2, 456 (1926).

Tyndall, E. P. T.

E. P. T. Tyndall, Chromaticity Sensibility to Wave Length Difference as a Function of Purity, J. Opt. Soc. Am. 23, 15 (1933).
[Crossref]

K. S. Gibson and E. P. T. Tyndall, Visibility of Radiant Energy, Bur. Stand. Sci. Pap. 19, 131 (1923–24); S475. See first column of their Table III, p. 174.
[Crossref]

Warburton, F. L.

L. C. Martin, F. L. Warburton, and W. J. Morgan, Determination of the Sensitiveness of the Eye to Differences in the Saturation of Colours, , Special Report Series, No. 188, London, 1933.

Watson, W.

W. Watson, Note on the Sensibility of the Eye to Variations of Wave Length, Proc. Roy. Soc. B84, 118 (1911).
[Crossref]

Wright,

Wright and Pitt, Proc. Phys. Soc. 46, 466 (1934).

Wright, W. D.

W. D. Wright and F. H. G. Pitt, Hue-Discrimination in Normal Colour-Vision, Proc. Phys. Soc. 46, 459 (1934).
[Crossref]

Am. J. Physiol. (1)

H. Laurens and W. F. Hamilton, The Sensibility of the Eye to Differences in Wave Length, Am. J. Physiol. 65, 547 (1923).

Ann. d. Physik (4) (1)

E. Schrödinger, Grundlinien einer Theorie der Farbenmetrik im Tagessehen, Ann. d. Physik (4),  63, 481 (1920); Die Gesichtsempfindungen, Müller-Pouillets Lehrbuch der Physik, 2nd Ed. 2, 456 (1926).

Brit. J. Psych. (Gen. Sec.) (1)

D. McL. Purdy, On the Saturations and Chromatic Thresholds of the Spectral Colours, Brit. J. Psych. (Gen. Sec.) 21 (Part 3), 283 (1931).

Bur. Stand. Sci. Pap. (1)

K. S. Gibson and E. P. T. Tyndall, Visibility of Radiant Energy, Bur. Stand. Sci. Pap. 19, 131 (1923–24); S475. See first column of their Table III, p. 174.
[Crossref]

Bur. Standards J. Research (2)

K. S. Gibson and G. W. Haupt, Standardization of Lovibond Red Glasses in Combination with Lovibond 35 Yellow, Bur. Standards J. Research,  13, 433 (1934), RP718.
[Crossref]

R. Davis, A Correlated Color Temperature for Illuminants, Bur. Standards J. Research 7, 659 (1931); RP365.
[Crossref]

J. Opt. Soc. Am. (15)

J. Opt. Soc. Am. and Rev. Sci. Inst. (3)

L. A. Jones and E. M. Lowry, Retinal Sensibility to Saturation Differences, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 25 (1926).
[Crossref]

I. G. Priest and F. G. Brickwedde, The Minimum Perceptible Colorimetric Purity as a Function of Dominant Wave Length with Sunlight as Neutral Standard, J. Opt. Soc. Am. and Rev. Sci. Inst. 13, 306 (1926); see also footnote 1.

I. G. Priest and K. S. Gibson, Standardizing the Red and Yellow Lovibond Glasses, J. Opt. Soc. Am. and Rev. Sci. Inst. 16, 116 (1928).

Misc. Pub. Bur. Stand. (1)

R. Davis and K. S. Gibson, Filters for the Reproduction of Sunlight and Daylight and the Determination of Color Temperature, Misc. Pub. Bur. Stand. 114, 16 (1931).

Neue Psych. Stud. (1)

F. Donath, Die funktionale Abhängigkeit zwischen Reiz und Empfindung bei der Farbensättigung, Neue Psych. Stud. 2, 143 (1926).

Phys. Rev. (2)

I. G. Priest, A Precision Method for Producing Artificial Daylight, Phys. Rev. 11, 502 (1918); J. Opt. Soc. Am. and Rev. Sci. Inst. 12, 479 (1926). D. B. Judd, Reduction of Data on Mixture of Color Stimuli, Bur. Standards J. Research 4, 525 (1930); RP163.

I. G. Priest, The Complete Scale of Color Temperature …, Phys. Rev. 20, 93 (1922); The Colorimetry and Photometry of Daylight and Incandescent Illuminants …, J. Opt. Soc. Am. and Rev. Sci. Inst. 7, 1175 (1923).
[Crossref]

Proc. Phys. Soc. (2)

W. D. Wright and F. H. G. Pitt, Hue-Discrimination in Normal Colour-Vision, Proc. Phys. Soc. 46, 459 (1934).
[Crossref]

Wright and Pitt, Proc. Phys. Soc. 46, 466 (1934).

Proc. Roy. Soc. (1)

W. Watson, Note on the Sensibility of the Eye to Variations of Wave Length, Proc. Roy. Soc. B84, 118 (1911).
[Crossref]

Trans. Illum. Eng. Soc. (1)

P. G. Nutting, The Retinal Sensibilities Related to Illuminating Engineering, Trans. Illum. Eng. Soc. 11, 16 (1916).

Other (7)

L. C. Martin, F. L. Warburton, and W. J. Morgan, Determination of the Sensitiveness of the Eye to Differences in the Saturation of Colours, , Special Report Series, No. 188, London, 1933.

Reference 6, Table I.

Proc. 8th Session, International Commission on Illumination, Cambridge, pp. 19–29, September, 1931. D. B. Judd, The 1931 I. C. I. Standard Observer and Coordinate System for Colorimetry, J. Opt. Soc. Am. 23, 359 (1933). T. Smith and J. Guild, The C. I. E. Colorimetric Standards and Their Use, Trans. Opt. Soc. 33, 73 (1931–32).
[Crossref]

Report of Color Committee of the American Oil Chemists’ Society, Year 1932–1933, Oil and Soap10, 114 (1933).
[Crossref]

In this instrument no provision at all is made for equalizing the brightnesses of the two fields; hence, the problem, strictly a tridimensional one, is reduced to a single specification by neglecting both small chromaticity and small brilliance differences.

Note distinction from x¯ and y¯ of relation (3).

G. E. Müller, Über die Farbenempfindungen, Leipzig: Barth, 1930.

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Figures (10)

Fig. 1
Fig. 1

The uniform-chromaticity-scale triangle. Wavelength along the spectrum locus is indicated in millimicrons; color temperature along the Planckian locus is given in degrees Kelvin.

Fig. 2
Fig. 2

Chromaticity sensibility to wavelength change in the spectrum.

Fig. 3
Fig. 3

Chromaticity sensibility to dominant-wavelength change as a function of purity.

Fig. 4
Fig. 4

Chromaticity sensibility to purity change as a function of purity.

Fig. 5
Fig. 5

Chromaticity sensibility to purity change as a function of purity.

Fig. 6
Fig. 6

Chromaticity sensibility to purity change near zero purity as a function of dominant wavelength.

Fig. 7
Fig. 7

Number of chromaticity steps from a Planckian radiator at 4800°K to the spectrum as a function of dominant wavelength.

Fig. 8
Fig. 8

Sensibility to color-temperature change.

Fig. 9
Fig. 9

Sensibility to change in Lovibond yellow.

Fig. 10
Fig. 10

Sensibility to change in Lovibond red combined with Lovibond 35-yellow.

Tables (1)

Tables Icon

Table I Trilinear coordinates on the uniform-chromaticity-scale triangle. Observer: 1931 I. C. I. Standard.

Equations (18)

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

K Δ E = D ,
D = { 2 [ ( Δ r ) 2 + ( Δ g ) 2 + ( Δ b ) 2 ] / 3 } 1 2 ,
D = ( 2 Δ v / 3 1 2 ) [ ( Δ q / Δ v ) 2 + ( Δ q / Δ v ) + 1 ] 1 2 ,
K Δ E = Δ c = Δ r , Δ g , or Δ b , whichever is the largest ; = ( Δ r + Δ g + Δ b ) / 2 ,
r ¯ = 3.1956 x ¯ + 2.4478 y ¯ - 0.1434 z ¯ g ¯ = - 2.5455 x ¯ + 7.0492 y ¯ + 0.9963 z ¯ b ¯ = 0.0000 x ¯ + 0.0000 y ¯ + 1.0000 z ¯ The reverse transformation is given by : x ¯ = 0.24513 r ¯ - 0.08512 g ¯ + 0.11996 b ¯ y ¯ = 0.08852 r ¯ + 0.11112 g ¯ - 0.09802 b ¯ z ¯ = 0.00000 r ¯ + 0.00000 g ¯ + 1.00000 b ¯ }
O . S . A . t o U n i f o r m - S c a l e U n i f o r m - S c a l e t o O . S . A . 1 , 0 , 0.1 0 , 1 , 0.1 0 , 0 , 0.2 1 , 0 , - 0.5 0 , 1 , - 0.5 0 , 0 , 5.0
d λ / d E = K / ( d c h / d λ ) p = 1 ,
( d Λ / d E ) p ( d Λ / d E ) p = 1 = [ s h ( 1 - p ) + s w p ] 2 ( d c h / d λ ) s w p { [ s h ( 1 - p ) + s w p ] ( d c h / d λ ) + ( 1 - p ) ( c w - c h ) ( d s h / d λ ) } ,
( d p d E ) Λ constant = K 2 [ 3 ( Δ q / Δ v ) 2 + ( Δ q / Δ v ) + 1 ] 1 2 × [ s h ( 1 - p ) + s w p ] 2 s h s w ( v h - v w ) ,
( d p d E ) p 0 = K 2 ( 3 ( Δ q / Δ v ) 2 + ( Δ q / Δ v ) + 1 ) 1 2 × [ s h s w ( v h - v w ) ] .
Δ E = ( 1 / K ) { 2 [ ( Δ r ) 2 + ( Δ g ) 2 + ( Δ b ) 2 ] / 3 } 1 2 ,
d ( 1 / θ ) / d E = a constant .
d ( 1 / θ ) / d E = K d ( 1 / θ ) / d c .
d ( 1 / θ ) d E = 6 1 2 K d ( 1 / θ ) 2 [ ( d r ) 2 + ( d g ) 2 + ( d b ) 2 ] 1 2 ,
d N d E = 6 1 2 K d N 2 [ ( d r ) 2 + ( d g ) 2 + ( d b ) 2 ] 1 2 ,
x = ( 2 b + g ) / 3 1 2 , y = g ,
D = ( Δ x ¯ 2 + Δ y ¯ 2 ) 1 2
D = { Δ x [ ( Δ y / Δ x ) 2 + 1 ] , 1 2 Δ y [ ( Δ x / Δ y ) 2 + 1 ] 1 2 .             or