Abstract

A theory of color vision is presented which attempts to account for the physics, physiology, and psychology of the color-vision process. Three types of photopigments are assumed to be distributed among five types of cones. It is suggested that color signals are of an opponent-colors variety from retina to lateral geniculate body, then coded in terms of the four psychologically unique colors from the lateral geniculate to the visual cortex. The theory is quantitative and provides an explanation of protanopia, deuteranopia, and tritanopia. A new color diagram is developed, based upon the simplest version of the theory. Suggestions are made concerning how this diagram might be modified to produce a more uniform color space, and the meaning of such modifications is discussed in terms of the theory.

© 1960 Optical Society of America

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  1. (a)D. Jameson and L. M. Hurvich, J. Opt. Soc. Am. 45, 546 (1955); (b)L. M. Hurvich and D. Jameson, ibid. 45, 602 (1955); (c)D. Jameson and L. M. Hurvich, ibid. 46, 405 (1956); (d)D. Jameson and L. M. Hurvich, ibid. 46, 416 (1956).
  2. Hurvich and Jameson are not at all clear on this point. Linearity is implied by their Eqs. (5) and (6) in the second article of their series (p. 603). Equation 5, for example, states that yλ−bλ=k1(Yλ−Bλ), and Eq. 6 states that rλ−gλ=k2(Rλ−Bλ). Since Yλ and Bλ are defined linearly in terms of the tristimulus values of the CIE system (by their Eq. 1 and Eq. 3), then Yλ and Bλ must logically represent the sensitivity curves of the Y and B receptor substances for an equal energy spectrum (these curves are called “spectral distribution curves” and “photochemical excitation functions” by them). However, on p. 604, they state that “… the constants k1 and k2 … in the equations relating the photochemical excitation functions and the chromatic … response functions … are not fixed in value, but are assumed to be defined by different ascending functions of stimulus luminance….” In Fig. 1, however, they plot their chromatic response functions, defined by Eqs. (5) and (6), for fixed values of k1 and k2 (said to be 1.00 for their “reference” luminance level of 10 mL). But an equal-energy spectrum produces different luminances at different wavelengths in proportion to the photopic luminosity function; therefore all points in their Fig. 1 should be weighted accordingly (but are not) and the dependence of k1 and k2 upon luminance should be spelled out in Eqs. 5 and 6 (but is not). It might be thought that this problem could be remedied by changing the assumption that k1 and k2 are functions of luminance, in order to assume instead that they are functions of radiance. However, this raises a still more serious logical problem: there are many metameric pairs that differ greatly in energy, yet produce equivalent visual effects. It seems impossible to imagine a mechanism in the eye that could signal the relative amount of energy impinging upon it.
  3. S. Hecht, Report of a Joint Discussion on Vision (University Press, Cambridge, England, 1932) p. 157.
  4. J. Guild, Report of a Joint Discussion on Vision (University Press, Cambridge, England, 1932) p. 157.
  5. See p. 611 of footnote reference 1b.
  6. D. McL and Purdy Am, J. Psychol. 43, 541 (1931).
    [Crossref]
  7. W. de W. Abney, Researches in Colour Vision and Trichromatic Theory (Longmans Green and Company, Ltd., London, 1913).
  8. H. Grassman, Phil. Mag. Ser. 4 7, 254 (1853).
  9. Y. Le Grand, Light, Colour and Vision, translated by R. W. G. Hunt, J. W. T. Walsh, and F. R. W. Hunt from Optique Physiologique, Tome Deuxiéme, “Lumière et Couleurs” editions de la “Revue d’Optique,” Paris, 1948 (John Wiley & Sons, Inc., New York, 1957). See p. 401 for Le Grand’s statement of what a color theory should explain.
  10. D. B. Judd, “Basic correlates of the visual stimulus,” Handbook of Experimental Psychology, S.S Stevens, ed. (John Wiley & Sons, Inc., New York, 1951), pp. 123–124.
  11. W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).
  12. H. Hartridge, Recent Advances in the Physiology of Vision (Blakison Company, Philadelphia, 1950), pp. 187–199.
  13. S. Newhall, D. Nickerson, and D. B. Judd, J. Opt. Soc. Am. 33, 385 (1943).
    [Crossref]
  14. D. L. MacAdam, J. Opt. Soc. Am. 32, 247 (1942).
    [Crossref]
  15. See footnote 9, p. 401, and footnote reference 10, pp. 830–836.
  16. See footnote reference 9, pp. 123–124.
  17. G. S. Brindley, “Human color vision,” Progress in Biophysics, J. A. V. Butler and B. Katz eds. (Pergamon Press, New York, 1951), Vol. 8.
  18. H. L. F. von Helmholtz, Phil. Mag. 4, 519 (1852); Treatise on Physiological Optics, translated by J. P. Southall, Rochester, New York, Opt. Soc Am., 1924–25 (3 Vol.) p. 426–439.
  19. E. Hering, Grundzuge der Lehre vom Lichsinn (Springer-Verlag, Berlin, 1920).
  20. See references 9, 10, 11, and 17. The most recent review of color theory is that of C. H. Graham, “Color theory,” Psychology: a Study of a Science, S. Koch, ed. (McGraw-Hill Book Company, Inc., New York, 1959). Vol. 1, Chap. 19.
  21. D. B. Judd, J. Res. Natl. Bur. Standards 42, 1 (1946).
    [Crossref]
  22. These curves would require correction for the effects of the ocular media. They may be considered to be the photopigment curves multiplied at each wavelength by the spectral transmittance of the ocular media.
  23. R. Granit, Sensory Mechanisms of the Retina (Oxford University Press, New York, 1947).
  24. H. J. A. Dartnall, Brit. Med. Bull. 9, 24 (1953).
  25. Her Majesty’s Stationary Office, London, 1958.
  26. G. Wald, Retinal Chemistry and the Physiology of Vision (Her Majesty’s Stationary Office, London, 1958), p. 7.
  27. W. A. H. Rushton, The Cone Pigments of the Human Fovea in Colour Blind and Normal (Her Majesty’s Stationary Office, London, 1958), p. 71; (a)Table II, p. 84; (b)Fig. 7, p. 87.
  28. W. A. H. Rushton, F. W. Campbell, W. A. Hagins, and G. S. Brindley, Optica Acta 1, 183 (1955).
    [Crossref]
  29. F. H. G. Pitt, Proc. Roy. Soc. (London) B132, 101 (1944).
  30. H. R. Blackwell and O. M. Blackwell, J. Opt. Soc. Am. 49, 499 (1959). Abstract.
  31. W. S. Stiles, Documenta Opthal. 3, 138 (1949); Proc. Natl. Acad. Sci. U. S. 45, 100 (1959).
    [Crossref]
  32. R. M. Boynton, G. Kandel, and J. W. Onley, J. Opt. Soc. Am. 49, 654 (1959).
    [Crossref] [PubMed]
  33. E. Auerbach and G. Wald, Science 120, 401 (1954).
    [Crossref] [PubMed]
  34. Sinden, J. Opt. Soc. Am. 40, 647 (1950).
    [Crossref]
  35. Henri Piéron, The Sensations (Yale University Press, New Haven, 1952).
  36. G. L. Walls, Am. J. Ophthal. 39, 8 (1955).
  37. G. Svaetichin, Acta Physiol. Scand. 39Suppl. 134, 17 (1956); Acta Physiol. Scand. 29Suppl. 106, 565 (1952); E. F. MacNichol and G. Svaetichin, Am. J. Ophthalmol. 46, 26 (1958); G. Svaetichin and E. F. MacNichol, Ann. N. Y. Acad. Sci. 74, 385 (1958).
    [Crossref]
  38. R. L. DeValois, C. J. Smith, S. T. Kitai, and A. J. Karoly, Science 127, 238 (1958).
    [Crossref]
  39. R. W. Doty, J. Neurophysiol. 21, 437 (1958).
    [PubMed]
  40. W. Penfield and T. Rasmussen, The Cerebral Cortex of Man. A Clinical Study of Localization of Function (The Macmillan Company, New York, 1950).
  41. S. Polyak, The Vertebrate Visual System (University of Chicago Press, Chicago, 1957).
  42. R. M. Boynton, J. M. Enoch, and W. R. Bush, J. Opt Soc. Am. 44, 879 (1954); D. W. DeMott and R. M. Boynton, ibid. 48, 120 (1958); 13 (1958).
    [Crossref] [PubMed]
  43. C. H. Graham (see footnote reference 20).
  44. L. Clark and G. G. Penman, Proc. Roy. Soc. (London),  B114, 291 (1934).
  45. G. L. Walls, Univ. Calif. Publ. Physiol. 9, 1 (1953).
  46. S. S. Stevens, Psychol. Rev. 64, 153 (1957).
    [Crossref] [PubMed]
  47. In Eq. (24), the minus signs must not be interpreted as meaning that the saturation values for red and green (or for yellow and blue) are subtracted from one another. This cannot happen, since by Eq. (23) one of them must have a value of zero. In fact, the minus signs in Eq. (24) could be replaced by plus signs without affecting the result, since the values are squared in each case. Equation (24) is written this way merely to be consistent with Eq. (25). The latter establishes the arbitrary way in which color space is represented in the ϕ−ψ system. Similarly, the negative signs preceding ψg and ψb in Eq. (28) should be taken to mean that if one of the indicated calculations turns out to be negative, the sensation which is represented is either green or blue, and not red or yellow. It should be remembered that no value of ψ may ever be negative.
  48. E. Q. Adams, J. Opt Soc. Am. 32, 168 (1942).
    [Crossref]
  49. C. H. Graham and Yun Hsia, Science 127, 675 (1958).
    [Crossref] [PubMed]
  50. G. L. Walls, Am. J. Optometry 35, 449 (1958).
    [Crossref]
  51. H. G. Sperling, J. Opt. Soc. Am. 30, 156 (1960).
    [Crossref]
  52. L. C. Thomson and W. D. Wright, J. Opt. Soc. Am. 43, 890 (1953).
    [Crossref] [PubMed]
  53. D. B. Judd, J. Research Natl. Bur. Standards 33, 407 (1944).
    [Crossref]
  54. Footnote 9, pp. 124 and 125.

1960 (1)

H. G. Sperling, J. Opt. Soc. Am. 30, 156 (1960).
[Crossref]

1959 (2)

H. R. Blackwell and O. M. Blackwell, J. Opt. Soc. Am. 49, 499 (1959). Abstract.

R. M. Boynton, G. Kandel, and J. W. Onley, J. Opt. Soc. Am. 49, 654 (1959).
[Crossref] [PubMed]

1958 (4)

R. L. DeValois, C. J. Smith, S. T. Kitai, and A. J. Karoly, Science 127, 238 (1958).
[Crossref]

R. W. Doty, J. Neurophysiol. 21, 437 (1958).
[PubMed]

C. H. Graham and Yun Hsia, Science 127, 675 (1958).
[Crossref] [PubMed]

G. L. Walls, Am. J. Optometry 35, 449 (1958).
[Crossref]

1957 (1)

S. S. Stevens, Psychol. Rev. 64, 153 (1957).
[Crossref] [PubMed]

1956 (1)

G. Svaetichin, Acta Physiol. Scand. 39Suppl. 134, 17 (1956); Acta Physiol. Scand. 29Suppl. 106, 565 (1952); E. F. MacNichol and G. Svaetichin, Am. J. Ophthalmol. 46, 26 (1958); G. Svaetichin and E. F. MacNichol, Ann. N. Y. Acad. Sci. 74, 385 (1958).
[Crossref]

1955 (3)

1954 (2)

R. M. Boynton, J. M. Enoch, and W. R. Bush, J. Opt Soc. Am. 44, 879 (1954); D. W. DeMott and R. M. Boynton, ibid. 48, 120 (1958); 13 (1958).
[Crossref] [PubMed]

E. Auerbach and G. Wald, Science 120, 401 (1954).
[Crossref] [PubMed]

1953 (3)

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

L. C. Thomson and W. D. Wright, J. Opt. Soc. Am. 43, 890 (1953).
[Crossref] [PubMed]

G. L. Walls, Univ. Calif. Publ. Physiol. 9, 1 (1953).

1950 (1)

1949 (1)

W. S. Stiles, Documenta Opthal. 3, 138 (1949); Proc. Natl. Acad. Sci. U. S. 45, 100 (1959).
[Crossref]

1946 (1)

D. B. Judd, J. Res. Natl. Bur. Standards 42, 1 (1946).
[Crossref]

1944 (2)

F. H. G. Pitt, Proc. Roy. Soc. (London) B132, 101 (1944).

D. B. Judd, J. Research Natl. Bur. Standards 33, 407 (1944).
[Crossref]

1943 (1)

1942 (2)

D. L. MacAdam, J. Opt. Soc. Am. 32, 247 (1942).
[Crossref]

E. Q. Adams, J. Opt Soc. Am. 32, 168 (1942).
[Crossref]

1934 (1)

L. Clark and G. G. Penman, Proc. Roy. Soc. (London),  B114, 291 (1934).

1931 (1)

D. McL and Purdy Am, J. Psychol. 43, 541 (1931).
[Crossref]

1853 (1)

H. Grassman, Phil. Mag. Ser. 4 7, 254 (1853).

1852 (1)

H. L. F. von Helmholtz, Phil. Mag. 4, 519 (1852); Treatise on Physiological Optics, translated by J. P. Southall, Rochester, New York, Opt. Soc Am., 1924–25 (3 Vol.) p. 426–439.

Abney, W. de W.

W. de W. Abney, Researches in Colour Vision and Trichromatic Theory (Longmans Green and Company, Ltd., London, 1913).

Adams, E. Q.

E. Q. Adams, J. Opt Soc. Am. 32, 168 (1942).
[Crossref]

Am, Purdy

D. McL and Purdy Am, J. Psychol. 43, 541 (1931).
[Crossref]

Auerbach, E.

E. Auerbach and G. Wald, Science 120, 401 (1954).
[Crossref] [PubMed]

Blackwell, H. R.

H. R. Blackwell and O. M. Blackwell, J. Opt. Soc. Am. 49, 499 (1959). Abstract.

Blackwell, O. M.

H. R. Blackwell and O. M. Blackwell, J. Opt. Soc. Am. 49, 499 (1959). Abstract.

Boynton, R. M.

R. M. Boynton, G. Kandel, and J. W. Onley, J. Opt. Soc. Am. 49, 654 (1959).
[Crossref] [PubMed]

R. M. Boynton, J. M. Enoch, and W. R. Bush, J. Opt Soc. Am. 44, 879 (1954); D. W. DeMott and R. M. Boynton, ibid. 48, 120 (1958); 13 (1958).
[Crossref] [PubMed]

Brindley, G. S.

W. A. H. Rushton, F. W. Campbell, W. A. Hagins, and G. S. Brindley, Optica Acta 1, 183 (1955).
[Crossref]

G. S. Brindley, “Human color vision,” Progress in Biophysics, J. A. V. Butler and B. Katz eds. (Pergamon Press, New York, 1951), Vol. 8.

Bush, W. R.

R. M. Boynton, J. M. Enoch, and W. R. Bush, J. Opt Soc. Am. 44, 879 (1954); D. W. DeMott and R. M. Boynton, ibid. 48, 120 (1958); 13 (1958).
[Crossref] [PubMed]

Campbell, F. W.

W. A. H. Rushton, F. W. Campbell, W. A. Hagins, and G. S. Brindley, Optica Acta 1, 183 (1955).
[Crossref]

Clark, L.

L. Clark and G. G. Penman, Proc. Roy. Soc. (London),  B114, 291 (1934).

Dartnall, H. J. A.

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

DeValois, R. L.

R. L. DeValois, C. J. Smith, S. T. Kitai, and A. J. Karoly, Science 127, 238 (1958).
[Crossref]

Doty, R. W.

R. W. Doty, J. Neurophysiol. 21, 437 (1958).
[PubMed]

Enoch, J. M.

R. M. Boynton, J. M. Enoch, and W. R. Bush, J. Opt Soc. Am. 44, 879 (1954); D. W. DeMott and R. M. Boynton, ibid. 48, 120 (1958); 13 (1958).
[Crossref] [PubMed]

Graham, C. H.

C. H. Graham and Yun Hsia, Science 127, 675 (1958).
[Crossref] [PubMed]

C. H. Graham (see footnote reference 20).

See references 9, 10, 11, and 17. The most recent review of color theory is that of C. H. Graham, “Color theory,” Psychology: a Study of a Science, S. Koch, ed. (McGraw-Hill Book Company, Inc., New York, 1959). Vol. 1, Chap. 19.

Granit, R.

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

Grassman, H.

H. Grassman, Phil. Mag. Ser. 4 7, 254 (1853).

Guild, J.

J. Guild, Report of a Joint Discussion on Vision (University Press, Cambridge, England, 1932) p. 157.

Hagins, W. A.

W. A. H. Rushton, F. W. Campbell, W. A. Hagins, and G. S. Brindley, Optica Acta 1, 183 (1955).
[Crossref]

Hartridge, H.

H. Hartridge, Recent Advances in the Physiology of Vision (Blakison Company, Philadelphia, 1950), pp. 187–199.

Hecht, S.

S. Hecht, Report of a Joint Discussion on Vision (University Press, Cambridge, England, 1932) p. 157.

Hering, E.

E. Hering, Grundzuge der Lehre vom Lichsinn (Springer-Verlag, Berlin, 1920).

Hsia, Yun

C. H. Graham and Yun Hsia, Science 127, 675 (1958).
[Crossref] [PubMed]

Hurvich, L. M.

Jameson, D.

Judd, D. B.

D. B. Judd, J. Res. Natl. Bur. Standards 42, 1 (1946).
[Crossref]

D. B. Judd, J. Research Natl. Bur. Standards 33, 407 (1944).
[Crossref]

S. Newhall, D. Nickerson, and D. B. Judd, J. Opt. Soc. Am. 33, 385 (1943).
[Crossref]

D. B. Judd, “Basic correlates of the visual stimulus,” Handbook of Experimental Psychology, S.S Stevens, ed. (John Wiley & Sons, Inc., New York, 1951), pp. 123–124.

Kandel, G.

Karoly, A. J.

R. L. DeValois, C. J. Smith, S. T. Kitai, and A. J. Karoly, Science 127, 238 (1958).
[Crossref]

Kitai, S. T.

R. L. DeValois, C. J. Smith, S. T. Kitai, and A. J. Karoly, Science 127, 238 (1958).
[Crossref]

Le Grand, Y.

Y. Le Grand, Light, Colour and Vision, translated by R. W. G. Hunt, J. W. T. Walsh, and F. R. W. Hunt from Optique Physiologique, Tome Deuxiéme, “Lumière et Couleurs” editions de la “Revue d’Optique,” Paris, 1948 (John Wiley & Sons, Inc., New York, 1957). See p. 401 for Le Grand’s statement of what a color theory should explain.

MacAdam, D. L.

McL, D.

D. McL and Purdy Am, J. Psychol. 43, 541 (1931).
[Crossref]

Newhall, S.

Nickerson, D.

Onley, J. W.

Penfield, W.

W. Penfield and T. Rasmussen, The Cerebral Cortex of Man. A Clinical Study of Localization of Function (The Macmillan Company, New York, 1950).

Penman, G. G.

L. Clark and G. G. Penman, Proc. Roy. Soc. (London),  B114, 291 (1934).

Piéron, Henri

Henri Piéron, The Sensations (Yale University Press, New Haven, 1952).

Pitt, F. H. G.

F. H. G. Pitt, Proc. Roy. Soc. (London) B132, 101 (1944).

Polyak, S.

S. Polyak, The Vertebrate Visual System (University of Chicago Press, Chicago, 1957).

Rasmussen, T.

W. Penfield and T. Rasmussen, The Cerebral Cortex of Man. A Clinical Study of Localization of Function (The Macmillan Company, New York, 1950).

Rushton, W. A. H.

W. A. H. Rushton, F. W. Campbell, W. A. Hagins, and G. S. Brindley, Optica Acta 1, 183 (1955).
[Crossref]

W. A. H. Rushton, The Cone Pigments of the Human Fovea in Colour Blind and Normal (Her Majesty’s Stationary Office, London, 1958), p. 71; (a)Table II, p. 84; (b)Fig. 7, p. 87.

Sinden,

Smith, C. J.

R. L. DeValois, C. J. Smith, S. T. Kitai, and A. J. Karoly, Science 127, 238 (1958).
[Crossref]

Sperling, H. G.

H. G. Sperling, J. Opt. Soc. Am. 30, 156 (1960).
[Crossref]

Stevens, S. S.

S. S. Stevens, Psychol. Rev. 64, 153 (1957).
[Crossref] [PubMed]

Stiles, W. S.

W. S. Stiles, Documenta Opthal. 3, 138 (1949); Proc. Natl. Acad. Sci. U. S. 45, 100 (1959).
[Crossref]

Svaetichin, G.

G. Svaetichin, Acta Physiol. Scand. 39Suppl. 134, 17 (1956); Acta Physiol. Scand. 29Suppl. 106, 565 (1952); E. F. MacNichol and G. Svaetichin, Am. J. Ophthalmol. 46, 26 (1958); G. Svaetichin and E. F. MacNichol, Ann. N. Y. Acad. Sci. 74, 385 (1958).
[Crossref]

Thomson, L. C.

von Helmholtz, H. L. F.

H. L. F. von Helmholtz, Phil. Mag. 4, 519 (1852); Treatise on Physiological Optics, translated by J. P. Southall, Rochester, New York, Opt. Soc Am., 1924–25 (3 Vol.) p. 426–439.

Wald, G.

E. Auerbach and G. Wald, Science 120, 401 (1954).
[Crossref] [PubMed]

G. Wald, Retinal Chemistry and the Physiology of Vision (Her Majesty’s Stationary Office, London, 1958), p. 7.

Walls, G. L.

G. L. Walls, Am. J. Optometry 35, 449 (1958).
[Crossref]

G. L. Walls, Am. J. Ophthal. 39, 8 (1955).

G. L. Walls, Univ. Calif. Publ. Physiol. 9, 1 (1953).

Wright, W. D.

L. C. Thomson and W. D. Wright, J. Opt. Soc. Am. 43, 890 (1953).
[Crossref] [PubMed]

W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).

Acta Physiol. Scand. (1)

G. Svaetichin, Acta Physiol. Scand. 39Suppl. 134, 17 (1956); Acta Physiol. Scand. 29Suppl. 106, 565 (1952); E. F. MacNichol and G. Svaetichin, Am. J. Ophthalmol. 46, 26 (1958); G. Svaetichin and E. F. MacNichol, Ann. N. Y. Acad. Sci. 74, 385 (1958).
[Crossref]

Am. J. Ophthal. (1)

G. L. Walls, Am. J. Ophthal. 39, 8 (1955).

Am. J. Optometry (1)

G. L. Walls, Am. J. Optometry 35, 449 (1958).
[Crossref]

Brit. Med. Bull. (1)

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

Documenta Opthal. (1)

W. S. Stiles, Documenta Opthal. 3, 138 (1949); Proc. Natl. Acad. Sci. U. S. 45, 100 (1959).
[Crossref]

J. Neurophysiol. (1)

R. W. Doty, J. Neurophysiol. 21, 437 (1958).
[PubMed]

J. Opt Soc. Am. (2)

R. M. Boynton, J. M. Enoch, and W. R. Bush, J. Opt Soc. Am. 44, 879 (1954); D. W. DeMott and R. M. Boynton, ibid. 48, 120 (1958); 13 (1958).
[Crossref] [PubMed]

E. Q. Adams, J. Opt Soc. Am. 32, 168 (1942).
[Crossref]

J. Opt. Soc. Am. (8)

J. Psychol. (1)

D. McL and Purdy Am, J. Psychol. 43, 541 (1931).
[Crossref]

J. Res. Natl. Bur. Standards (1)

D. B. Judd, J. Res. Natl. Bur. Standards 42, 1 (1946).
[Crossref]

J. Research Natl. Bur. Standards (1)

D. B. Judd, J. Research Natl. Bur. Standards 33, 407 (1944).
[Crossref]

Optica Acta (1)

W. A. H. Rushton, F. W. Campbell, W. A. Hagins, and G. S. Brindley, Optica Acta 1, 183 (1955).
[Crossref]

Phil. Mag. (1)

H. L. F. von Helmholtz, Phil. Mag. 4, 519 (1852); Treatise on Physiological Optics, translated by J. P. Southall, Rochester, New York, Opt. Soc Am., 1924–25 (3 Vol.) p. 426–439.

Phil. Mag. Ser. 4 (1)

H. Grassman, Phil. Mag. Ser. 4 7, 254 (1853).

Proc. Roy. Soc. (London) (2)

F. H. G. Pitt, Proc. Roy. Soc. (London) B132, 101 (1944).

L. Clark and G. G. Penman, Proc. Roy. Soc. (London),  B114, 291 (1934).

Psychol. Rev. (1)

S. S. Stevens, Psychol. Rev. 64, 153 (1957).
[Crossref] [PubMed]

Science (3)

C. H. Graham and Yun Hsia, Science 127, 675 (1958).
[Crossref] [PubMed]

R. L. DeValois, C. J. Smith, S. T. Kitai, and A. J. Karoly, Science 127, 238 (1958).
[Crossref]

E. Auerbach and G. Wald, Science 120, 401 (1954).
[Crossref] [PubMed]

Univ. Calif. Publ. Physiol. (1)

G. L. Walls, Univ. Calif. Publ. Physiol. 9, 1 (1953).

Other (25)

C. H. Graham (see footnote reference 20).

W. Penfield and T. Rasmussen, The Cerebral Cortex of Man. A Clinical Study of Localization of Function (The Macmillan Company, New York, 1950).

S. Polyak, The Vertebrate Visual System (University of Chicago Press, Chicago, 1957).

In Eq. (24), the minus signs must not be interpreted as meaning that the saturation values for red and green (or for yellow and blue) are subtracted from one another. This cannot happen, since by Eq. (23) one of them must have a value of zero. In fact, the minus signs in Eq. (24) could be replaced by plus signs without affecting the result, since the values are squared in each case. Equation (24) is written this way merely to be consistent with Eq. (25). The latter establishes the arbitrary way in which color space is represented in the ϕ−ψ system. Similarly, the negative signs preceding ψg and ψb in Eq. (28) should be taken to mean that if one of the indicated calculations turns out to be negative, the sensation which is represented is either green or blue, and not red or yellow. It should be remembered that no value of ψ may ever be negative.

Hurvich and Jameson are not at all clear on this point. Linearity is implied by their Eqs. (5) and (6) in the second article of their series (p. 603). Equation 5, for example, states that yλ−bλ=k1(Yλ−Bλ), and Eq. 6 states that rλ−gλ=k2(Rλ−Bλ). Since Yλ and Bλ are defined linearly in terms of the tristimulus values of the CIE system (by their Eq. 1 and Eq. 3), then Yλ and Bλ must logically represent the sensitivity curves of the Y and B receptor substances for an equal energy spectrum (these curves are called “spectral distribution curves” and “photochemical excitation functions” by them). However, on p. 604, they state that “… the constants k1 and k2 … in the equations relating the photochemical excitation functions and the chromatic … response functions … are not fixed in value, but are assumed to be defined by different ascending functions of stimulus luminance….” In Fig. 1, however, they plot their chromatic response functions, defined by Eqs. (5) and (6), for fixed values of k1 and k2 (said to be 1.00 for their “reference” luminance level of 10 mL). But an equal-energy spectrum produces different luminances at different wavelengths in proportion to the photopic luminosity function; therefore all points in their Fig. 1 should be weighted accordingly (but are not) and the dependence of k1 and k2 upon luminance should be spelled out in Eqs. 5 and 6 (but is not). It might be thought that this problem could be remedied by changing the assumption that k1 and k2 are functions of luminance, in order to assume instead that they are functions of radiance. However, this raises a still more serious logical problem: there are many metameric pairs that differ greatly in energy, yet produce equivalent visual effects. It seems impossible to imagine a mechanism in the eye that could signal the relative amount of energy impinging upon it.

S. Hecht, Report of a Joint Discussion on Vision (University Press, Cambridge, England, 1932) p. 157.

J. Guild, Report of a Joint Discussion on Vision (University Press, Cambridge, England, 1932) p. 157.

See p. 611 of footnote reference 1b.

These curves would require correction for the effects of the ocular media. They may be considered to be the photopigment curves multiplied at each wavelength by the spectral transmittance of the ocular media.

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

Henri Piéron, The Sensations (Yale University Press, New Haven, 1952).

E. Hering, Grundzuge der Lehre vom Lichsinn (Springer-Verlag, Berlin, 1920).

See references 9, 10, 11, and 17. The most recent review of color theory is that of C. H. Graham, “Color theory,” Psychology: a Study of a Science, S. Koch, ed. (McGraw-Hill Book Company, Inc., New York, 1959). Vol. 1, Chap. 19.

See footnote 9, p. 401, and footnote reference 10, pp. 830–836.

See footnote reference 9, pp. 123–124.

G. S. Brindley, “Human color vision,” Progress in Biophysics, J. A. V. Butler and B. Katz eds. (Pergamon Press, New York, 1951), Vol. 8.

Her Majesty’s Stationary Office, London, 1958.

G. Wald, Retinal Chemistry and the Physiology of Vision (Her Majesty’s Stationary Office, London, 1958), p. 7.

W. A. H. Rushton, The Cone Pigments of the Human Fovea in Colour Blind and Normal (Her Majesty’s Stationary Office, London, 1958), p. 71; (a)Table II, p. 84; (b)Fig. 7, p. 87.

Y. Le Grand, Light, Colour and Vision, translated by R. W. G. Hunt, J. W. T. Walsh, and F. R. W. Hunt from Optique Physiologique, Tome Deuxiéme, “Lumière et Couleurs” editions de la “Revue d’Optique,” Paris, 1948 (John Wiley & Sons, Inc., New York, 1957). See p. 401 for Le Grand’s statement of what a color theory should explain.

D. B. Judd, “Basic correlates of the visual stimulus,” Handbook of Experimental Psychology, S.S Stevens, ed. (John Wiley & Sons, Inc., New York, 1951), pp. 123–124.

W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).

H. Hartridge, Recent Advances in the Physiology of Vision (Blakison Company, Philadelphia, 1950), pp. 187–199.

Footnote 9, pp. 124 and 125.

W. de W. Abney, Researches in Colour Vision and Trichromatic Theory (Longmans Green and Company, Ltd., London, 1913).

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Figures (7)

Fig. 1
Fig. 1

Absorption spectra for the three photopic visual pigments, according to Eq. (1).

Fig. 2
Fig. 2

Spectral sensitivity functions for the four postulated receptors.

Fig. 3
Fig. 3

Opponent-colors sensitivity functions RλGλ and YλBλ. (Chrominance for the equal-energy spectrum.)

Fig. 4
Fig. 4

A unit-k ϕψ diagram (see text). This is a nonlinear transformation of the CIE chromaticity diagram; translation from the xy chromaticity coefficients to the ϕ and ψ values is accomplished by means of Eq. 29. The spectral locus is shown together with a number of the Munsell renotations for Value 5.

Fig. 5
Fig. 5

Munsell chroma values as a function of ψ, taken from Fig. 4 in the four principal directions. Measurements have been made starting at the point of zero chroma in Fig. 4.

Fig. 6
Fig. 6

Comparison of the luminosity curve of the protanope, as obtained experimentally, with that calculated from the theory. Data are from Pitt.29

Fig. 7
Fig. 7

Method for calculating the copunctal point of the protanope (see text).

Tables (2)

Tables Icon

Table I Values of α, β, and γ calculated from Eq. 1. Values with asterisks have been considered as zero in further computations.

Tables Icon

Table II Comparison between Judd’s values and those of the present theory.

Equations (50)

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α = 0.5163 x ¯ + 0.1496 y ¯ - 0.1033 z ¯ , β = - 0.5163 x ¯ + 1.3034 y ¯ + 0.1033 z ¯ , γ = 0.4000 z ¯ .
R λ = 84 α +     9 β + 40 γ , W λ = Y λ = 44 α + 44 β , G λ =             80 β , B λ = 22 α + 22 β + 80 γ ,
R λ - G λ = 84 α - 71 β + 40 γ , Y λ - B λ = 22 α + 22 β - 80 γ ,
R λ - G λ = 80.053 x ¯ - 79.975 y ¯ - 0.0115 z ¯ , Y λ - B λ = 31.966 y ¯ - 32.000 z ¯ ,
R λ - G λ = 80 ( x ¯ - y ¯ ) , Y λ - B λ = 32 ( y ¯ - z ¯ ) .
Y λ = 44 α + 44 β = 44 ( 1.453 y ¯ ) = 63.932 y ¯ ,
Y λ = 64 y ¯ .
L = E λ W λ d λ = E λ Y λ d λ .
S r g = R λ - G λ ,             S y b = Y λ - B λ .
C r g = E λ ( R λ - G λ ) d λ C y b = E λ ( Y λ - B λ ) d λ .
R = m 1 log C r g , ( if C r g > + t ) G = m 2 log ( - C r g ) , ( if C r g < - t ) Y = m 3 log C y b , ( if C y b > + t ) B = m 4 log ( - C y b ) , ( if C y b < - t ) .
W = m 5 log L .
B = L k 5
log B = k 5 log L .
W = m 5 log L ,
log B = ( k 5 / m 5 ) W .
log Q r = ( k 1 / m 1 ) R , log Q g = ( k 2 / m 2 ) G , log Q y = ( k 3 / m 3 ) Y , log Q b = ( k 4 / m 4 ) B .
ψ r = Q r / B
log ψ r = log Q r - log B .
log ψ r = ( k 1 / m 1 ) R - ( k 5 / m 5 ) W .
log ψ r = ( k 1 / m 1 ) ( m 1 log C r g ) - ( k 5 / m 5 ) ( m 5 log L ) = log [ ( C r g ) k 1 / L k 5 ] ,
ψ r = ( C r g ) k 1 / L k 5 .
ψ g = 0 , ψ r = ( C r g ) k 1 / L k 5 ( when C r g > + t ) , ψ r = 0 , - ψ g = ( C r g ) k 5 / L k 5 ( when C r g < - t ) , ψ b = 0 , ψ y = ( C y b ) k 5 / L k 5 ( when C y b > + t , ψ y = 0 , - ψ b = ( C y b ) k 5 / L k 5 ( when C y b < - t ) .
ψ r = ψ g = 0 ( when + t < C r g < - t ) , ψ y = ψ b = 0 ( when + t < C y b < - t ) .
ψ = [ ( ψ r - ψ g ) 2 + ( ψ y - ψ b ) 2 ] 1 2 ,
ϕ = arc tan [ ( ψ y - ψ b ) / ( ψ r - ψ g ) ] .
X = x ( X + Y + Z ) , Y = y ( X + Y + Z ) , Z = z ( X + Y + Z ) .
C r y / L = E λ ( R λ - G λ ) d λ / E λ ( Y λ ) d λ .
C r y / L = 80 E λ ( x ¯ - y ¯ ) d λ / 64 E λ y ¯ d λ = 1.25 [ ( E λ x ¯ d λ - E λ y ¯ d λ ) / E λ y ¯ d λ ] .
C r g / L = 1.25 [ ( X - Y ) / Y ] , = 1.25 { [ x ( X + Y + Z ) - y ( X + Y + Z ) ] / y ( X + Y + Z ) } , = 1.25 [ ( x - y ) / y ] .
ψ g = 0 , ψ r = 1.25 [ ( x - y ) / y ] ( when C r g > t ) , ψ r = 0 , - ψ g = 1.25 [ ( x - y ) / y ] ( when C r g < t ) , ψ b = 0 , ψ y = 0.5 [ ( y - z ) / y ] ( when C y b > t ) , ψ y = 0 , - ψ b = 0.5 [ ( y - z ) / y ] ( when C y b < t ) .
ϕ = arc tan [ 1.25 ( x - y ) / 0.5 ( y - z ) ] = 2.5 ( x - y ) / ( y - z ) ,
ψ = [ 25 ( x - y ) 2 + 4 ( y - z ) 2 ] 1 2 / 4 y .
Y λ = 4 α + 44 β ,             B λ = 80 γ .
Y λ = 44 α + 44 β ,             B λ = 22 α + 22 β + 80 γ .
x = X / ( X + Y + Z ) , y = Y / ( X + Y + Z ) , z = Z / ( X + Y + Z ) ,
X = E λ x ¯ λ = E x ¯ 1 + f E x ¯ 2 = E ( x ¯ 1 + f x ¯ 2 ) .
X = E ( x ¯ 1 + f x ¯ 2 ) , Y = E ( y ¯ 1 + f y ¯ 2 ) , Z = E ( z ¯ 1 + f z ¯ 2 ) .
x = x ¯ 1 + f x ¯ 2 ( x ¯ 1 + y ¯ 1 + z ¯ 1 ) + f ( x ¯ 2 + y ¯ 2 + z ¯ 2 ) y = y ¯ 1 + f x ¯ 2 ( x ¯ 1 + y ¯ 1 + z ¯ 1 ) + f ( x ¯ 2 + y ¯ 2 + z ¯ 2 ) , z = z ¯ 1 + f z ¯ 2 ( x ¯ 1 + y ¯ 1 + z ¯ 1 ) + f ( x ¯ 2 + y ¯ 2 + z ¯ 2 ) .
x 1 = x ¯ 1 / ( x ¯ 1 + y ¯ 1 + z ¯ 1 ) ,
similarly for P 2 ( λ 2 ) x ¯ 1 + y ¯ 1 + z ¯ 1 = x ¯ 1 / x 1 ; x ¯ 2 + y ¯ 2 + z ¯ 2 = x ¯ 2 / x 2 . }
x = x ¯ 1 + f x ¯ 2 ( x ¯ 1 / x 1 ) + f ( x ¯ 2 / x 2 ) , y = y ¯ 1 + f y ¯ 2 ( x ¯ 1 / x 1 ) + f ( x ¯ 2 / x 2 ) , z = z ¯ 1 + f z ¯ 2 ( x ¯ 1 / x ¯ 1 ) + f ( x ¯ 2 / x 2 ) ,
f ( Y - B ) 2 + ( Y - B ) 1 f Y 2 + Y 1 = f ( Y - B ) 3 + ( Y - B ) 1 f Y 3 + Y 1 ,
f = B 1 Y 2 - B 2 Y 1 ( B 2 Y 3 - B 3 Y 2 ) + f - 1 ( B 1 Y 3 - B 3 Y 1 ) .
x = x ¯ 1 + f x ¯ 3 ( x ¯ 1 / x 1 ) + f ( x ¯ 3 / x 3 ) , y = y ¯ 1 + f y ¯ 3 ( x ¯ 1 / x 1 ) + f ( x ¯ 3 / x 3 ) , z = z ¯ 1 + f z ¯ 3 ( x ¯ 1 / x 1 ) + f ( x ¯ 3 / x 3 ) .
x = 0.751 , y = 0.250 ,
x = 1.070 ,             y = - 0.055.
R λ = 84 α + 9 β ,             G λ = 80 β ,             W λ = 44 α + 44 β .
x = 0.168 ,             y = 0.004.
S λ = W λ + k [ ( C r g ) 2 + ( C y b ) 2 ] 1 2 ,