Abstract

A quantitative model for an opponent-colors theory of vision is presented that is based on the CIE color mixture data for the standard observer. The model is used to account for spectral brightness, saturation, and hue and some of their associated psychophysical functions in both normal and dichromatic vision. Special attention is given to an account of the Bezold-Brücke hue shift, and to changes in saturation and wavelength discrimination with changes in stimulus luminance.

© 1955 Optical Society of America

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References

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  1. D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 45, 546 (1955).
    [Crossref]
  2. D. B. Judd, Handbook of Experimental Psychology (edited by S. S. Stevens) (John Wiley and Sons, Inc., New York, 1951), pp. 811–867.
  3. A. v. Tschermak, Handb. Norm. Path. Physiol. 12, 295 (1929), p.342 ff.
  4. E. Hering, Grundzüge der Lehre vom Lichtsinn (Julius Springer, Berlin, 1920), p. 112 ff.
  5. E. Schrödinger, Sitzber. Akad. Wiss. Wien. Math.-naturw. Klasse,  134, 471 (1925).
  6. R. Hiecke, Z. Sinnesphysiol. 58, 111 (1927).
  7. A. Brückner, Z. Sinnesphysiol. 58, 322 (1927), p. 340 ff.
  8. Reference 2, p. 831.
  9. J. F. Schouten, Proc. Acad. Sci. (Amsterdam) 38, 590 (1935).
  10. J. Guild, in Joint Discussion on Vision (The Physical Society, London, 1932), pp. 1–26.
  11. M. H. Pirenne, Vision and the Eye (Chapman and Hall Ltd., London, 1948), pp. 159–160.
  12. H. J. A. Dartnall, Brit. Med. Bull. 9, 24 (1953).
  13. R. Granit, Sensory Mechanisms of the Retina (Oxford University Press, London, 1947).
  14. These responses may be related to different physiological structures or, more likely, they may be correlates of different physiological states within the same structural elements.
  15. S. A. Talbot, J. Opt. Soc. Am. 41, 918 (1951).
    [Crossref] [PubMed]
  16. W. A. H. Rushton and R. D. Cohen, Nature 173, 301 (1954).
    [Crossref] [PubMed]
  17. G. Wald, Science 119, 887 (1954).
    [Crossref] [PubMed]
  18. H. Piéron, Année Psychol. 40, 1 (1939).
    [Crossref]
  19. L. T. Troland, Trans. Illum. Eng. Soc. 11, 957 (1916).
  20. D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 43, 552 (1953).
    [Crossref] [PubMed]
  21. For a list of references see: L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 43, 490–492 (1953).
    [Crossref]
  22. W. J. Crozier, J. Gen. Physiol. 34, 87 (1950).
  23. W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 47, 207–208 (1935).
    [Crossref]
  24. W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 49, 331 (1937).
    [Crossref]
  25. D. M. Purdy, “Chroma as a function of retinal illumination,” dissertation, Harvard University, 1–190 (1929), Table VI.
  26. L. M. Hurvich and D. Jameson, Science 114, 199 (1951).
    [Crossref] [PubMed]
  27. E. N. Willmer and W. D. Wright, Nature 156, 119 (1945).
    [Crossref]
  28. H. Hartridge, Nature 155, 657 (1945).
    [Crossref]
  29. D. B. Judd, Natl. Bur. Standards (U.S.) 42, 13 (1949).
  30. D. M. Purdy, Am. J. Psychol. 49, 313 (1937).
    [Crossref]
  31. Reference 2, p. 855.
  32. A. König and C. Dieterici, Ann. Phys. Chem. 22, 579 (1884).
  33. L. T. Troland, The Principles of Psychophysiology (D. Van Nostrand Company, Inc., New York, 1930), Vol. II, pp. 142, 144.
  34. E. Hering, Lotos, Jahrb. Naturwiss. N. F. 1, 95, 96 (1880).
  35. S. Hecht and S. Shlaer, J. Gen. Physiol. 20, 83 (1936).
  36. R. A. Weale, J. Physiol. 113, 115 (1951).
  37. A. C. Hardy, Handbook of Colorimetry (The Technology Press, Cambridge, 1936), p. 31.
  38. E. Hering, Arch. Ophthal. 36, 1 (1890).
  39. D. B. Judd, Natl. Bur. Standards (U. S.) 41, 247 (1948).
    [Crossref]
  40. D. B. Judd, Documenta Ophthal. 3, 251 (1949).
    [Crossref]
  41. This assumption is not inconsistent with the established fact that rod pigments peak at different wavelengths for different lower organisms and even undergo a shift during development in some instances [G. Wald, Ann. Rev. Biochem. 22, 497 (1953)].
    [Crossref]
  42. A. Chapanis, J. Exptl. Psychol. 34, 24 (1944).
    [Crossref]
  43. F. H. G. Pitt, (1935).
  44. P. M. Ladekarl, Acta Ophthal. 12 (Supplement III) (1934).
  45. E. Brodhun, Z. Sinnesphysiol. 3, 97 (1892).
  46. W. D. Wright, J. Opt. Soc. Am. 42, 509 (1952).
    [Crossref] [PubMed]
  47. The measured luminosity function for one tritanopic observer reported by Judd, Plaza, and Farnsworth did show a peak strongly displaced toward the long wavelengths, but they attribute this exceptional case to abnormally heavy macular pigmentation. [ Judd, Plaza, and Farnsworth, J. Opt. Soc. Am. 40, 833 (1950).]
    [Crossref]
  48. G. E. Müller, Darstellung nud Erklärung der verschiedenen Typen der Farbenblindheit (Vandenhoeck and Ruprecht, Göttingen, 1924), p. 72 ff.
  49. Fischer, Bouman, and ten Doesschate, Documenta Ophthal. 5–6, 73 (1951).
    [Crossref]
  50. S. Hecht, Documenta Ophthal. 3, 289 (1949).
    [Crossref]
  51. C. H. Graham and Y. Hsia, Science 120, 780 (A) (1954).

1955 (1)

1954 (3)

W. A. H. Rushton and R. D. Cohen, Nature 173, 301 (1954).
[Crossref] [PubMed]

G. Wald, Science 119, 887 (1954).
[Crossref] [PubMed]

C. H. Graham and Y. Hsia, Science 120, 780 (A) (1954).

1953 (4)

D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 43, 552 (1953).
[Crossref] [PubMed]

For a list of references see: L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 43, 490–492 (1953).
[Crossref]

H. J. A. Dartnall, Brit. Med. Bull. 9, 24 (1953).

This assumption is not inconsistent with the established fact that rod pigments peak at different wavelengths for different lower organisms and even undergo a shift during development in some instances [G. Wald, Ann. Rev. Biochem. 22, 497 (1953)].
[Crossref]

1952 (1)

1951 (4)

L. M. Hurvich and D. Jameson, Science 114, 199 (1951).
[Crossref] [PubMed]

R. A. Weale, J. Physiol. 113, 115 (1951).

S. A. Talbot, J. Opt. Soc. Am. 41, 918 (1951).
[Crossref] [PubMed]

Fischer, Bouman, and ten Doesschate, Documenta Ophthal. 5–6, 73 (1951).
[Crossref]

1950 (2)

1949 (3)

D. B. Judd, Natl. Bur. Standards (U.S.) 42, 13 (1949).

S. Hecht, Documenta Ophthal. 3, 289 (1949).
[Crossref]

D. B. Judd, Documenta Ophthal. 3, 251 (1949).
[Crossref]

1948 (1)

D. B. Judd, Natl. Bur. Standards (U. S.) 41, 247 (1948).
[Crossref]

1945 (2)

E. N. Willmer and W. D. Wright, Nature 156, 119 (1945).
[Crossref]

H. Hartridge, Nature 155, 657 (1945).
[Crossref]

1944 (1)

A. Chapanis, J. Exptl. Psychol. 34, 24 (1944).
[Crossref]

1939 (1)

H. Piéron, Année Psychol. 40, 1 (1939).
[Crossref]

1937 (2)

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 49, 331 (1937).
[Crossref]

D. M. Purdy, Am. J. Psychol. 49, 313 (1937).
[Crossref]

1936 (1)

S. Hecht and S. Shlaer, J. Gen. Physiol. 20, 83 (1936).

1935 (2)

J. F. Schouten, Proc. Acad. Sci. (Amsterdam) 38, 590 (1935).

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 47, 207–208 (1935).
[Crossref]

1934 (1)

P. M. Ladekarl, Acta Ophthal. 12 (Supplement III) (1934).

1929 (1)

A. v. Tschermak, Handb. Norm. Path. Physiol. 12, 295 (1929), p.342 ff.

1927 (2)

R. Hiecke, Z. Sinnesphysiol. 58, 111 (1927).

A. Brückner, Z. Sinnesphysiol. 58, 322 (1927), p. 340 ff.

1925 (1)

E. Schrödinger, Sitzber. Akad. Wiss. Wien. Math.-naturw. Klasse,  134, 471 (1925).

1916 (1)

L. T. Troland, Trans. Illum. Eng. Soc. 11, 957 (1916).

1892 (1)

E. Brodhun, Z. Sinnesphysiol. 3, 97 (1892).

1890 (1)

E. Hering, Arch. Ophthal. 36, 1 (1890).

1884 (1)

A. König and C. Dieterici, Ann. Phys. Chem. 22, 579 (1884).

1880 (1)

E. Hering, Lotos, Jahrb. Naturwiss. N. F. 1, 95, 96 (1880).

Bouman,

Fischer, Bouman, and ten Doesschate, Documenta Ophthal. 5–6, 73 (1951).
[Crossref]

Brodhun, E.

E. Brodhun, Z. Sinnesphysiol. 3, 97 (1892).

Brückner, A.

A. Brückner, Z. Sinnesphysiol. 58, 322 (1927), p. 340 ff.

Chapanis, A.

A. Chapanis, J. Exptl. Psychol. 34, 24 (1944).
[Crossref]

Cohen, R. D.

W. A. H. Rushton and R. D. Cohen, Nature 173, 301 (1954).
[Crossref] [PubMed]

Crozier, W. J.

W. J. Crozier, J. Gen. Physiol. 34, 87 (1950).

Dartnall, H. J. A.

H. J. A. Dartnall, Brit. Med. Bull. 9, 24 (1953).

Dieterici, C.

A. König and C. Dieterici, Ann. Phys. Chem. 22, 579 (1884).

Farnsworth,

Fischer,

Fischer, Bouman, and ten Doesschate, Documenta Ophthal. 5–6, 73 (1951).
[Crossref]

Graham, C. H.

C. H. Graham and Y. Hsia, Science 120, 780 (A) (1954).

Granit, R.

R. Granit, Sensory Mechanisms of the Retina (Oxford University Press, London, 1947).

Guild, J.

J. Guild, in Joint Discussion on Vision (The Physical Society, London, 1932), pp. 1–26.

Hardy, A. C.

A. C. Hardy, Handbook of Colorimetry (The Technology Press, Cambridge, 1936), p. 31.

Hartridge, H.

H. Hartridge, Nature 155, 657 (1945).
[Crossref]

Hecht, S.

S. Hecht, Documenta Ophthal. 3, 289 (1949).
[Crossref]

S. Hecht and S. Shlaer, J. Gen. Physiol. 20, 83 (1936).

Hering, E.

E. Hering, Arch. Ophthal. 36, 1 (1890).

E. Hering, Lotos, Jahrb. Naturwiss. N. F. 1, 95, 96 (1880).

E. Hering, Grundzüge der Lehre vom Lichtsinn (Julius Springer, Berlin, 1920), p. 112 ff.

Hiecke, R.

R. Hiecke, Z. Sinnesphysiol. 58, 111 (1927).

Hsia, Y.

C. H. Graham and Y. Hsia, Science 120, 780 (A) (1954).

Hurvich, L. M.

D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 45, 546 (1955).
[Crossref]

D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 43, 552 (1953).
[Crossref] [PubMed]

For a list of references see: L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 43, 490–492 (1953).
[Crossref]

L. M. Hurvich and D. Jameson, Science 114, 199 (1951).
[Crossref] [PubMed]

Jameson, D.

D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 45, 546 (1955).
[Crossref]

For a list of references see: L. M. Hurvich and D. Jameson, J. Opt. Soc. Am. 43, 490–492 (1953).
[Crossref]

D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 43, 552 (1953).
[Crossref] [PubMed]

L. M. Hurvich and D. Jameson, Science 114, 199 (1951).
[Crossref] [PubMed]

Judd,

Judd, D. B.

D. B. Judd, Documenta Ophthal. 3, 251 (1949).
[Crossref]

D. B. Judd, Natl. Bur. Standards (U.S.) 42, 13 (1949).

D. B. Judd, Natl. Bur. Standards (U. S.) 41, 247 (1948).
[Crossref]

D. B. Judd, Handbook of Experimental Psychology (edited by S. S. Stevens) (John Wiley and Sons, Inc., New York, 1951), pp. 811–867.

König, A.

A. König and C. Dieterici, Ann. Phys. Chem. 22, 579 (1884).

Ladekarl, P. M.

P. M. Ladekarl, Acta Ophthal. 12 (Supplement III) (1934).

Müller, G. E.

G. E. Müller, Darstellung nud Erklärung der verschiedenen Typen der Farbenblindheit (Vandenhoeck and Ruprecht, Göttingen, 1924), p. 72 ff.

Piéron, H.

H. Piéron, Année Psychol. 40, 1 (1939).
[Crossref]

Pirenne, M. H.

M. H. Pirenne, Vision and the Eye (Chapman and Hall Ltd., London, 1948), pp. 159–160.

Pitt, F. H. G.

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 49, 331 (1937).
[Crossref]

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 47, 207–208 (1935).
[Crossref]

F. H. G. Pitt, (1935).

Plaza,

Purdy, D. M.

D. M. Purdy, Am. J. Psychol. 49, 313 (1937).
[Crossref]

D. M. Purdy, “Chroma as a function of retinal illumination,” dissertation, Harvard University, 1–190 (1929), Table VI.

Rushton, W. A. H.

W. A. H. Rushton and R. D. Cohen, Nature 173, 301 (1954).
[Crossref] [PubMed]

Schouten, J. F.

J. F. Schouten, Proc. Acad. Sci. (Amsterdam) 38, 590 (1935).

Schrödinger, E.

E. Schrödinger, Sitzber. Akad. Wiss. Wien. Math.-naturw. Klasse,  134, 471 (1925).

Shlaer, S.

S. Hecht and S. Shlaer, J. Gen. Physiol. 20, 83 (1936).

Talbot, S. A.

ten Doesschate,

Fischer, Bouman, and ten Doesschate, Documenta Ophthal. 5–6, 73 (1951).
[Crossref]

Troland, L. T.

L. T. Troland, Trans. Illum. Eng. Soc. 11, 957 (1916).

L. T. Troland, The Principles of Psychophysiology (D. Van Nostrand Company, Inc., New York, 1930), Vol. II, pp. 142, 144.

Tschermak, A. v.

A. v. Tschermak, Handb. Norm. Path. Physiol. 12, 295 (1929), p.342 ff.

Wald, G.

G. Wald, Science 119, 887 (1954).
[Crossref] [PubMed]

This assumption is not inconsistent with the established fact that rod pigments peak at different wavelengths for different lower organisms and even undergo a shift during development in some instances [G. Wald, Ann. Rev. Biochem. 22, 497 (1953)].
[Crossref]

Weale, R. A.

R. A. Weale, J. Physiol. 113, 115 (1951).

Willmer, E. N.

E. N. Willmer and W. D. Wright, Nature 156, 119 (1945).
[Crossref]

Wright, W. D.

W. D. Wright, J. Opt. Soc. Am. 42, 509 (1952).
[Crossref] [PubMed]

E. N. Willmer and W. D. Wright, Nature 156, 119 (1945).
[Crossref]

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 49, 331 (1937).
[Crossref]

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 47, 207–208 (1935).
[Crossref]

Acta Ophthal. (1)

P. M. Ladekarl, Acta Ophthal. 12 (Supplement III) (1934).

Am. J. Psychol. (1)

D. M. Purdy, Am. J. Psychol. 49, 313 (1937).
[Crossref]

Ann. Phys. Chem. (1)

A. König and C. Dieterici, Ann. Phys. Chem. 22, 579 (1884).

Ann. Rev. Biochem. (1)

This assumption is not inconsistent with the established fact that rod pigments peak at different wavelengths for different lower organisms and even undergo a shift during development in some instances [G. Wald, Ann. Rev. Biochem. 22, 497 (1953)].
[Crossref]

Année Psychol. (1)

H. Piéron, Année Psychol. 40, 1 (1939).
[Crossref]

Arch. Ophthal. (1)

E. Hering, Arch. Ophthal. 36, 1 (1890).

Brit. Med. Bull. (1)

H. J. A. Dartnall, Brit. Med. Bull. 9, 24 (1953).

Documenta Ophthal. (3)

D. B. Judd, Documenta Ophthal. 3, 251 (1949).
[Crossref]

Fischer, Bouman, and ten Doesschate, Documenta Ophthal. 5–6, 73 (1951).
[Crossref]

S. Hecht, Documenta Ophthal. 3, 289 (1949).
[Crossref]

Handb. Norm. Path. Physiol. (1)

A. v. Tschermak, Handb. Norm. Path. Physiol. 12, 295 (1929), p.342 ff.

J. Exptl. Psychol. (1)

A. Chapanis, J. Exptl. Psychol. 34, 24 (1944).
[Crossref]

J. Gen. Physiol. (2)

S. Hecht and S. Shlaer, J. Gen. Physiol. 20, 83 (1936).

W. J. Crozier, J. Gen. Physiol. 34, 87 (1950).

J. Opt. Soc. Am. (6)

J. Physiol. (1)

R. A. Weale, J. Physiol. 113, 115 (1951).

Lotos, Jahrb. Naturwiss. N. F. (1)

E. Hering, Lotos, Jahrb. Naturwiss. N. F. 1, 95, 96 (1880).

Natl. Bur. Standards (U. S.) (1)

D. B. Judd, Natl. Bur. Standards (U. S.) 41, 247 (1948).
[Crossref]

Natl. Bur. Standards (U.S.) (1)

D. B. Judd, Natl. Bur. Standards (U.S.) 42, 13 (1949).

Nature (3)

E. N. Willmer and W. D. Wright, Nature 156, 119 (1945).
[Crossref]

H. Hartridge, Nature 155, 657 (1945).
[Crossref]

W. A. H. Rushton and R. D. Cohen, Nature 173, 301 (1954).
[Crossref] [PubMed]

Proc. Acad. Sci. (Amsterdam) (1)

J. F. Schouten, Proc. Acad. Sci. (Amsterdam) 38, 590 (1935).

Proc. Phys. Soc. (London) (2)

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 47, 207–208 (1935).
[Crossref]

W. D. Wright and F. H. G. Pitt, Proc. Phys. Soc. (London) 49, 331 (1937).
[Crossref]

Science (3)

L. M. Hurvich and D. Jameson, Science 114, 199 (1951).
[Crossref] [PubMed]

G. Wald, Science 119, 887 (1954).
[Crossref] [PubMed]

C. H. Graham and Y. Hsia, Science 120, 780 (A) (1954).

Sitzber. Akad. Wiss. Wien. Math.-naturw. Klasse (1)

E. Schrödinger, Sitzber. Akad. Wiss. Wien. Math.-naturw. Klasse,  134, 471 (1925).

Trans. Illum. Eng. Soc. (1)

L. T. Troland, Trans. Illum. Eng. Soc. 11, 957 (1916).

Z. Sinnesphysiol. (3)

R. Hiecke, Z. Sinnesphysiol. 58, 111 (1927).

A. Brückner, Z. Sinnesphysiol. 58, 322 (1927), p. 340 ff.

E. Brodhun, Z. Sinnesphysiol. 3, 97 (1892).

Other (13)

F. H. G. Pitt, (1935).

G. E. Müller, Darstellung nud Erklärung der verschiedenen Typen der Farbenblindheit (Vandenhoeck and Ruprecht, Göttingen, 1924), p. 72 ff.

Reference 2, p. 831.

D. B. Judd, Handbook of Experimental Psychology (edited by S. S. Stevens) (John Wiley and Sons, Inc., New York, 1951), pp. 811–867.

E. Hering, Grundzüge der Lehre vom Lichtsinn (Julius Springer, Berlin, 1920), p. 112 ff.

J. Guild, in Joint Discussion on Vision (The Physical Society, London, 1932), pp. 1–26.

M. H. Pirenne, Vision and the Eye (Chapman and Hall Ltd., London, 1948), pp. 159–160.

R. Granit, Sensory Mechanisms of the Retina (Oxford University Press, London, 1947).

These responses may be related to different physiological structures or, more likely, they may be correlates of different physiological states within the same structural elements.

Reference 2, p. 855.

A. C. Hardy, Handbook of Colorimetry (The Technology Press, Cambridge, 1936), p. 31.

L. T. Troland, The Principles of Psychophysiology (D. Van Nostrand Company, Inc., New York, 1930), Vol. II, pp. 142, 144.

D. M. Purdy, “Chroma as a function of retinal illumination,” dissertation, Harvard University, 1–190 (1929), Table VI.

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Figures (16)

Fig. 1
Fig. 1

Chromatic response functions for the CIE standard observer.

Fig. 2
Fig. 2

Spectral distribution curves for four receptor substances.

Fig. 3
Fig. 3

Spectral distribution curves for three receptor substances.

Fig. 4
Fig. 4

Variability of frequency-of-seeing functions. See text.

Fig. 5
Fig. 5

Saturation discrimination for two experimental methods.

Fig. 6
Fig. 6

Saturation discrimination for two luminance levels.

Fig. 7
Fig. 7

Spectral hue coefficients. Standard luminance.

Fig. 8
Fig. 8

Spectral hue coefficients. High luminance.

Fig. 9
Fig. 9

Constant hue contours.

Fig. 10
Fig. 10

Wavelength discrimination for two luminance levels.

Fig. 11
Fig. 11

Chromatic and achromatic response functions for protanopia and deuteranopia.

Fig. 12
Fig. 12

Saturation discrimination for protanopia and deuteranopia.

Fig. 13
Fig. 13

Wavelength discrimination for protanopia and deuteranopia.

Fig. 14
Fig. 14

Chromatic and achromatic response functions for tritanopia and tetartanopia.

Fig. 15
Fig. 15

Saturation discrimination for tritanopia and tetartanopia.

Fig. 16
Fig. 16

Wavelength discrimination for tritanopia and tetartanopia.

Equations (22)

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

y - b = 0.4 Y - 0.4 Z , r - g = 1.0 X - 1.0 Y .
y λ - b λ = 0.4 y ¯ λ - 0.4 z ¯ λ , r λ - g λ = 1.0 x ¯ λ - 1.0 y ¯ λ ,
B λ = 13.0682 y ¯ λ + 0.2672 z ¯ λ ,
G λ = - 0.6736 x ¯ λ + 14.0018 y ¯ λ + 0.0040 z ¯ λ ,
Y λ = - 0.0039 x ¯ λ + 13.4680 y ¯ λ - 0.1327 z ¯ λ ,
R λ = 0.3329 x ¯ λ + 13.0012 y ¯ λ - 0.0011 z ¯ λ ,
y λ - b λ = k 1 ( Y λ - B λ ) ,
r λ - g λ = k 2 ( R λ - G λ ) ,
w λ - b k λ = k 3 ( 0.5 B λ + 0.5 G λ + 1.0 Y λ + 1.0 R λ ) - k 4 ( 0.5 B λ + 0.5 G λ + 1.0 Y λ + 1.0 R λ ) .
w λ - b k λ = k 5 y ¯ λ .
α λ = 6.5341 y ¯ λ + 0.1336 z ¯ λ ,
β λ = - 0.3368 x ¯ λ + 7.0009 y ¯ λ + 0.0020 z ¯ λ ,
γ λ = 0.3329 x ¯ λ + 6.4671 y ¯ λ - 0.1347 z ¯ λ .
y λ - b λ = k 1 ( β λ + γ λ - 2 α λ ) ,
r λ - g λ = k 2 ( α λ + λ λ - 2 B λ ) ,
w λ - b k λ = k 3 ( α λ + β λ + γ λ ) - k 4 ( α λ + β λ + γ λ ) .
y λ - b λ = k 1 ( Y λ - B λ ) , ( deuteranope ) y λ p - b λ p = k 1 ( Y λ p - B λ p ) . ( protanope )
w λ - b k λ = k 3 ( 0.5 B λ + 0.5 G λ + 1.0 Y λ + 1.0 R λ ) - k 4 ( 0.5 B λ + 0.5 G λ + 1.0 Y λ + 1.0 R λ )             ( deuteranope ) w λ p - b k λ p = k 3 ( 0.5 B λ p + 0.5 G λ p + 1.0 Y λ p + 1.0 R λ p ) - k 4 ( 0.5 B λ p + 0.5 G λ p + 1.0 Y λ p + 1.0 R λ p )             ( protanope ) .
r λ - g λ = R λ - G λ , w λ - b k λ = k 3 ( 0.5 B λ + 0.5 G λ + 1.0 Y λ + 1.0 R λ ) - k 4 ( 0.5 B λ + 0.5 G λ + 1.0 Y λ + 1.0 R λ ) .
R λ tr . = 0.6658 x ¯ λ + 12.9342 y ¯ λ - 0.2694 z ¯ λ .
r λ tr . - g λ tr . = R λ tr . - G λ , w λ tr . - b k λ tr . = k 3 ( G λ + Y λ + R λ tr . ) - k 4 ( G λ + Y λ + R λ tr . ) .
r λ tr . - g λ tr . = γ λ - β λ , w λ tr . - b k λ tr . = k 3 ( β λ + γ λ ) - k 4 ( β λ + γ λ ) .