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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 56, Iss. 9 — Sep. 1, 1966
  • pp: 1256–1257

Basic Equations Used in Computer Color Matching

EUGENE ALLEN  »View Author Affiliations

JOSA, Vol. 56, Issue 9, pp. 1256-1257 (1966)

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If we are given the spectrophotometric curves of a color and three colorants to be used in matching it, the computation of the concentrations of the three colorants required for a tristimulus match is a complicated nonlinear problem. However, with the help of an approximating assumption, a linear solution may be obtained by a matrix inversion technique. Although this is an approximate solution, it is better the less metameric the match. With this rough solution as a starting point, iteration may be used to approach an exact match to any desired degree of accuracy. The inverted matrix used for the iterative computation is identical to that used for the rough solution.

EUGENE ALLEN, "Basic Equations Used in Computer Color Matching," J. Opt. Soc. Am. 56, 1256-1257 (1966)

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  1. F. W. Billmeyer, Jr., J. K. Beasley, and J. A. Sheldon, J. Opt. Soc. Am. 50, 70 (1960).
  2. J. V. Alderson, E. Atherton, and A. N. Derbyshire, J. Soc. Dyers Colourists 77, 657 (1961).
  3. R. H. Park and E. I. Stearns, J. Opt. Soc. Am. 34, 112 (1944).
  4. H. R. Davidson, H. Hemmendinger, and J. L. R. Landry, Jr., J. Soc. Dyers Colourists 79, 577 (1963).
  5. Manufactured by Davidson and Hemmendinger, Easton, Pa.
  6. Matrix notation as applied to colorimetric problems is explained by E. Allen, Color Eng. 4, No. 4, p. 24 (1966).
  7. The Ciba Q Method [E. Ganz, Textil-Rundschau 20, 255 (1965)] is a graphical method for doing just this. The Q values of the dyes are the tristimulus-integrated Kubelka-Munk K/S values, previously computed and tabulated. It is understandable that the dR/dƒ(R) values cannot be incorporated into the Q values as they should, because they vary with the sample to be matched. Park and Stearns's Eqs. (5) also call for summation of the ƒ(R) values at "suitably selected ordinates,"

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