OSA's Digital Library

Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 59, Iss. 12 — Dec. 1, 1969
  • pp: 1670–1676

Fourier Analysis and Color Discrimination

GERARD J. C. VAN DER HORST  »View Author Affiliations

JOSA, Vol. 59, Issue 12, pp. 1670-1676 (1969)

View Full Text Article

Acrobat PDF (728 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The contrast thresholds of equiluminous chromaticity-modulated gratings are measured for various waveforms (sine-, square-, and triangular-wave gratings). The expectation is expressed that only the fundamental Fourier component is of significance in the threshold visibility of colored gratings. In addition, the Fourier transformation is applied to the chromatic spatial-sensitivity curves. The transformed functions illustrate clearly the spatial organization of the contrast mechanisms. For 160 trolands, the summation area of the red–green chromatic activity extends over 10′, whereas the yellow–blue activity integrates over about 25′. A comparison of the Fourier transforms of a luminance- and chromatic-threshold contrast curve shows (1) inhibitory qualities and (2) the greater spatial sensitivity of the luminous function. The assumption is made that the visual resolution for differences of brightness, as well as chromaticity, is limited by the diffraction of light by the pupil. The visual acuity for differences of hue as a function of the background wavelength is thus predicted for a 30-cpd grating and compared with an empirical function. There is good agreement.

GERARD J. C. VAN DER HORST, "Fourier Analysis and Color Discrimination," J. Opt. Soc. Am. 59, 1670-1676 (1969)

Sort:  Author  |  Journal  |  Reset


  1. O. Dupuy, Vision Res. 8, 1507 (1968).
  2. J. P. Thomas, Vision Res. 8, 49 (1968).
  3. O. H. Schade, J. Soc. Motion Picture Television Engr. 67, 801 (1958).
  4. D. G. Green, J. Physiol. (London) 196, 415 (1968).
  5. H. Schober and H. Munker, Vision Res. 7, 1015 (1967).
  6. F. J. J. Clarke, Symposium: Colour Measurement in Industry (the Colour Group, London, 1967), p. 132.
  7. G. J. C. van der Horst and M. A. Bouman, J. Opt. Soc. Am. 59, 1482 (1969).
  8. F. W. Campbell and J. J. Kulikowski, J. Physiol. (London) 187, 437 (1966).
  9. F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).
  10. G. J. C. van der Horst, J. Opt. Soc. Am. 59, 1213 (1969).
  11. See also Table II in Ref. 7.
  12. We Use here the distance between the zero crossings in the plot.
  13. G. J. C. van der Horst, C. M. M. de Weert, and M. A. Bouman, J. Opt. Soc. Am. 57, 1260 (1967).
  14. In Ref. 7 and 10. The viewing distance was increased in this particular case from 3.70 to 7.80 m, in order to have a greater range of spatial frequencies. One observer (the author) is used as subject. Pupil diameter was now 1.5 mm.
  15. The chromaticity contrast at the reference color Y is defined as follows: ΔC= {(Δx)2+(Δy)2}½ = {(xx0)2+(yy0)2}½, where (x0,y0) are the chromaticity coordinates of the reference point Y.
  16. G. von Békésy, J. Opt. Soc. Am. 50, 1060 (1960).
  17. G. von Békésy, Vision Res. 8, 1483 (1968).
  18. O. Bryngdahl, Pflüg. Arch. Ces. Physiol. 280, 362 (1964).
  19. O. Bryngdahl, Vision Res. 6, 553 (1966).
  20. A. S. Patel, J. Opt. Soc. Am. 56, 689 (1966).
  21. V. D. Glazer, Vision Res. 5, 497 (1965).
  22. A. Maréchal and M. Françon, Diffraction, Structure des Images (Ed. Revue d'Optique Théorique et Instrumentale, Paris, 1960).
  23. The reader may be referred to the discussion on this matter in Ref. 13.
  24. We now make the important assumption that the perception of a grating is dependent on only the chromatic contrast and not on the grating frequency. Because of the variation of receptive fields with the eccentricity, e.g., a varying ratio of rods and cones, this assumption may be contestable.
  25. W. D. Wright, Researches in Normal and Defective Colour Vision (Henry Kimpton, London, 1946).
  26. For this transformation, we used Pitt's fundamental response curves, as revised by P. L. Walraven and M. A. Bouman. [Vision Res. 6, 567 (1966).] Using the 1931 CIE tristimulus values, substantially the same results were obtained as those plotted in Fig. 7.
  27. C. R. Cavonius, Science 152, 1276 (1966). In his study Cavonius used an artificial pupil of 1.5 mm. The stimulus size was 1°. Retinal illuminance 42 td. The hue-discrimination data of Wright were obtained for a 2° field, 70 td.
  28. A. C. S. van Heel, J. Opt. Soc. Am. 36, 237 (1946).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited