OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 7 — Jul. 1, 2013
  • pp: 1417–1421

Retinal light distributions, the Stiles–Crawford effect and apodization

Gerald Westheimer  »View Author Affiliations

JOSA A, Vol. 30, Issue 7, pp. 1417-1421 (2013)

View Full Text Article

Enhanced HTML    Acrobat PDF (252 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Analysis of retinal image formation for beams of coherent and incoherent radiation emphasizes the role of the Poynting vector’s inclination with respect to the retinal image plane. Coherent beams interfere and give rise to a single Poynting vector that highlights the unique direction of incidence of energy flow, whereas multiple incoherent beams, especially incoherent extended sources in the pupil, generate electro-magnetic disturbances in the image plane each characterized by Poynting vectors of their own. As a result, the Stiles–Crawford diminution of luminant efficiency adds differently depending on the coherence of the entering light. Two practical considerations follow: first, in performing diffraction calculations for the retinal image from known wavefronts in the pupil plane, apodization terms should not be factored in, and, second, in principle, for perfect imaging in standard target viewing, Stiles–Crawford integration with increasing pupil diameter is not expected.

© 2013 Optical Society of America

OCIS Codes
(330.5370) Vision, color, and visual optics : Physiological optics
(330.4595) Vision, color, and visual optics : Optical effects on vision
(330.7331) Vision, color, and visual optics : Visual optics, receptor optics

ToC Category:
Vision, Color, and Visual Optics

Original Manuscript: March 4, 2013
Revised Manuscript: April 27, 2013
Manuscript Accepted: May 3, 2013
Published: June 27, 2013

Virtual Issues
Vol. 8, Iss. 8 Virtual Journal for Biomedical Optics

Gerald Westheimer, "Retinal light distributions, the Stiles–Crawford effect and apodization," J. Opt. Soc. Am. A 30, 1417-1421 (2013)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. W. S. Stiles and B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. B 112, 428–450 (1933).
  2. F. Flamant and W. S. Stiles, “The directional and spectral sensitivities of retinal rods to adapting fields of different wavelengths,” J. Physiol. 107, 187–202 (1948).
  3. G. Westheimer, “Phase distribution in Young’s interference experiment,” J. Opt. Soc. Am. 50, 1338 (1960). [CrossRef]
  4. B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 11(1), 19 (2010). [CrossRef]
  5. L. J. Bour and J. C. M. Verhoosel, “Directional sensitivity of photoreceptors for different degrees of coherence and direction of polarization of the incident light,” Vis. Res. 19, 717–719 (1979). [CrossRef]
  6. G. C. Steward, The Symmetrical Optical System (Cambridge University, 1928).
  7. P. Jacquinot, P. Bougron, and B. Dossier, “Calcul et realisation des distributions d’amplitude pupillaire, permettant a suppression des franges laterale dans les figures de diffraction,” in La Theorie des Images Optiques, P. Fleury, A. Marechal, and C. Anglade, eds. (Editions de la Revue d’Optique, 1949), pp. 183–193.
  8. G. Westheimer, “Retinal light distribution for circular apertures in Maxwellian view,” J. Opt. Soc. Am. 49, 41–44 (1959). [CrossRef]
  9. H. Metcalf, “Stiles–Crawford apodization,” J. Opt. Soc. Am. 55, 72–74 (1965). [CrossRef]
  10. J. P. Carroll, “Apodization model of the Stiles–Crawford effect,” J. Opt. Soc. Am. 70, 1155–1156 (1980). [CrossRef]
  11. D. A. Palmer, “Stiles–Crawford apodization and the Campbell effect,” J. Opt. Soc. Am. A 2, 1371–1374 (1985). [CrossRef]
  12. P. Artal, “Incorporation of directional effects of the retina into computations of optical transfer functions of human eyes,” J. Opt. Soc. Am. A 6, 1941–1944 (1989). [CrossRef]
  13. X. Zhang, M. Ye, A. Bradley, and L. Thibos, “Apodization by the Stiles–Crawford effect moderates the visual impact of retinal image defocus,” J. Opt. Soc. Am. A 16, 812–820 (1999). [CrossRef]
  14. D. A. Atchison, D. H. Scott, N. C. Strang, and P. Artal, “Influence of Stiles–Crawford apodization on visual acuity,” J. Opt. Soc. Am. A 19, 1073–1083 (2002). [CrossRef]
  15. G. Westheimer, “Specifying and controlling the optical image on the retina,” Prog. Retinal Eye Res. 25, 19–42 (2006).
  16. W. Makous, “A transient Stiles–Crawford effect,” Vis. Res. 8, 1271–1284 (1968). [CrossRef]
  17. B. Vohnsen, “Photoreceptor waveguides and effective retinal image quality,” J. Opt. Soc. Am. A 24, 597–607 (2007). [CrossRef]
  18. G. Westheimer, “Directional sensitivity of the retina: 75 years of Stiles–Crawford effect,” Proc. R. Soc. B 275, 2777–2786 (2008).
  19. H. S. He, S. Marcos, and S. A. Burns, “Comparison of cone directionality determined by psychophysical and reflectometric techniques,” J. Opt. Soc. Am. A 16, 2363–2369 (1999). [CrossRef]
  20. J. M. Enoch and V. Lakshminarayanan, “Integration of the Stiles–Crawford effect of the first kind,” J. Mod. Opt. 56, 2240–2250 (2009). [CrossRef]
  21. A. M. Ercoles, A. M. Ronchi, and G. Toraldo di Francia, “The relation between pupil efficiencies for small and extended pupils of entry,” Opt. Acta 3, 84–89 (1956). [CrossRef]
  22. J. M. Enoch, “Summated response of the retina to light entering different parts of the pupil,” J. Opt. Soc. Am. 48, 392–405 (1958). [CrossRef]
  23. B. Drum, “Additivity of the Stiles–Crawford effect for a Fraunhofer image,” Vis. Res. 15, 291–298 (1975). [CrossRef]
  24. L. Ronchi, “Influence d'un mydriatique sur l'effet Stiles–Crawford,” Opt. Acta 2, 47–49 (1954).
  25. L. T. Troland, “On the measurement of visual stimulation intensities,” J. Exp. Psychol. 2, 1–33 (1917). [CrossRef]
  26. Y. LeGrand, Optique Physiologique, 2 (Editions de la Revue d’Optique, 1949).

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.


Fig. 1. Fig. 2. Fig. 3.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited