Abstract

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

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References

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  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).
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  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]
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    [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).

2010 (1)

B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 11(1), 19 (2010).
[CrossRef]

2009 (1)

J. M. Enoch and V. Lakshminarayanan, “Integration of the Stiles–Crawford effect of the first kind,” J. Mod. Opt. 56, 2240–2250 (2009).
[CrossRef]

2008 (1)

G. Westheimer, “Directional sensitivity of the retina: 75 years of Stiles–Crawford effect,” Proc. R. Soc. B 275, 2777–2786 (2008).

2007 (1)

2006 (1)

G. Westheimer, “Specifying and controlling the optical image on the retina,” Prog. Retinal Eye Res. 25, 19–42 (2006).

2002 (1)

1999 (2)

1989 (1)

1985 (1)

1980 (1)

1979 (1)

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]

1975 (1)

B. Drum, “Additivity of the Stiles–Crawford effect for a Fraunhofer image,” Vis. Res. 15, 291–298 (1975).
[CrossRef]

1968 (1)

W. Makous, “A transient Stiles–Crawford effect,” Vis. Res. 8, 1271–1284 (1968).
[CrossRef]

1965 (1)

1960 (1)

1959 (1)

1958 (1)

1956 (1)

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]

1954 (1)

L. Ronchi, “Influence d'un mydriatique sur l'effet Stiles–Crawford,” Opt. Acta 2, 47–49 (1954).

1948 (1)

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).

1933 (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).

1917 (1)

L. T. Troland, “On the measurement of visual stimulation intensities,” J. Exp. Psychol. 2, 1–33 (1917).
[CrossRef]

Artal, P.

Atchison, D. A.

Bougron, P.

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.

Bour, L. J.

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]

Bradley, A.

Burns, S. A.

Carroll, J. P.

Crawford, B. H.

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).

Dossier, B.

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.

Drum, B.

B. Drum, “Additivity of the Stiles–Crawford effect for a Fraunhofer image,” Vis. Res. 15, 291–298 (1975).
[CrossRef]

Enoch, J. M.

J. M. Enoch and V. Lakshminarayanan, “Integration of the Stiles–Crawford effect of the first kind,” J. Mod. Opt. 56, 2240–2250 (2009).
[CrossRef]

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]

Ercoles, A. M.

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]

Flamant, F.

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).

He, H. S.

Jacquinot, P.

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.

Lakshminarayanan, V.

J. M. Enoch and V. Lakshminarayanan, “Integration of the Stiles–Crawford effect of the first kind,” J. Mod. Opt. 56, 2240–2250 (2009).
[CrossRef]

LeGrand, Y.

Y. LeGrand, Optique Physiologique, 2 (Editions de la Revue d’Optique, 1949).

Makous, W.

W. Makous, “A transient Stiles–Crawford effect,” Vis. Res. 8, 1271–1284 (1968).
[CrossRef]

Marcos, S.

Metcalf, H.

Palmer, D. A.

Rativa, D.

B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 11(1), 19 (2010).
[CrossRef]

Ronchi, A. M.

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]

Ronchi, L.

L. Ronchi, “Influence d'un mydriatique sur l'effet Stiles–Crawford,” Opt. Acta 2, 47–49 (1954).

Scott, D. H.

Steward, G. C.

G. C. Steward, The Symmetrical Optical System (Cambridge University, 1928).

Stiles, W. S.

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).

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).

Strang, N. C.

Thibos, L.

Toraldo di Francia, G.

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]

Troland, L. T.

L. T. Troland, “On the measurement of visual stimulation intensities,” J. Exp. Psychol. 2, 1–33 (1917).
[CrossRef]

Verhoosel, J. C. M.

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]

Vohnsen, B.

B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 11(1), 19 (2010).
[CrossRef]

B. Vohnsen, “Photoreceptor waveguides and effective retinal image quality,” J. Opt. Soc. Am. A 24, 597–607 (2007).
[CrossRef]

Westheimer, G.

G. Westheimer, “Directional sensitivity of the retina: 75 years of Stiles–Crawford effect,” Proc. R. Soc. B 275, 2777–2786 (2008).

G. Westheimer, “Specifying and controlling the optical image on the retina,” Prog. Retinal Eye Res. 25, 19–42 (2006).

G. Westheimer, “Phase distribution in Young’s interference experiment,” J. Opt. Soc. Am. 50, 1338 (1960).
[CrossRef]

G. Westheimer, “Retinal light distribution for circular apertures in Maxwellian view,” J. Opt. Soc. Am. 49, 41–44 (1959).
[CrossRef]

Ye, M.

Zhang, X.

J. Exp. Psychol. (1)

L. T. Troland, “On the measurement of visual stimulation intensities,” J. Exp. Psychol. 2, 1–33 (1917).
[CrossRef]

J. Mod. Opt. (1)

J. M. Enoch and V. Lakshminarayanan, “Integration of the Stiles–Crawford effect of the first kind,” J. Mod. Opt. 56, 2240–2250 (2009).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (6)

J. Physiol. (1)

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).

J. Vis. (1)

B. Vohnsen and D. Rativa, “Absence of an integrated Stiles–Crawford function for coherent light,” J. Vis. 11(1), 19 (2010).
[CrossRef]

Opt. Acta (2)

L. Ronchi, “Influence d'un mydriatique sur l'effet Stiles–Crawford,” Opt. Acta 2, 47–49 (1954).

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]

Proc. R. Soc. B (2)

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).

G. Westheimer, “Directional sensitivity of the retina: 75 years of Stiles–Crawford effect,” Proc. R. Soc. B 275, 2777–2786 (2008).

Prog. Retinal Eye Res. (1)

G. Westheimer, “Specifying and controlling the optical image on the retina,” Prog. Retinal Eye Res. 25, 19–42 (2006).

Vis. Res. (3)

W. Makous, “A transient Stiles–Crawford effect,” Vis. Res. 8, 1271–1284 (1968).
[CrossRef]

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]

B. Drum, “Additivity of the Stiles–Crawford effect for a Fraunhofer image,” Vis. Res. 15, 291–298 (1975).
[CrossRef]

Other (3)

Y. LeGrand, Optique Physiologique, 2 (Editions de la Revue d’Optique, 1949).

G. C. Steward, The Symmetrical Optical System (Cambridge University, 1928).

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.

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Figures (3)

Fig. 1.
Fig. 1.

Formation of diffraction image when a coherent bundle is imaged by a lens with (left) full and (right) small eccentrically placed aperture. The equal-phase planes and the Poynting vectors normal to them have different orientations in the two cases. This will produce different effects on the light-transducing apparatus, depending on the shape and orientation of its acceptance lobe (bottom).

Fig. 2.
Fig. 2.

A pair of symmetrically placed incoming bundles will generate different image situations depending whether they are (left) coherent or (right) incoherent. Because coherent light is capable of interference, it will produce an interference pattern whose equal-phase plane and direction of propagation have normal incidence on a receiving layer parallel to the lens plane. The two incoherent bundles will each give rise to their own obliquely directed equal-phase planes and Poynting vectors.

Fig. 3.
Fig. 3.

Typical arrangement for measuring the “integrated Stiles–Crawford effect.” Instead of direct viewing of a target with natural pupils of varying diameter, an extended incoherent source is imaged in the plane of the pupil via an intermediate stage controlling the diameter of the source image in the pupil. The source S1, an incandescent ribbon filament, is first imaged by lens L1 in a variable-size aperture A3, which lens L2 in turn makes conjugate to the pupil. The beam, in addition, passes through aperture A4, conjugate to the retina and defining the target area. Diffraction and aberrations may introduce partial coherence in the pupil image of the originally incoherent source (from Enoch [22], with permission).

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