Abstract

A digital computer was programed to calculate the concentrations required to produce a given transparent color by mixing soluble dyes. The computation is based on Beer’s law calculations at 65 wavelengths across the visible spectrum. The color to be formulated is specified in terms of CIE tristimulus values derived from instrumental measurement. The computer formulation technique was tested by making up to computed formulas a series of mixtures of dyes in a solvent and in an acrylic resin. The correspondence was good between the measured colors of the mixtures and those for which the formulations were calculated, as indicated by color differences averaging about 1 NBS unit (Adams chromatic value formula, normalized as in ASTM Method D 1482-57T).

© 1960 Optical Society of America

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References

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  1. D. B. Judd, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1952).
  2. R. H. Park and E. I. Stearns, J. Opt. Soc. Am. 34, 112 (1944).
    [CrossRef]
  3. G. W. Haupt and F. L. Douglas, J. Opt. Soc. Am. 37, 698 (1947).
    [CrossRef]
  4. Forrest, Kreidl, and Pett, J. Opt. Soc. Am. 38, 554 (1948).
    [CrossRef] [PubMed]
  5. D. L. MacAdam, J. Opt. Soc. Am. 39, 22 (1949).
    [CrossRef] [PubMed]
  6. W. J. Foote, Paper Trade J. 109, T531 (1939).
  7. D. R. Duncan, J. Oil and Colour Chemists’ Assoc. 32, 296 (1949).
  8. J. L. Saunderson, J. Opt. Soc. Am. 32, 727 (1942).
    [CrossRef]
  9. H. R. Davidson and H. Hemmendinger, J. Opt. Soc. Am. 48, 281(A) (1958).
    [CrossRef]
  10. A correction may be introduced for loss in transmittance by surface reflection or in a substrate, and the effect of sample thickness can be accounted for, by suitable modifications of Eq. (1).
  11. Billmeyer, Beasley, and Sheldon, “A color order system predicting constant hue” (paper in preparation).
  12. F. W. Billmeyer, “Use of a digital readout unit in converting spectrophotometric data to color coordinates,” J. Opt. Soc. Am. (to be published).
  13. All color differences referred to in this paper were calculated by the Adams chromatic value formula, normalized to the NBS unit by the factor adopted in ASTM Designation D 1482-57T. See also E. Q. Adams, J. Opt. Soc. Am. 32, 168 (1942); D. Nickerson and K. F. Stultz, J. Opt. Soc. Am. 34, 550 (1944).
    [CrossRef]
  14. The samples referred to make up the full chroma transparent section of the Faber Birren Color Library in “Lucite” acrylic resin; see “Color styling in acrylic resins,” F. W. Billmeyer and I. K. de Blieu (paper in preparation).
  15. While the tolerance limits in this experiment were selected to be comparable to the probable error of color measurement,12 they can readily be made to correspond more nearly to steps of equal visual perception.

1958 (1)

H. R. Davidson and H. Hemmendinger, J. Opt. Soc. Am. 48, 281(A) (1958).
[CrossRef]

1949 (2)

D. R. Duncan, J. Oil and Colour Chemists’ Assoc. 32, 296 (1949).

D. L. MacAdam, J. Opt. Soc. Am. 39, 22 (1949).
[CrossRef] [PubMed]

1948 (1)

1947 (1)

1944 (1)

1942 (2)

1939 (1)

W. J. Foote, Paper Trade J. 109, T531 (1939).

Adams, E. Q.

Beasley,

Billmeyer, Beasley, and Sheldon, “A color order system predicting constant hue” (paper in preparation).

Billmeyer,

Billmeyer, Beasley, and Sheldon, “A color order system predicting constant hue” (paper in preparation).

Billmeyer, F. W.

F. W. Billmeyer, “Use of a digital readout unit in converting spectrophotometric data to color coordinates,” J. Opt. Soc. Am. (to be published).

The samples referred to make up the full chroma transparent section of the Faber Birren Color Library in “Lucite” acrylic resin; see “Color styling in acrylic resins,” F. W. Billmeyer and I. K. de Blieu (paper in preparation).

Davidson, H. R.

H. R. Davidson and H. Hemmendinger, J. Opt. Soc. Am. 48, 281(A) (1958).
[CrossRef]

de Blieu, I. K.

The samples referred to make up the full chroma transparent section of the Faber Birren Color Library in “Lucite” acrylic resin; see “Color styling in acrylic resins,” F. W. Billmeyer and I. K. de Blieu (paper in preparation).

Douglas, F. L.

Duncan, D. R.

D. R. Duncan, J. Oil and Colour Chemists’ Assoc. 32, 296 (1949).

Foote, W. J.

W. J. Foote, Paper Trade J. 109, T531 (1939).

Forrest,

Haupt, G. W.

Hemmendinger, H.

H. R. Davidson and H. Hemmendinger, J. Opt. Soc. Am. 48, 281(A) (1958).
[CrossRef]

Judd, D. B.

D. B. Judd, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1952).

Kreidl,

MacAdam, D. L.

Park, R. H.

Pett,

Saunderson, J. L.

Sheldon,

Billmeyer, Beasley, and Sheldon, “A color order system predicting constant hue” (paper in preparation).

Stearns, E. I.

J. Oil and Colour Chemists’ Assoc. (1)

D. R. Duncan, J. Oil and Colour Chemists’ Assoc. 32, 296 (1949).

J. Opt. Soc. Am. (7)

Paper Trade J. (1)

W. J. Foote, Paper Trade J. 109, T531 (1939).

Other (6)

D. B. Judd, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1952).

The samples referred to make up the full chroma transparent section of the Faber Birren Color Library in “Lucite” acrylic resin; see “Color styling in acrylic resins,” F. W. Billmeyer and I. K. de Blieu (paper in preparation).

While the tolerance limits in this experiment were selected to be comparable to the probable error of color measurement,12 they can readily be made to correspond more nearly to steps of equal visual perception.

A correction may be introduced for loss in transmittance by surface reflection or in a substrate, and the effect of sample thickness can be accounted for, by suitable modifications of Eq. (1).

Billmeyer, Beasley, and Sheldon, “A color order system predicting constant hue” (paper in preparation).

F. W. Billmeyer, “Use of a digital readout unit in converting spectrophotometric data to color coordinates,” J. Opt. Soc. Am. (to be published).

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Figures (1)

Fig. 1
Fig. 1

Traditional and computer formulated approaches to a two-dye amber color match at the point indicated by the filled circle. The ellipse has a radius of 2.5 NBS units,13 and the square indicates tolerance limits of ±0.001 in x and y. Solid line, path of traditional formulations; dashed line, path of computer iterations.

Tables (1)

Tables Icon

Table I Computer formulated colors based on dye solutions.

Equations (4)

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T λ = exp ( c 1 D 1 λ + c 2 D 2 λ + c 3 D 3 λ ) ,
X = λ = 1 65 T λ E λ x ¯ λ ,
X c i = λ = 1 65 E λ x ¯ λ D i λ exp ( c 1 D 1 λ + c 2 D 2 λ + c 3 D 3 λ ) , Y c i = λ = 1 65 E λ y ¯ λ D i λ exp ( c 1 D 1 λ + c 2 D 2 λ + c 3 D 3 λ ) , Z c i = λ = 1 65 E λ z ¯ λ D i λ exp ( c 1 D 1 λ + c 2 D 2 λ + c 3 D 3 λ ) ,
Δ X = X / c 1 Δ c 1 + X / c 2 Δ c 2 + X / c 3 Δ c 3 , Δ Y = Y / c 1 Δ c 1 + Y / c 2 Δ c 2 + Y / c 3 Δ c 3 , Δ Z = Z / c 1 Δ c 1 + Z / c 2 Δ c 2 + Z / c 3 Δ c 3 .