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References

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  1. D. L. MacAdam, “Visual sensitivities to color differences in daylight,” J. Opt. Soc. Am. 32, 247–274 (1942).
    [Crossref]
  2. L. Silberstein, “Investigations on the intrinsic properties of the color domain,” J. Opt. Soc. Am. 28, 63–85 (1938).
    [Crossref]
  3. H. V. Helmholtz, “Kürzeste Linien im Farbensystem,” Sitz. Akad. Wiss. Berlin, Phys. Math.1071–1083 (1891); Wiss. Abhandl. 3, 460–475 (1895).
  4. Erwin Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen,” Ann. d. Physik 63, 397–426, 427–456, 481–520 (1920).
    [Crossref]
  5. R. H. Sinden, “A further search for the ideal color system,” J. Opt. Soc. Am. 27, 124–131 (1937); J. Opt. Soc. Am. 28, 339–347 (1938).
    [Crossref]
  6. P. J. Bouma, “Grundlagen einer allgemeinen Theorie der Farbenmetrik,” K. Akad. v. Wetenschappen Amst. Afdeel. Nat. 38, 35–45, 148–166, 258–281 (1935).
  7. D. E. Spencer, “Adaptation in color space,” J. Opt. Soc. Am. 32, 632A (1942).
  8. T. Smith, “The colour triangle and colour discrimination,” Discussion on Vision (Physical Society, London, 1932), pp. 212–226.
  9. D. B. Judd, “A Maxwell triangle yielding uniform chromaticity scales,” J. Opt. Soc. Am. 25, 24–35 (1935).
    [Crossref]
  10. D. B. Judd, “Estimation of chromaticity differences and nearest color temperature on the standard 1931 I.C.I. colorimetric coordinate system,” J. Opt. Soc. Am. 26, 421–426 (1936).
    [Crossref]
  11. F. C. Breckenridge and W. R. Schaub, “Rectangular uniform-chromaticity-scale coordinates,” J. Opt. Soc. Am. 29, 370–380 (1939).
    [Crossref]
  12. F. Scofield, D. B. Judd, and R. S. Hunter, “A proposed method of designating color,” Bull. A.S.T.M.19–24 (May, 1941).
  13. W. D. Wright, “The sensitivity of the eye to small colour differences,” Proc. Phys. Soc. London 53, 93–112 (1941).
    [Crossref]
  14. D. L. MacAdam, “Projective transformations of color-mixture diagrams,” J. Opt. Soc. Am. 32. 2–6 (1942).
    [Crossref]

1942 (3)

1941 (1)

W. D. Wright, “The sensitivity of the eye to small colour differences,” Proc. Phys. Soc. London 53, 93–112 (1941).
[Crossref]

1939 (1)

1938 (1)

1937 (1)

1936 (1)

1935 (2)

P. J. Bouma, “Grundlagen einer allgemeinen Theorie der Farbenmetrik,” K. Akad. v. Wetenschappen Amst. Afdeel. Nat. 38, 35–45, 148–166, 258–281 (1935).

D. B. Judd, “A Maxwell triangle yielding uniform chromaticity scales,” J. Opt. Soc. Am. 25, 24–35 (1935).
[Crossref]

1920 (1)

Erwin Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen,” Ann. d. Physik 63, 397–426, 427–456, 481–520 (1920).
[Crossref]

1891 (1)

H. V. Helmholtz, “Kürzeste Linien im Farbensystem,” Sitz. Akad. Wiss. Berlin, Phys. Math.1071–1083 (1891); Wiss. Abhandl. 3, 460–475 (1895).

Bouma, P. J.

P. J. Bouma, “Grundlagen einer allgemeinen Theorie der Farbenmetrik,” K. Akad. v. Wetenschappen Amst. Afdeel. Nat. 38, 35–45, 148–166, 258–281 (1935).

Breckenridge, F. C.

Helmholtz, H. V.

H. V. Helmholtz, “Kürzeste Linien im Farbensystem,” Sitz. Akad. Wiss. Berlin, Phys. Math.1071–1083 (1891); Wiss. Abhandl. 3, 460–475 (1895).

Hunter, R. S.

F. Scofield, D. B. Judd, and R. S. Hunter, “A proposed method of designating color,” Bull. A.S.T.M.19–24 (May, 1941).

Judd, D. B.

MacAdam, D. L.

Schaub, W. R.

Schrödinger, Erwin

Erwin Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen,” Ann. d. Physik 63, 397–426, 427–456, 481–520 (1920).
[Crossref]

Scofield, F.

F. Scofield, D. B. Judd, and R. S. Hunter, “A proposed method of designating color,” Bull. A.S.T.M.19–24 (May, 1941).

Silberstein, L.

Sinden, R. H.

Smith, T.

T. Smith, “The colour triangle and colour discrimination,” Discussion on Vision (Physical Society, London, 1932), pp. 212–226.

Spencer, D. E.

D. E. Spencer, “Adaptation in color space,” J. Opt. Soc. Am. 32, 632A (1942).

Wright, W. D.

W. D. Wright, “The sensitivity of the eye to small colour differences,” Proc. Phys. Soc. London 53, 93–112 (1941).
[Crossref]

Ann. d. Physik (1)

Erwin Schrödinger, “Grundlinien einer Theorie der Farbenmetrik im Tagessehen,” Ann. d. Physik 63, 397–426, 427–456, 481–520 (1920).
[Crossref]

J. Opt. Soc. Am. (8)

K. Akad. v. Wetenschappen Amst. Afdeel. Nat. (1)

P. J. Bouma, “Grundlagen einer allgemeinen Theorie der Farbenmetrik,” K. Akad. v. Wetenschappen Amst. Afdeel. Nat. 38, 35–45, 148–166, 258–281 (1935).

Proc. Phys. Soc. London (1)

W. D. Wright, “The sensitivity of the eye to small colour differences,” Proc. Phys. Soc. London 53, 93–112 (1941).
[Crossref]

Sitz. Akad. Wiss. Berlin, Phys. Math. (1)

H. V. Helmholtz, “Kürzeste Linien im Farbensystem,” Sitz. Akad. Wiss. Berlin, Phys. Math.1071–1083 (1891); Wiss. Abhandl. 3, 460–475 (1895).

Other (2)

F. Scofield, D. B. Judd, and R. S. Hunter, “A proposed method of designating color,” Bull. A.S.T.M.19–24 (May, 1941).

T. Smith, “The colour triangle and colour discrimination,” Discussion on Vision (Physical Society, London, 1932), pp. 212–226.

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Figures (5)

Fig. 1
Fig. 1

Values of the coefficient g11 (to be multiplied by 104) for various locations in the I.C.I. chromaticity diagram.

Fig. 2
Fig. 2

Values of the coefficient 2g12 (to be multiplied by 104) for various locations in the I.C.I. chromaticity diagram.

Fig. 3
Fig. 3

Values of the coefficient g22 (to be multiplied by 104) for various locations in the I.C.I. chromaticity diagram.

Fig. 4
Fig. 4

Construction for graphical determination of nearest color temperature for source not exactly matching any Planckian radiator.

Fig. 5
Fig. 5

Oblique I.C.I. coordinate system for restricted chromaticity range, within which equal distances correspond to equally noticeable chromaticity differences.

Equations (31)

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g 11 d x 2 + 2 g 12 d x d y + g 22 d y 2 = 1.
g 11 = cos 2 θ / a 2 + sin 2 θ / b 2 ,
g 12 = sin θ cos θ ( 1 / a 2 - 1 / b 2 ) ,
g 22 = sin 2 θ / a 2 + cos 2 θ / b 2 .
g 11 = 1 / d x 0 2 ,
2 g 12 = 1 / d p 2 - 1 / d q 2 ,
g 22 = 1 / d y 0 2 .
tan 2 θ = 2 g 12 / ( g 11 - g 22 )             θ < 90 ° when g 12 < 0 , θ > 90 ° when g 12 > 0 ,
1 / a 2 = g 22 + g 12 cot θ ,
1 / b 2 = g 11 - g 12 cot θ .
d s 2 = g 11 d x 2 + 2 g 12 d x d y + g 22 d y 2 .
d s 2 = 42 × 0.1225 + 38 × 0.1225 + 37 × 0.1225 = 14.35. d s = 3.8 ,
d s 2 = 39 × 0.45 2 - 43 × 0.45 × 0.29 + 25 × 0.29 2 = 4.44 , d s = 2.11 ,
tan 2 θ = - 42 / ( 39 - 24 ) = - 2.8
1 / a 2 = ( 24 - 21 × 0.5765 ) × 10 4 = 12 × 10 4 ,             a = 0.00288 ; 1 / b 2 = ( 39 + 21 × 0.5765 ) × 10 4 = 51 × 10 4 ,             b = 0.00140.
m = - ( g 11 + g 12 m ) / ( g 12 + g 22 m ) .
m = - ( 39 - 21 × 0.64 ) / ( - 21 + 24 × 0.64 ) = 26 / 6 = 4.3.
d s 2 = 39 × 0.02 - 42 × 0.081 + 24 × 0.337 = 5.48 ,             d s = 2.34.
cos ω = g 12 / ( g 11 g 22 ) 1 3 .
cos ω = - 50 / ( 102 × 53 ) 1 2 = - 0.679 ,             ω = 132.8 ° .
u = c 3 + ( e 1 x + e 2 y ) / ( c 7 x + c 8 y + 1 ) ,
v = c 6 + ( e 4 x + e 5 y ) / ( c 7 x + c 8 y + 1 ) .
d s 2 = d u 2 + d v 2 .
g 11 = ( A 1 + A 4 y 2 + 2 A 5 y ) / ( c 7 x + c 8 y + 1 ) 4 ,
g 12 = ( A 2 - A 4 x y - A 5 x - A 6 y ) / ( c 7 x + c 8 y + 1 ) 4 ,
g 22 = ( A 3 + A 4 x 2 + 2 A 6 x ) / ( c 7 x + c 8 y + 1 ) 4 ,
A 1 = e 1 2 + e 4 2 , A 2 = e 1 e 2 + e 4 e 5 , A 3 = e 2 2 + e 5 2 , A 4 = A 1 c 8 2 - 2 A 2 c 7 c 8 + A 3 c 7 2 , A 5 = A 1 c 8 - A 2 c 7 , A 6 = A 3 c 7 - A 2 c 8 .
d s = B 2 d x / ( c 7 x + c 8 y + 1 ) 2 ,
B 2 2 = A 1 + 2 A 2 m + A 3 m 2 + A 4 B 1 2 + 2 A 5 B 1 - 2 A 6 B 1 m .
d s = B 3 d D / D 2 ,
B 3 2 = ( 1 + m 2 ) B 2 2 / ( c 7 + c 8 m ) 4 .