Abstract

The adjustable parameters in a MacAdam-modified version of Friele’s 1965 proposal for calculating color differences have been optimized, according to a criterion of MacAdam, to fit PGN experimental data. The mean-square error of fitting is 0.030. The distribution of the resulting color-metric coefficients more closely approximates those of the PGN data than do previous versions of Friele’s proposals. The optimized primaries have chromaticity coordinates of x = 0.74054, y = 0.25946 for the red; x = −1.11696, y = 2.11696 for the green; and x = 0.13939, y = −0.03454 for the blue primary.

© 1967 Optical Society of America

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References

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  1. L. F. C. Friele, Die Farbe 10, 193 (1961).
  2. D. L. MacAdam, J. Opt. Soc. Am. 54, 249 (1964).
    [Crossref]
  3. D. L. MacAdam, J. Opt. Soc. Am. 54, 1161 (1964).
    [Crossref]
  4. D. L. MacAdam, J. Opt. Soc. Am. 55, 91 (1965).
    [Crossref]
  5. D. L. MacAdam, Official Digest, Journal of Paint Technology,  37, 1488 (1965).
  6. D. L. MacAdam, Acta Chromatica 1, (4) 1 (1965).
  7. L. F. C. Friele, J. Opt. Soc. Am. 55, 1314 (1965).
    [Crossref]
  8. L. F. C. Friele, J. Opt. Soc. Am. 56, 259 (1966).
    [Crossref]
  9. D. L. MacAdam, J. Opt. Soc. Am. 56, 1784 (1966).
    [Crossref]
  10. L. Silberstein and D. L. MacAdam, J. Opt. Soc. Am. 35, 32 (1945).
    [Crossref]
  11. D. L. MacAdam, J. Opt. Soc. Am. 47, 268 (1957).
    [Crossref]
  12. A complete set of comparison ellipses has been deposited as Document number 9298 with the ADI Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D. C. 20540. A copy may be secured by citing the Document number and by remitting $3.75 for photoprints, or $2.00 for 35 mm microfilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress.

1966 (2)

1965 (4)

D. L. MacAdam, J. Opt. Soc. Am. 55, 91 (1965).
[Crossref]

D. L. MacAdam, Official Digest, Journal of Paint Technology,  37, 1488 (1965).

D. L. MacAdam, Acta Chromatica 1, (4) 1 (1965).

L. F. C. Friele, J. Opt. Soc. Am. 55, 1314 (1965).
[Crossref]

1964 (2)

1961 (1)

L. F. C. Friele, Die Farbe 10, 193 (1961).

1957 (1)

1945 (1)

Acta Chromatica (1)

D. L. MacAdam, Acta Chromatica 1, (4) 1 (1965).

Die Farbe (1)

L. F. C. Friele, Die Farbe 10, 193 (1961).

J. Opt. Soc. Am. (8)

Journal of Paint Technology (1)

D. L. MacAdam, Official Digest, Journal of Paint Technology,  37, 1488 (1965).

Other (1)

A complete set of comparison ellipses has been deposited as Document number 9298 with the ADI Auxiliary Publications Project, Photoduplication Service, Library of Congress, Washington, D. C. 20540. A copy may be secured by citing the Document number and by remitting $3.75 for photoprints, or $2.00 for 35 mm microfilm. Advance payment is required. Make checks or money orders payable to: Chief, Photoduplication Service, Library of Congress.

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Figures (11)

Fig. 1
Fig. 1

Color-mixture functions [from Eqs. (2)] for Friele primaries optimized to fit PGN data.

Fig. 2
Fig. 2

Contours of equal g11 values. Numerical values should be multiplied by 104.

Fig. 3
Fig. 3

Contours of equal g12 values. Numerical values should be multiplied by 104.

Fig. 4
Fig. 4

Contours of equal g22 values. Numerical values should be multiplied by 104.

Fig. 5
Fig. 5

Contours of equal g13 values. Numerical values should be multiplied by 104.

Fig. 6
Fig. 6

Contours of equal g23 values. Numerical values should be multiplied by 104.

Fig. 7
Fig. 7

Contours of equal g33 values. Numerical values should be multiplied by 104.

Fig. 8
Fig. 8

The best-fitted chromaticity-discrimination ellipse. PGN experimental shown solid; this optimization shown dashed.

Fig. 9
Fig. 9

The poorest-fitted chromaticity-discrimination ellipse. PGN experimental shown solid; this optimization shown dashed.

Fig. 10
Fig. 10

A typically fitted chromaticity-discrimination ellipse. PGN experimental shown solid; this optimization shown dashed.

Fig. 11
Fig. 11

Location of optimized Friele primaries in relation to C.I.E. 1931 chromaticity diagram.

Equations (11)

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( Δ E ) 2 = ( l Δ L / a ) 2 + ( Δ C r - g / a - f n Δ C y - b / b ) 2 + ( n Δ C y - b / b ) 2 .
a 2 = α 2 ( P 2 + Q 2 ) / [ 1 + N P 2 Q 2 / ( P 4 + Q 4 ) ] .
d x 1 = ( g 11 ) - 1 2 d y 1 = 0 d x 2 = 3 2 d x 1 - g 12 g 11 d y 2 d y 2 = 1 2 ( g 11 g 11 g 22 - g 12 2 ) 1 2 d x 3 = 3 d x 2 - d x 1 d y 3 = 3 d y 2 d x 4 = 2 d x 2 - 3 d x 1 d y 4 = 2 d y 2 d x 5 = 3 d x 2 - 2 d x 1 d y 5 = d y 3 d x 6 = d x 2 - 3 d x 1 d y 6 = d y 2 .
P = 0.724 X + 0.382 Y - 0.098 Z Q = - 0.480 X + 1.370 Y + 0.1276 Z S = 0.686 Z .
P = 0.743 X + 0.382 Y - 0.0945 Z Q = - 0.490 X + 1.4008 Y + 0.121 Z S = 0.686 Z .
p ¯ = 0.724 x ¯ + 0.382 y ¯ - 0.098 z ¯ q ¯ = - 0.480 x ¯ + 1.370 y ¯ + 0.1276 z ¯ s ¯ = 0.686 z ¯ .
( Δ E ) 2 = 0.0778 ( Δ L / a ) 2 + ( Δ C r - g / a ) 2 + ( Δ C y - b / b ) 2 ,
a 2 = 17.3 × 10 - 6 ( P 2 + Q 2 ) / [ 1 + 2.73 P 2 Q 2 / ( P 4 + Q 4 ) ] b 2 = 3.098 × 10 - 4 ( S 2 + 0.2015 Y 2 ) Δ C r - g = ( Q Δ P - P Δ Q ) / ( P 2 + Q 2 ) 1 2 Δ L = ( P Δ P + Q Δ Q ) / ( P 2 + Q 2 ) 1 2 Δ C y - b = S Δ L / ( P 2 + Q 2 ) 1 2 - Δ S Δ P = 0.724 Δ X + 0.382 Δ Y - 0.098 Δ Z Δ Q = - 0.480 Δ X + 1.370 Δ Y + 0.1276 Δ Z Δ S = 0.686 Δ Z
( Δ E ) 2 = C 11 ( Δ P ) 2 + 2 C 12 Δ P Δ Q + C 22 ( Δ Q ) 2 + 2 C 13 Δ P Δ S + C 33 Δ S 2 + 2 C 23 Δ Q Δ S ,
C 11 = [ A 2 ( 0.0778 P 2 + Q 2 ) + P 2 S 2 b 2 ] / ( P 2 + Q 2 ) 2 , C 12 = [ - 0.9222 A 2 P Q + P Q S 2 b 2 ] / ( P 2 + Q 2 ) 2 , C 22 = [ A 2 ( P 2 + 0.0778 Q 2 ) + Q 2 S 2 b 2 ] / ( P 2 + Q 2 ) 2 , C 13 = - P S / b 2 ( P 2 + Q 2 ) , C 33 = 1 / b 2 , C 23 = Q C 13 / P ,
A 2 = 57780 [ 1 + 2.73 P 2 Q 2 / ( P 4 + Q 4 ) ]