Abstract

In a three-color print, the color of any area that is large in comparison with the size of the dots of the structured image can be regarded as an additive mixture of eight colors: the unprinted paper stock; the cyan, magenta, and yellow of the individual ink dots; the red, green, and blue that result when ink dots overlap in pairs; and the black that results when all three ink dots overlap. Since the extent of overlapping is determined by the sizes of the dots, the color of the additive mixture can be expressed by three equations. The straightforward attack on the problem of color reproduction is to solve these fundamental equations for the required dot sizes on the assumption that, in every area, the tristimulus values of the reproduction should be equal to those of the original. This has not been accomplished hitherto, because it involves solving three simultaneous equations of third degree, each containing eight terms. However, a relatively simple electronic equation-solving network has been constructed which solves these equations with ample precision in 0.001 second. By using this network in connection with a scanning machine of the type described in the preceding paper, full color correction is achieved. A corresponding set of equations can be written for the additive mixture produced in four-color printing, wherein the fourth color is black. Since the three equations now contain four unknowns, an additional condition must be imposed. From the standpoint of the printing requirements, it is desirable that at least one of the color dots be absent, or of some predetermined minimal size, in every region of the reproduction. An extension of the principles embodied in the electronic network mentioned above imposes this condition and yields a continuous solution to the three fourth-degree equations.

© 1948 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Extension of paper presented at the October, 1946meeting of the O.S.A.
  2. A. C. Hardy and F. L. Wurzburg, J. Opt. Soc. Am. 16, 295 (1948).
    [Crossref]
  3. Since there may be areas of the subject which are unlike in spectral composition but nevertheless appear to the eye to be of the same color, it is evident that the color-separation negatives must evaluate these areas in the same manner as does the human eye. In other words, the gammas of the three emulsions must be independent of wave-length within the spectral range transmitted by each filter and the spectral sensitivity curves of the three filter-emulsion combinations must correspond to the color-mixture curves of a normal observer for some set of basic stimuli. In the cycle of operations to be described below, these are the only requirements that need be imposed on the filter-emulsion combinations used in making the color-separation negatives. In other words, the spectral sensitivities of the filter-emulsion combinations are quite independent of the colors of the printing inks.
  4. Neugebauer, Zeits. f. tech. Physik 36, 22 (1937).
  5. American Standards Association, “Specification and description of color,” Z44—1942.
  6. The assumption of standard colorimetric procedures is made in the interest of clarity of presentation, inasmuch as the meaning of tristimulus values in the I.C.I. system is now widely understood. By adopting this colorimetric system, however, freedom of selection of filter-emulsion combinations for the color-separation negatives is restricted to a single set; namely, a set whose spectral sensitivity curves correspond to the mixture curves for the basic stimuli of the I.C.I. system.
  7. Edward C. Dench took part in this development and is a co-author of the following paper which describes in greater detail the means devised for achieving color correction in both three- and four-color printing.
  8. A. C. Hardy and F. L. Wurzburg, “The theory of three-color reproduction,” J. Opt. Soc. Am. 27, 227 (1937).
    [Crossref]

1948 (1)

1942 (1)

American Standards Association, “Specification and description of color,” Z44—1942.

1937 (2)

Dench, Edward C.

Edward C. Dench took part in this development and is a co-author of the following paper which describes in greater detail the means devised for achieving color correction in both three- and four-color printing.

Hardy, A. C.

Neugebauer,

Neugebauer, Zeits. f. tech. Physik 36, 22 (1937).

Wurzburg, F. L.

J. Opt. Soc. Am. (2)

Specification and description of color (1)

American Standards Association, “Specification and description of color,” Z44—1942.

Zeits. f. tech. Physik (1)

Neugebauer, Zeits. f. tech. Physik 36, 22 (1937).

Other (4)

Since there may be areas of the subject which are unlike in spectral composition but nevertheless appear to the eye to be of the same color, it is evident that the color-separation negatives must evaluate these areas in the same manner as does the human eye. In other words, the gammas of the three emulsions must be independent of wave-length within the spectral range transmitted by each filter and the spectral sensitivity curves of the three filter-emulsion combinations must correspond to the color-mixture curves of a normal observer for some set of basic stimuli. In the cycle of operations to be described below, these are the only requirements that need be imposed on the filter-emulsion combinations used in making the color-separation negatives. In other words, the spectral sensitivities of the filter-emulsion combinations are quite independent of the colors of the printing inks.

The assumption of standard colorimetric procedures is made in the interest of clarity of presentation, inasmuch as the meaning of tristimulus values in the I.C.I. system is now widely understood. By adopting this colorimetric system, however, freedom of selection of filter-emulsion combinations for the color-separation negatives is restricted to a single set; namely, a set whose spectral sensitivity curves correspond to the mixture curves for the basic stimuli of the I.C.I. system.

Edward C. Dench took part in this development and is a co-author of the following paper which describes in greater detail the means devised for achieving color correction in both three- and four-color printing.

Extension of paper presented at the October, 1946meeting of the O.S.A.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Schematic representation of a scanning machine adapted for scanning three photographic positives simultaneously. The three positives A are attached to circular platens in the proper register. The platens are clamped to a carriage whose motions are identical with those described in connection with Fig. 2 of the preceding paper. Three scanning beams produce photo-tube signals which are fed to computing channels in relay rack B whose output signals control the dot-producing circuit in relay rack C. The output signal from the latter actuates a light valve in the recording head D producing an intermittent exposure that results in recording a structured image on an unexposed photographic plate clamped to the fourth platen. The circular platens are rotated through an appropriate angle after each recording.

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

R = ( 1 - c ) ( 1 - m ) ( 1 - y ) R w + c ( 1 - m ) ( 1 - y ) R c + m ( 1 - c ) ( 1 - y ) R m + y ( 1 - c ) ( 1 - m ) R y + m y ( 1 - c ) R m y + c y ( 1 - m ) R c y + c m ( 1 - y ) R c m + c m y R c m y ,
G = ( 1 - c ) ( 1 - m ) ( 1 - y ) G w + c ( 1 - m ) ( 1 - y ) G c + m ( 1 - c ) ( 1 - y ) G m + y ( 1 - c ) ( 1 - m ) G y + m y ( 1 - c ) G m y + c y ( 1 - m ) G c y + c m ( 1 - y ) G c m + c m y G c m y ,
B = ( 1 - c ) ( 1 - m ) ( 1 - y ) B w + c ( 1 - m ) ( 1 - y ) B c + m ( 1 - c ) ( 1 - y ) B m + y ( 1 - c ) ( 1 - m ) B y + m y ( 1 - c ) B m y + c y ( 1 - m ) B c y + c m ( 1 - y ) B c m + c m y B c m y .
R = R = 1.000 ( 1 - c ) ( 1 - m ) ( 1 - y ) + 0.146 c ( 1 - m ) ( 1 - y ) + 0.442 m ( 1 - c ) ( 1 - y ) + 0.857 y ( 1 - c ) ( 1 - m ) + 0.398 m y ( 1 - c ) + 0.064 c y ( 1 - m ) + 0.033 c m ( 1 - y ) + 0.023 c m y ,
G = G = 1.000 ( 1 - c ) ( 1 - m ) ( 1 - y ) + 0.197 c ( 1 - m ) ( 1 - y ) + 0.219 m ( 1 - c ) ( 1 - y ) + 0.980 y ( 1 - c ) ( 1 - m ) + 0.206 m y ( 1 - c ) + 0.196 c y ( 1 - m ) + 0.014 c m ( 1 - y ) + 0.019 c m y .
B = B = 1.000 ( 1 - c ) ( 1 - m ) ( 1 - y ) + 0.613 c ( 1 - m ) ( 1 - y ) + 0.185 m ( 1 - c ) ( 1 - y ) + 0.148 y ( 1 - c ) ( 1 - m ) + 0.012 m y ( 1 - c ) + 0.103 c y ( 1 - m ) + 0.120 c m ( 1 - y ) + 0.016 c m y .
R = R = 1.000 ( 1 - c ) ( 1 - m ) ( 1 - y ) ( 1 - n ) + 0.146 c ( 1 - m ) ( 1 - y ) ( 1 - n ) + 0.442 m ( 1 - c ) ( 1 - y ) ( 1 - n ) + 0.857 y ( 1 - c ) ( 1 - m ) ( 1 - n ) + 0.398 m y ( 1 - c ) ( 1 - n ) + 0.064 c y ( 1 - m ) ( 1 - n ) + 0.033 c m ( 1 - y ) ( 1 - n ) + 0.023 c m y ( 1 - n ) + 0.023 n ,
G = G = 1.000 ( 1 - c ) ( 1 - m ) ( 1 - y ) ( 1 - n ) + 0.197 c ( 1 - m ) ( 1 - y ) ( 1 - n ) + 0.219 m ( 1 - c ) ( 1 - y ) ( 1 - n ) + 0.980 y ( 1 - c ) ( 1 - m ) ( 1 - n ) + 0.206 m y ( 1 - c ) ( 1 - n ) + 0.196 c y ( 1 - m ) ( 1 - n ) + 0.014 c m ( 1 - y ) ( 1 - n ) + 0.019 c m y ( 1 - n ) + 0.019 n ,
B = B = 1.000 ( 1 - c ) ( 1 - m ) ( 1 - y ) ( 1 - n ) + 0.613 c ( 1 - m ) ( 1 - y ) ( 1 - n ) + 0.185 m ( 1 - c ) ( 1 - y ) ( 1 - n ) + 0.148 y ( 1 - c ) ( 1 - m ) ( 1 - n ) + 0.012 m y ( 1 - c ) ( 1 - n ) + 0.103 c y ( 1 - m ) ( 1 - n ) + 0.120 c m ( 1 - y ) ( 1 - n ) + 0.016 c m y ( 1 - n ) + 0.016 n .
R = R w - ( R w - R c ) c - ( R w - R m ) m - ( R w - R y ) y + ( R w - R m - R y + R m y ) m y + ( R w - R c - R y + R c y ) c y + ( R w - R c - R m + R c m ) c m - ( R w - R c - R m - R y + R m y + R c y + R c m - R c m y ) c m y ,
G = G w - ( G w - G c ) c - ( G w - G m ) m - ( G w - G y ) y + ( G w - G m - G y + G m y ) m y + ( G w - G c - G y + G c y ) c y + ( G w - G c - G m + G c m ) c m - ( G w - G c - G m - G y + G m y + G c y + G c m - G c m y ) c m y ,
B = B w - ( B w - B c ) c - ( B w - B m ) m - ( B w - B y ) y + ( B w - B m - B y + B m y ) m y + ( B w - B c - B y + B c y ) c y + ( B w - B c - B m + B c m ) c m - ( B w - B c - B m - B y + B m y + B c y + B c m - B c m y ) c m y .
Δ R = - ( R / c ) Δ c , Δ G = - ( G / c ) Δ c , Δ B = - ( B / c ) Δ c .
R = R = R w - ( R w - R c ) c - ( R w - R m ) m - ( R w - R y ) y ,
G = G = G w - ( G w - G c ) c - ( G w - G m ) m - ( G w - G y ) y ,
B = B = B w - ( B w - B c ) c - ( B w - B m ) m - ( B w - B y ) y .
- ( R / c ) = ( R w - R c ) , - ( G / c ) = ( G w - G c ) , - ( B / c ) = ( B w - B c ) .
- ( R / c ) = ( R w - R c ) - ( R w - R c - R y + R c y ) y - ( R w - R c - R m + R c m ) m + ( R w - R c - R m - R y + R m y + R c y + R c m - R c m y ) m y ,
- ( G / c ) = ( G w - G c ) - ( G w - G c - G y + G c y ) y - ( G w - G c - G m + G c m ) m + ( G w - G c - G m - G y + G m y + G c y + G c m - G c m y ) m y ,
- ( B / c ) = ( B w - B c ) - ( B w - B c - B y + B c y ) y - ( B w - B c - B m + B c m ) m + ( B w - B c - B m - B y + B m y + B c y + B c m - B c m y ) m y .