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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 44, Iss. 9 — Sep. 1, 1954
  • pp: 713–724

Orthogonal Color-Mixture Functions

D. L. MACADAM  »View Author Affiliations

JOSA, Vol. 44, Issue 9, pp. 713-724 (1954)

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Spectrophotometric curves uniquely determined by every set of color specifications can be based on a Fourier-type analysis, using normal and orthogonal color-mixture functions. Normal and orthogonal color-mixture functions are convenient for the investigation of the propagation of errors in spectrophoto-metric colorimetry. The space based on normal and orthogonal color-mixture functions serves as a suggestive model for the as yet unavailable visually homogeneous color space, in which visual thresholds of color shall be represented by equal-size spheres, at least for some fixed conditions of adaptation. Recent puzzling results of investigations of color discrimination and heterochromatic photometry can be explained in a straightforward manner in terms of general properties of visually homogeneous color space. Those properties are independent of the detailed structure of that space and are exemplified, though probably in a simplified manner, by the color space based on normal and orthogonal color-mixture functions.

D. L. MACADAM, "Orthogonal Color-Mixture Functions," J. Opt. Soc. Am. 44, 713-724 (1954)

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  1. D. L. MacAdam, J. Opt. Soc. Am. 43, 533–538 (1953).
  2. G. Wyszecki, Die Farbe 2, 39–52 (1953).
  3. W. L. Brewer and F. R. Holly, Jr., J. Opt. Soc. Am. 38, 858–874 (1948).
  4. I. Nimeroff, J. Opt. Soc. Am. 43, 531–533 (1953).
  5. See L. P. Eisenhart, Differential Geometry (Princeton University Press, 1947), pp. 282–293. This analysis is based on suggestions made by Dr. Herman von Schelling, U. S. Naval Medical Research Laboratory, Submarine Base, New London, Connecticut.
  6. D. L. MacAdam, J. Opt. Soc. Am. 32, 2–6 (1942).
  7. The name apeiron is based on the Greek word for infinity απεlpos.Apeiron (pronounced a˙ . pī′roEn) is defined in the Merriam-Webster "New International Dictionary" (unabridged) as "the indeterminate and indefinite ground, matter, or first principle of all being." In the present specialized application to colorimetry, apeiron may be defined as "The line in any chromaticity diagram which is indeterminate in a second chromaticity diagram, but which determines the plane of projection of the latter." For example, the alychne [lightless line, as defined by E. Schrödinger, Sitzber. Akad. Wiss. Wien, Abt. Ha, 134, 476 (1925), and D. B. Judd, J. Research, Natl. Bur. Standards 4, 545 (1929)] is the apeiron of all constant luminosity chromaticity diagrams, such as that represented by the (V=1)-plane in Fig. 3, and shown in Fig. 6 of reference 1. By definition, the apeiron of a chromaticity diagram cannot be represented in it. In all other chromaticity diagrams in which the apeiron of a particular diagram can be represented, it represents the same series of chromaticities. Like the alychne, the apeiron of every chromaticity diagram used in the past represents chromaticities all exceeding spectral purity.
  8. D. B. Judd, J. Opt. Soc. Am. 25, 24–35 (1935).
  9. OSA Committee on Colorimetry, The Science of Color (T. Y. Crowell, New York, 1953), p. 302.
  10. W. R. J. Brown and D. L. MacAdam, J. Opt. Soc. Am. 39, 808–835 (1949).
  11. A. Dresler, Trans. Illum. Eng. Soc. (London) 18, 141–165 (1953).
  12. H. E. Ives, Phil. Mag. 24, 353, 744, 845, and 853 (1912).
  13. M. Luckiesh, Elec. World 61, 620, 735, and 835 (1913); M. Luckiesh, Phys. Rev. 4, 1 (1914).
  14. E. Schrödinger, Ann. Physik 63, 397–456 (1920).
  15. On the basis of Schrödinger's criterion, the surfaces of constant brightness can be plane only if all the loci of constant chromaticness are parallel straight lines. Such would be the case if there were no Bézold-Brücke effect, and if the Weber-Fechner law applied to the incremental thresholds of the separate stimuli. The latter assumption has been tested, modified, and found wanting by H. von Helmholtz [Wiss. Abhandl. 3, 407–459, 460–475 (Leipzig, 1895)], Schrödinger (see reference 14), R. H. Sinden [J. Opt. Soc. Am. 27, 124–131 (1937); 28, 339–347 (1938)], L. Silberstein, [J. Opt. Soc. Am. 28, 63–85 (1938)], and W. S. Stiles, [Proc. Phys. Soc. (London) 18, 41–65 (1945)]. It seems most unlikely that the Bézold-Brücke effect would compensate for the discrepancies between the Weber-Fechner law and visually homogeneous color space, so as to yield straight, parallel loci of constant chromaticness and planes of constant brightness.
  16. L. Silberstein, J. Opt. Soc. Am. 33, 1–9 (1943).
  17. D. L. MacAdam, J. Franklin Inst. 238 195–209 (1944); D. L. MacAdam, Rev. optique 28, 161–173 (1949); and D. L. MacAdam, Ophthalmologica 3, 214–239 (1949).
  18. D. L. MacAdam, J. Opt. Soc. Am. 40, 589–595 (1950).
  19. M. Tessier and F. Blottiau, Rev. optique 30, 309–322 (1951).
  20. W. S. Stiles, Illum. Eng. 49, 77 (1954).

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