Abstract

This is an attempt to determine the primaries corresponding to the fundamental sensations of the Young-Helmholtz theory. Unlike previous attempts by various authors, this determination is based solely on color-mixture data pertaining to the trichromatic observer. It is shown that the primaries can be derived from the color-mixture data of the average trichromate with reasonably small uncertainty, if only the one hypothesis is made that each of the three response functions has a certain simple geometrical character, resembling the standard luminosity function. This hypothesis is suggested by the purely physico-chemical character of the retinal processes. An analysis of the situation shows that in order to explain the behavior of color blind observers by the response functions thus obtained it is necessary to assume that “inner” dichromatism—such as deuteranopia—consists not in the absence of one of the fundamental responses, but in the failure of the mental organ to distinguish qualitatively between two of the fundamental responses. A satisfactory quantitative account is given of all the known forms of dichromatism.

A colorimetric system based on the “natural” or Young primaries compares favorably with the conventional I.C.I. system.

© 1948 Optical Society of America

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References

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  1. A. König and C. Dieterici, Zeits. Psychol. 4, 241 (1893).
  2. D. B. Judd, J. Opt. Soc. Am. 35, 199 (1945).
    [Crossref]
  3. F. H. G. Pitt, Medical Research Council, “Report of the Committee on the Physiology of Vision,” 14, (London, 1935).
  4. S. Hecht and S. Schlaer, J. Gen. Physiol. 20, 57 (1936).
  5. Dresler, Das Licht 7, 203 (1937).
  6. J. v. Kries, “Die Gesichtsempfindungen,” Nagel’s Handbuch der Physiology des Menschen (Braunschweig, 1905), Vol. 3.
  7. P. Moon, The Scientific Basis of Illumination Engineering (1936).
  8. Here we have made use of the assumption that the red-response curve has a simple bell-shaped form and not the camel-back type as supposed, by some authors, on psychical grounds. (See for example, C. Ladd-Franklin, Color and Color Theories (New York, 1929).
  9. W. M. McKeon and W. D. Wright, Proc. Phys. Soc. London 52, 464 (1940).
    [Crossref]
  10. J. H. Nelson, Proc. Phys. Soc. London 50, 661 (1938).
    [Crossref]
  11. L. L. Sloan and S. M. Newhall, Am. J. Ophtal. 25, 945 (1942).
  12. W. D. Wright, Trans. Opt. Soc. London 30, 141 (1928–29).
    [Crossref]
  13. Exner, Sitz. Akad. Wiss. Wien 119, 233 (1910).
  14. D. B. Judd, J. Opt. Soc. Am. 23, 366 (1933).
  15. W. Dieter, Zeits. Sinnesphysiol. 58, 73 (1927).

1945 (1)

1942 (1)

L. L. Sloan and S. M. Newhall, Am. J. Ophtal. 25, 945 (1942).

1940 (1)

W. M. McKeon and W. D. Wright, Proc. Phys. Soc. London 52, 464 (1940).
[Crossref]

1938 (1)

J. H. Nelson, Proc. Phys. Soc. London 50, 661 (1938).
[Crossref]

1937 (1)

Dresler, Das Licht 7, 203 (1937).

1936 (2)

P. Moon, The Scientific Basis of Illumination Engineering (1936).

S. Hecht and S. Schlaer, J. Gen. Physiol. 20, 57 (1936).

1933 (1)

D. B. Judd, J. Opt. Soc. Am. 23, 366 (1933).

1927 (1)

W. Dieter, Zeits. Sinnesphysiol. 58, 73 (1927).

1910 (1)

Exner, Sitz. Akad. Wiss. Wien 119, 233 (1910).

1893 (1)

A. König and C. Dieterici, Zeits. Psychol. 4, 241 (1893).

Dieter, W.

W. Dieter, Zeits. Sinnesphysiol. 58, 73 (1927).

Dieterici, C.

A. König and C. Dieterici, Zeits. Psychol. 4, 241 (1893).

Dresler,

Dresler, Das Licht 7, 203 (1937).

Exner,

Exner, Sitz. Akad. Wiss. Wien 119, 233 (1910).

Hecht, S.

S. Hecht and S. Schlaer, J. Gen. Physiol. 20, 57 (1936).

Judd, D. B.

D. B. Judd, J. Opt. Soc. Am. 35, 199 (1945).
[Crossref]

D. B. Judd, J. Opt. Soc. Am. 23, 366 (1933).

König, A.

A. König and C. Dieterici, Zeits. Psychol. 4, 241 (1893).

Kries, J. v.

J. v. Kries, “Die Gesichtsempfindungen,” Nagel’s Handbuch der Physiology des Menschen (Braunschweig, 1905), Vol. 3.

Ladd-Franklin, C.

Here we have made use of the assumption that the red-response curve has a simple bell-shaped form and not the camel-back type as supposed, by some authors, on psychical grounds. (See for example, C. Ladd-Franklin, Color and Color Theories (New York, 1929).

McKeon, W. M.

W. M. McKeon and W. D. Wright, Proc. Phys. Soc. London 52, 464 (1940).
[Crossref]

Moon, P.

P. Moon, The Scientific Basis of Illumination Engineering (1936).

Nelson, J. H.

J. H. Nelson, Proc. Phys. Soc. London 50, 661 (1938).
[Crossref]

Newhall, S. M.

L. L. Sloan and S. M. Newhall, Am. J. Ophtal. 25, 945 (1942).

Pitt, F. H. G.

F. H. G. Pitt, Medical Research Council, “Report of the Committee on the Physiology of Vision,” 14, (London, 1935).

Schlaer, S.

S. Hecht and S. Schlaer, J. Gen. Physiol. 20, 57 (1936).

Sloan, L. L.

L. L. Sloan and S. M. Newhall, Am. J. Ophtal. 25, 945 (1942).

Wright, W. D.

W. M. McKeon and W. D. Wright, Proc. Phys. Soc. London 52, 464 (1940).
[Crossref]

W. D. Wright, Trans. Opt. Soc. London 30, 141 (1928–29).
[Crossref]

Am. J. Ophtal. (1)

L. L. Sloan and S. M. Newhall, Am. J. Ophtal. 25, 945 (1942).

Das Licht (1)

Dresler, Das Licht 7, 203 (1937).

J. Gen. Physiol. (1)

S. Hecht and S. Schlaer, J. Gen. Physiol. 20, 57 (1936).

J. Opt. Soc. Am. (2)

D. B. Judd, J. Opt. Soc. Am. 35, 199 (1945).
[Crossref]

D. B. Judd, J. Opt. Soc. Am. 23, 366 (1933).

Proc. Phys. Soc. London (2)

W. M. McKeon and W. D. Wright, Proc. Phys. Soc. London 52, 464 (1940).
[Crossref]

J. H. Nelson, Proc. Phys. Soc. London 50, 661 (1938).
[Crossref]

Sitz. Akad. Wiss. Wien (1)

Exner, Sitz. Akad. Wiss. Wien 119, 233 (1910).

The Scientific Basis of Illumination Engineering (1)

P. Moon, The Scientific Basis of Illumination Engineering (1936).

Trans. Opt. Soc. London (1)

W. D. Wright, Trans. Opt. Soc. London 30, 141 (1928–29).
[Crossref]

Zeits. Psychol. (1)

A. König and C. Dieterici, Zeits. Psychol. 4, 241 (1893).

Zeits. Sinnesphysiol. (1)

W. Dieter, Zeits. Sinnesphysiol. 58, 73 (1927).

Other (3)

F. H. G. Pitt, Medical Research Council, “Report of the Committee on the Physiology of Vision,” 14, (London, 1935).

Here we have made use of the assumption that the red-response curve has a simple bell-shaped form and not the camel-back type as supposed, by some authors, on psychical grounds. (See for example, C. Ladd-Franklin, Color and Color Theories (New York, 1929).

J. v. Kries, “Die Gesichtsempfindungen,” Nagel’s Handbuch der Physiology des Menschen (Braunschweig, 1905), Vol. 3.

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Equations (33)

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f r ( 1 ) , f g ( 1 ) , f v ( 1 ) ; f r ( 2 ) , f g ( 2 ) , f v ( 2 ) ; f r ( 3 ) , f g ( 3 ) , f v ( 3 ) ,
F r = x ¯ · f r ( 1 ) + y ¯ · f r ( 2 ) + z ¯ · f r ( 3 ) , F g = x ¯ · f g ( 1 ) + y ¯ · f g ( 2 ) + z ¯ · f g ( 3 ) , F v = x ¯ · f v ( 1 ) + y ¯ · f v ( 2 ) + z ¯ · f v ( 3 ) .
X r =     1.8517 , Y r = 0.6642 , Z r = 0.0000 , X g = - 1.0630 , Y g = 0.3321 , Z g = 0.0020 , X v =     0.2113 , Y v = 0.0037 , Z v = 0.9980.
Z r = 0 ,             X r / Y r = 0.7360 / 0.2640 = 2.7879.
X v / Z v = 0.2117 ,             Y v / Z v = 0.0037.
Y r / Y g = 2.000.
α r X r + α g X g = 0.4441 ,             α r Y r + α g Y g = 0.5547 , α g Z g = 0.0012.
α g ( 2.788 Y g - X g ) = 1.10 ,
Z g / 2.788 Y g - X g = 0.0012 / 1.10 = 0.0011.
X r + X g + X v = 1 ,             Y r + Y g + Y v = 1 , Z r + Z g + Z v = 1.
F r =     0.2513 X + 0.8049 Y - 0.0562 Z , F g = - 0.5027 X + 1.4015 Y + 0.1012 Z , F v =     0.0010 X - 0.0028 Y + 1.0018 Z .
l r = 0.6642 ,             l g = 0.3321 ,             l v = 0.0037.
l v / l g = 0.0111 ,             l r / l g = 2.
L r = l r · F r ,             L g = l g · F g ,             L v = l v · F v ,
L = L r + L g + L v = l r · F r + l g · F g + l v · F v .
F r = f r ( λ ) · W λ · d λ , F g = f g ( λ ) · W λ · d λ , F v = f v ( λ ) · W λ · d λ ,
f y = ( α / 1 + α ) · f r + ( 1 / 1 + α ) · f g ,
F v / F y = constant ,
F v / F g + α · F r = constant .
F v = 0 ,             F g + α · F r = 0 ,
0.0010 x - 0.0028 y + 1.0018 z = 0 , ( 0.2513 α - 0.5027 ) x + ( 0.8049 α + 1.4015 ) y + ( 0.1012 - 0.0562 α ) z = 0.
x = 1.001 - 1.004 y ,             y = 1 - 0.5 α / 3.8 + 1.1 α .
( 3.16 f r + f g + 0.011 f v ) / 4.10.
3.16 4.16 f r + 1 4.16 f g = 1 0.87 · f v ,
f p = ( β / 1 + β ) f v + ( 1 / 1 + β ) f r ,
f p = 1 + 0.87 β 1 + β · f g ,
β 1 + 0.87 β · f v + 1 1 + 0.87 β · f r = f g .
F g = 0 ,             F r + β · F v = 0 ,
- 0.503 x + 1.401 y + 0.101 z = 0 , 0.251 x + 0.805 y + 0.079 z = 0 , x + y + z = 1 ,
F r = c ( λ ) · r · F r ,             F g = c ( λ ) · g · F g , F v = c ( λ ) · v · F v ,
ζ r = F r / F g , ζ v = F v / F g , e r = r / g , v = v / g ,
ζ r = F r / F g = e r · ζ r ,             ζ v = F v / F g = e v · ζ v .
η r = F r / F ,             η g = F g / F ,             η v = F v / F .