Abstract

Using theoretical estimates of the optical-transfer function and line-spread function as image-quality criteria, we predicted the influence of the Stiles–Crawford effect (SCE) on both optical performance of the eye and subjective measurements of transverse aberrations when pupils are decentered. The SCE was modeled as a pupil apodization. The SCE appears to improve image quality by providing compensation for aberrations induced by pupil decentration, but this improvement is usually small. When a criterion of the placement of the image is used as the centroid of the line-spread function, an average SCE reduces the influence of pupil decentration on subjective transverse chromatic aberrations (TCA’s) for 5-mm-diameter pupils by 30%. This reduction is much less than that obtained by previous experimental studies of TCA, and possible reasons for this discrepancy are discussed. Decentering the SCE produces an appreciable shift in subjective TCA for 5-mm-diameter pupils of 1.4 arc min per 1-mm decentration (at wavelengths 433 and 622 nm).

© 2001 Optical Society of America

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  1. D. A. Atchison, A. Joblin, G. Smith, “Influence of Stiles–Crawford effect apodization on spatial visual performance,” J. Opt. Soc. Am. A 15, 2545–2551 (1998).
    [CrossRef]
  2. D. G. Green, “Visual resolution when light enters the pupil through different parts of the pupil,” J. Physiol. (London) 190, 580–593 (1967).
  3. A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupils,” Vision Res. 23, 573–579 (1993).
    [CrossRef]
  4. P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
    [CrossRef] [PubMed]
  5. L. N. Thibos, “Calculation of the influence of lateral chromatic aberration on image quality across the visual field,” J. Opt. Soc. Am. A 4, 1673–1680 (1987).
    [CrossRef] [PubMed]
  6. M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2128 (1992).
    [CrossRef] [PubMed]
  7. B. Winn, A. Bradley, N. C. Strang, P. V. McGraw, L. N. Thibos, “Reversals of the colour-depth illusion explained by ocular chromatic aberration,” Vision Res. 35, 2675–2684 (1995).
    [CrossRef] [PubMed]
  8. M. C. Rynders, “The Stiles–Crawford effect and an experimental determination of its impact on vision,” unpublished Ph.D. thesis (available from School of Optometry, Indiana University, Bloomington, Ind., 1994).
  9. M. C. Rynders, L. N. Thibos, A. Bradley, N. Lopéz-Gil, “Apodization neutralization: a new technique for investigating the impact of the Stiles–Crawford effect on visual function,” in Basic and Clinical Applications of Visual Science, The Professor Jay M. Enoch Festschift Volume. V. Lakshminarayanan, ed. Doc. Ophthalmol. Proc. Series60, 57–61 (1997).
    [CrossRef]
  10. A. Bradley, L. N. Thibos, “Modelling off-axis vision-I: The optical effects of decentring visual targets or the eye’s entrance pupil,” in Vision Models for Target Decentration and Recognition, E. Peli, ed. (World Scientific, Singapore (1995)), Chap. 12, pp. 313–317.
  11. L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberrations in humans,” Appl. Opt. 31, 3594–3600 (1992).
    [CrossRef] [PubMed]
  12. L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599–607 (1991).
    [CrossRef]
  13. D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth–Heinemann, Stoneham, Mass., 2000), p. 41.
  14. For a 6-mm-diameter pupil, there are 0.049 and 0.019 waves-squared variance for wavelengths of 433 and 622 nm, respectively, owing to residual spherical aberration.
  15. G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), pp. 118–121.
  16. For a 6-mm diameter pupil at 589 nm, the total variance is 1.46 waves squared. The primary aberration term by itself would produce 1.87 waves-squared variance.
  17. D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth–Heinemann, Stoneham, Mass., 2000), pp. 143–145.
  18. J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
    [CrossRef]
  19. This procedure was given to us by D. Robert Iskander, School of Multimedia and Telecommunications, Gold Coast Campus, Griffith University, PMB 50, Gold Coast Mail Centre, Queensland 9726, Australia.
  20. R. A. Applegate, V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993).
    [CrossRef] [PubMed]
  21. Applegate and Lakshminarayanan21used the equation SCE=10-p10(X2+Y2).Their means and standard deviations for p10were horizontal meridian 0.048±0.013 mm-2,vertical meridian 0.053±0.012 mm-2.Converting to a natural logarithm base gives approximate mean and 97.5% upper limit to peof 0.12 and 0.17 mm-2, respectively, in Eq. (4).
  22. S. Marcos, S. A. Burns, E. Moreno-Burriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
    [CrossRef]
  23. J. C. He, S. Marcos, S. A. Burns, “Comparison of cone directionality determined by psychophysical and reflectometric techniques,” J. Opt. Soc. Am. A 16, 2363–2369 (1999).
    [CrossRef]
  24. C. J. Dunnewold, “On the Campbell and Stiles–Crawford effects and their clinical importance,” Ph.D. dissertation (Rijksuniversiteit te Utrecht, Utrecht, The Netherlands, 1964), pp. 1–84.
  25. Standard deviations of the peak of the SCE from Fig. 45 of Dunnewold23were determined by Applegate and Lakshminarayanan.21
  26. S. A. Burns, S. Marcos, “Evaluating the role of cone directionality in image formation,” in Digest of Topical Meeting on Vision Science and Its Applications (Optical Society of America, Washington D.C., 2000), pp. 7–10.
  27. J. Macdonald, “The calculation of the optical transfer function,” Opt. Acta 18, 269–290 (1971).
    [CrossRef]
  28. D. A. Atchison, D. H. Scott, G. Smith, “Pupil photometric efficiency and effective centre,” Ophthalmic Physiol. Opt. 20, 501–503 (2000).
    [CrossRef] [PubMed]
  29. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  30. D. A. Atchison, D. H. Scott, M. J. Cox, “Mathematical treatment of ocular aberrations: a user’s guide,” in Vision Sciences and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 110–130.
  31. Susana Marcos provided the aberration polynomial coefficients (Instituto de Optica, Consejo Superior de Investigaciones Científicas, Serrano 121, Madrid, 28006 Spain).
  32. H. Hartridge, “The visual perception of fine detail,” Philos. Trans. R. Soc. London, Ser. B 232, 517–671 (1947).
    [CrossRef]
  33. B. N. Kishto, “The colour stereoscopic effect,” Vision Res. 5, 313–329 (1965).
    [CrossRef]
  34. Y. U. Ogboso, H. E. Bedell, “Magnitude of lateral chromatic aberration across the retina of the human eye,” J. Opt. Soc. Am. A 4, 1666–1672 (1987).
    [CrossRef] [PubMed]
  35. M. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
    [CrossRef]
  36. L. N. Thibos, A. Bradley, D. L. Still, X. Xhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1988).
    [CrossRef]
  37. P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1988).
    [CrossRef]
  38. W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. London, Ser. B 123, 90–118 (1937).
    [CrossRef]
  39. W. S. Stiles, “The directional sensitivity of the retina and the spectral sensitivities of the rods and cones,” Proc. R. Soc. London, Ser. B 127, 64–105 (1939).
    [CrossRef]
  40. J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta 8, 329–358 (1961).
    [CrossRef]
  41. W. Wijngaard, J. van Kruysbergen, “The function of the non-guided light in some explanations of the Stiles-Crawford effects,” in Photoreceptor Optics, A. H. Snyder, R. Menzel, eds. (Springer–Verlag, New York, 1975), pp. 175–183.
  42. R. J. Watt, M. J. Morgan, “Mechanisms responsible for the assessment of visual location: theory and evidence,” Vision Res. 23, 97–109 (1983).
    [CrossRef] [PubMed]
  43. R. J. Watt, M. J. Morgan, R. M. Ward, “Stimulus features that determine the visual location of a bright bar,” Invest. Ophthalmol. Visual Sci. 24, 66–71 (1984).
  44. A. Toet, C. S. Smit, B. Nienhuis, J. J. Koenderink, “The visual assessment of the spatial location of a bright bar,” Vision Res. 30, 721–737 (1988).
    [CrossRef]
  45. D. Whitaker, P. V. McGraw, I. Pacey, B. T. Barrett, “Centroid analysis predicts visual localization of first- and second-order stimuli,” Vision Res. 36, 2597–2970 (1996).
    [CrossRef]
  46. D. Whitaker, P. V. McGraw, “The effect of suprathreshold contrast on stimulus centroid and its implications for the perceived location of objects,” Vision Res. 38, 3591–3599 (1998).
    [CrossRef]
  47. X. Zhang, M. Ye, A. Bradley, L. N. 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]
  48. C. Cui, V. Lakshminarayanan, “Choice of reference axis in ocular wave-front aberration measurement,” J. Opt. Soc. Am. A 15, 2488–2496 (1998).
    [CrossRef]

2000 (1)

D. A. Atchison, D. H. Scott, G. Smith, “Pupil photometric efficiency and effective centre,” Ophthalmic Physiol. Opt. 20, 501–503 (2000).
[CrossRef] [PubMed]

1999 (3)

1998 (4)

1996 (2)

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

D. Whitaker, P. V. McGraw, I. Pacey, B. T. Barrett, “Centroid analysis predicts visual localization of first- and second-order stimuli,” Vision Res. 36, 2597–2970 (1996).
[CrossRef]

1995 (2)

M. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
[CrossRef]

B. Winn, A. Bradley, N. C. Strang, P. V. McGraw, L. N. Thibos, “Reversals of the colour-depth illusion explained by ocular chromatic aberration,” Vision Res. 35, 2675–2684 (1995).
[CrossRef] [PubMed]

1993 (2)

1992 (2)

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2128 (1992).
[CrossRef] [PubMed]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberrations in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef] [PubMed]

1991 (1)

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599–607 (1991).
[CrossRef]

1988 (3)

L. N. Thibos, A. Bradley, D. L. Still, X. Xhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1988).
[CrossRef]

P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1988).
[CrossRef]

A. Toet, C. S. Smit, B. Nienhuis, J. J. Koenderink, “The visual assessment of the spatial location of a bright bar,” Vision Res. 30, 721–737 (1988).
[CrossRef]

1987 (2)

1984 (1)

R. J. Watt, M. J. Morgan, R. M. Ward, “Stimulus features that determine the visual location of a bright bar,” Invest. Ophthalmol. Visual Sci. 24, 66–71 (1984).

1983 (1)

R. J. Watt, M. J. Morgan, “Mechanisms responsible for the assessment of visual location: theory and evidence,” Vision Res. 23, 97–109 (1983).
[CrossRef] [PubMed]

1971 (1)

J. Macdonald, “The calculation of the optical transfer function,” Opt. Acta 18, 269–290 (1971).
[CrossRef]

1967 (1)

D. G. Green, “Visual resolution when light enters the pupil through different parts of the pupil,” J. Physiol. (London) 190, 580–593 (1967).

1965 (2)

B. N. Kishto, “The colour stereoscopic effect,” Vision Res. 5, 313–329 (1965).
[CrossRef]

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).

1961 (1)

J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta 8, 329–358 (1961).
[CrossRef]

1947 (1)

H. Hartridge, “The visual perception of fine detail,” Philos. Trans. R. Soc. London, Ser. B 232, 517–671 (1947).
[CrossRef]

1939 (1)

W. S. Stiles, “The directional sensitivity of the retina and the spectral sensitivities of the rods and cones,” Proc. R. Soc. London, Ser. B 127, 64–105 (1939).
[CrossRef]

1937 (1)

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. London, Ser. B 123, 90–118 (1937).
[CrossRef]

Applegate, R. A.

Artal, P.

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

Atchison, D. A.

D. A. Atchison, D. H. Scott, G. Smith, “Pupil photometric efficiency and effective centre,” Ophthalmic Physiol. Opt. 20, 501–503 (2000).
[CrossRef] [PubMed]

D. A. Atchison, A. Joblin, G. Smith, “Influence of Stiles–Crawford effect apodization on spatial visual performance,” J. Opt. Soc. Am. A 15, 2545–2551 (1998).
[CrossRef]

D. A. Atchison, D. H. Scott, M. J. Cox, “Mathematical treatment of ocular aberrations: a user’s guide,” in Vision Sciences and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 110–130.

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), pp. 118–121.

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth–Heinemann, Stoneham, Mass., 2000), pp. 143–145.

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth–Heinemann, Stoneham, Mass., 2000), p. 41.

Barrett, B. T.

D. Whitaker, P. V. McGraw, I. Pacey, B. T. Barrett, “Centroid analysis predicts visual localization of first- and second-order stimuli,” Vision Res. 36, 2597–2970 (1996).
[CrossRef]

Bedell, H. E.

Bradley, A.

X. Zhang, M. Ye, A. Bradley, L. N. 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]

B. Winn, A. Bradley, N. C. Strang, P. V. McGraw, L. N. Thibos, “Reversals of the colour-depth illusion explained by ocular chromatic aberration,” Vision Res. 35, 2675–2684 (1995).
[CrossRef] [PubMed]

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2128 (1992).
[CrossRef] [PubMed]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberrations in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599–607 (1991).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Xhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1988).
[CrossRef]

M. C. Rynders, L. N. Thibos, A. Bradley, N. Lopéz-Gil, “Apodization neutralization: a new technique for investigating the impact of the Stiles–Crawford effect on visual function,” in Basic and Clinical Applications of Visual Science, The Professor Jay M. Enoch Festschift Volume. V. Lakshminarayanan, ed. Doc. Ophthalmol. Proc. Series60, 57–61 (1997).
[CrossRef]

A. Bradley, L. N. Thibos, “Modelling off-axis vision-I: The optical effects of decentring visual targets or the eye’s entrance pupil,” in Vision Models for Target Decentration and Recognition, E. Peli, ed. (World Scientific, Singapore (1995)), Chap. 12, pp. 313–317.

Burns, S. A.

J. C. He, S. Marcos, S. A. Burns, “Comparison of cone directionality determined by psychophysical and reflectometric techniques,” J. Opt. Soc. Am. A 16, 2363–2369 (1999).
[CrossRef]

S. Marcos, S. A. Burns, E. Moreno-Burriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

S. A. Burns, S. Marcos, “Evaluating the role of cone directionality in image formation,” in Digest of Topical Meeting on Vision Science and Its Applications (Optical Society of America, Washington D.C., 2000), pp. 7–10.

Campbell, F. W.

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).

Campbell, M. C. W.

P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1988).
[CrossRef]

Chisholm, W.

Cox, M. J.

D. A. Atchison, D. H. Scott, M. J. Cox, “Mathematical treatment of ocular aberrations: a user’s guide,” in Vision Sciences and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 110–130.

Cui, C.

Dunnewold, C. J.

C. J. Dunnewold, “On the Campbell and Stiles–Crawford effects and their clinical importance,” Ph.D. dissertation (Rijksuniversiteit te Utrecht, Utrecht, The Netherlands, 1964), pp. 1–84.

Dunnewold, C. J. W.

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupils,” Vision Res. 23, 573–579 (1993).
[CrossRef]

Enoch, J. M.

J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta 8, 329–358 (1961).
[CrossRef]

Green, D. G.

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

D. G. Green, “Visual resolution when light enters the pupil through different parts of the pupil,” J. Physiol. (London) 190, 580–593 (1967).

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).

Hartridge, H.

H. Hartridge, “The visual perception of fine detail,” Philos. Trans. R. Soc. London, Ser. B 232, 517–671 (1947).
[CrossRef]

He, J. C.

Howarth, P. A.

L. N. Thibos, A. Bradley, D. L. Still, X. Xhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1988).
[CrossRef]

Iglesias, I.

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

Joblin, A.

Kishto, B. N.

B. N. Kishto, “The colour stereoscopic effect,” Vision Res. 5, 313–329 (1965).
[CrossRef]

Koenderink, J. J.

A. Toet, C. S. Smit, B. Nienhuis, J. J. Koenderink, “The visual assessment of the spatial location of a bright bar,” Vision Res. 30, 721–737 (1988).
[CrossRef]

Lakshminarayanan, V.

Lidkea, B.

Lopéz-Gil, N.

M. C. Rynders, L. N. Thibos, A. Bradley, N. Lopéz-Gil, “Apodization neutralization: a new technique for investigating the impact of the Stiles–Crawford effect on visual function,” in Basic and Clinical Applications of Visual Science, The Professor Jay M. Enoch Festschift Volume. V. Lakshminarayanan, ed. Doc. Ophthalmol. Proc. Series60, 57–61 (1997).
[CrossRef]

Macdonald, J.

J. Macdonald, “The calculation of the optical transfer function,” Opt. Acta 18, 269–290 (1971).
[CrossRef]

Marcos, S.

S. Marcos, S. A. Burns, E. Moreno-Burriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

J. C. He, S. Marcos, S. A. Burns, “Comparison of cone directionality determined by psychophysical and reflectometric techniques,” J. Opt. Soc. Am. A 16, 2363–2369 (1999).
[CrossRef]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

S. A. Burns, S. Marcos, “Evaluating the role of cone directionality in image formation,” in Digest of Topical Meeting on Vision Science and Its Applications (Optical Society of America, Washington D.C., 2000), pp. 7–10.

McGraw, P. V.

D. Whitaker, P. V. McGraw, “The effect of suprathreshold contrast on stimulus centroid and its implications for the perceived location of objects,” Vision Res. 38, 3591–3599 (1998).
[CrossRef]

D. Whitaker, P. V. McGraw, I. Pacey, B. T. Barrett, “Centroid analysis predicts visual localization of first- and second-order stimuli,” Vision Res. 36, 2597–2970 (1996).
[CrossRef]

B. Winn, A. Bradley, N. C. Strang, P. V. McGraw, L. N. Thibos, “Reversals of the colour-depth illusion explained by ocular chromatic aberration,” Vision Res. 35, 2675–2684 (1995).
[CrossRef] [PubMed]

Moreno-Burriuso, E.

S. Marcos, S. A. Burns, E. Moreno-Burriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

Morgan, M. J.

R. J. Watt, M. J. Morgan, R. M. Ward, “Stimulus features that determine the visual location of a bright bar,” Invest. Ophthalmol. Visual Sci. 24, 66–71 (1984).

R. J. Watt, M. J. Morgan, “Mechanisms responsible for the assessment of visual location: theory and evidence,” Vision Res. 23, 97–109 (1983).
[CrossRef] [PubMed]

Navarro, R.

S. Marcos, S. A. Burns, E. Moreno-Burriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

Nienhuis, B.

A. Toet, C. S. Smit, B. Nienhuis, J. J. Koenderink, “The visual assessment of the spatial location of a bright bar,” Vision Res. 30, 721–737 (1988).
[CrossRef]

Ogboso, Y. U.

Pacey, I.

D. Whitaker, P. V. McGraw, I. Pacey, B. T. Barrett, “Centroid analysis predicts visual localization of first- and second-order stimuli,” Vision Res. 36, 2597–2970 (1996).
[CrossRef]

Rynders, M.

Rynders, M. C.

M. C. Rynders, “The Stiles–Crawford effect and an experimental determination of its impact on vision,” unpublished Ph.D. thesis (available from School of Optometry, Indiana University, Bloomington, Ind., 1994).

M. C. Rynders, L. N. Thibos, A. Bradley, N. Lopéz-Gil, “Apodization neutralization: a new technique for investigating the impact of the Stiles–Crawford effect on visual function,” in Basic and Clinical Applications of Visual Science, The Professor Jay M. Enoch Festschift Volume. V. Lakshminarayanan, ed. Doc. Ophthalmol. Proc. Series60, 57–61 (1997).
[CrossRef]

Scott, D. H.

D. A. Atchison, D. H. Scott, G. Smith, “Pupil photometric efficiency and effective centre,” Ophthalmic Physiol. Opt. 20, 501–503 (2000).
[CrossRef] [PubMed]

D. A. Atchison, D. H. Scott, M. J. Cox, “Mathematical treatment of ocular aberrations: a user’s guide,” in Vision Sciences and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 110–130.

Simonet, P.

P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1988).
[CrossRef]

Smit, C. S.

A. Toet, C. S. Smit, B. Nienhuis, J. J. Koenderink, “The visual assessment of the spatial location of a bright bar,” Vision Res. 30, 721–737 (1988).
[CrossRef]

Smith, G.

D. A. Atchison, D. H. Scott, G. Smith, “Pupil photometric efficiency and effective centre,” Ophthalmic Physiol. Opt. 20, 501–503 (2000).
[CrossRef] [PubMed]

D. A. Atchison, A. Joblin, G. Smith, “Influence of Stiles–Crawford effect apodization on spatial visual performance,” J. Opt. Soc. Am. A 15, 2545–2551 (1998).
[CrossRef]

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth–Heinemann, Stoneham, Mass., 2000), p. 41.

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), pp. 118–121.

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth–Heinemann, Stoneham, Mass., 2000), pp. 143–145.

Stiles, W. S.

J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta 8, 329–358 (1961).
[CrossRef]

W. S. Stiles, “The directional sensitivity of the retina and the spectral sensitivities of the rods and cones,” Proc. R. Soc. London, Ser. B 127, 64–105 (1939).
[CrossRef]

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. London, Ser. B 123, 90–118 (1937).
[CrossRef]

Still, D. L.

L. N. Thibos, A. Bradley, D. L. Still, X. Xhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1988).
[CrossRef]

Strang, N. C.

B. Winn, A. Bradley, N. C. Strang, P. V. McGraw, L. N. Thibos, “Reversals of the colour-depth illusion explained by ocular chromatic aberration,” Vision Res. 35, 2675–2684 (1995).
[CrossRef] [PubMed]

Thibos, L. N.

X. Zhang, M. Ye, A. Bradley, L. N. 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]

M. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
[CrossRef]

B. Winn, A. Bradley, N. C. Strang, P. V. McGraw, L. N. Thibos, “Reversals of the colour-depth illusion explained by ocular chromatic aberration,” Vision Res. 35, 2675–2684 (1995).
[CrossRef] [PubMed]

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2128 (1992).
[CrossRef] [PubMed]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberrations in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599–607 (1991).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Xhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1988).
[CrossRef]

L. N. Thibos, “Calculation of the influence of lateral chromatic aberration on image quality across the visual field,” J. Opt. Soc. Am. A 4, 1673–1680 (1987).
[CrossRef] [PubMed]

M. C. Rynders, L. N. Thibos, A. Bradley, N. Lopéz-Gil, “Apodization neutralization: a new technique for investigating the impact of the Stiles–Crawford effect on visual function,” in Basic and Clinical Applications of Visual Science, The Professor Jay M. Enoch Festschift Volume. V. Lakshminarayanan, ed. Doc. Ophthalmol. Proc. Series60, 57–61 (1997).
[CrossRef]

A. Bradley, L. N. Thibos, “Modelling off-axis vision-I: The optical effects of decentring visual targets or the eye’s entrance pupil,” in Vision Models for Target Decentration and Recognition, E. Peli, ed. (World Scientific, Singapore (1995)), Chap. 12, pp. 313–317.

Toet, A.

A. Toet, C. S. Smit, B. Nienhuis, J. J. Koenderink, “The visual assessment of the spatial location of a bright bar,” Vision Res. 30, 721–737 (1988).
[CrossRef]

van Kruysbergen, J.

W. Wijngaard, J. van Kruysbergen, “The function of the non-guided light in some explanations of the Stiles-Crawford effects,” in Photoreceptor Optics, A. H. Snyder, R. Menzel, eds. (Springer–Verlag, New York, 1975), pp. 175–183.

van Meeteren, A.

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupils,” Vision Res. 23, 573–579 (1993).
[CrossRef]

Ward, R. M.

R. J. Watt, M. J. Morgan, R. M. Ward, “Stimulus features that determine the visual location of a bright bar,” Invest. Ophthalmol. Visual Sci. 24, 66–71 (1984).

Watt, R. J.

R. J. Watt, M. J. Morgan, R. M. Ward, “Stimulus features that determine the visual location of a bright bar,” Invest. Ophthalmol. Visual Sci. 24, 66–71 (1984).

R. J. Watt, M. J. Morgan, “Mechanisms responsible for the assessment of visual location: theory and evidence,” Vision Res. 23, 97–109 (1983).
[CrossRef] [PubMed]

Webb, R. H.

Whitaker, D.

D. Whitaker, P. V. McGraw, “The effect of suprathreshold contrast on stimulus centroid and its implications for the perceived location of objects,” Vision Res. 38, 3591–3599 (1998).
[CrossRef]

D. Whitaker, P. V. McGraw, I. Pacey, B. T. Barrett, “Centroid analysis predicts visual localization of first- and second-order stimuli,” Vision Res. 36, 2597–2970 (1996).
[CrossRef]

Wijngaard, W.

W. Wijngaard, J. van Kruysbergen, “The function of the non-guided light in some explanations of the Stiles-Crawford effects,” in Photoreceptor Optics, A. H. Snyder, R. Menzel, eds. (Springer–Verlag, New York, 1975), pp. 175–183.

Winn, B.

B. Winn, A. Bradley, N. C. Strang, P. V. McGraw, L. N. Thibos, “Reversals of the colour-depth illusion explained by ocular chromatic aberration,” Vision Res. 35, 2675–2684 (1995).
[CrossRef] [PubMed]

Xhang, X.

L. N. Thibos, A. Bradley, D. L. Still, X. Xhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1988).
[CrossRef]

Ye, M.

Zhang, X.

X. Zhang, M. Ye, A. Bradley, L. N. 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]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberrations in humans,” Appl. Opt. 31, 3594–3600 (1992).
[CrossRef] [PubMed]

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2128 (1992).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599–607 (1991).
[CrossRef]

Appl. Opt. (1)

Invest. Ophthalmol. Visual Sci. (1)

R. J. Watt, M. J. Morgan, R. M. Ward, “Stimulus features that determine the visual location of a bright bar,” Invest. Ophthalmol. Visual Sci. 24, 66–71 (1984).

J. Opt. Soc. Am. A (9)

X. Zhang, M. Ye, A. Bradley, L. N. 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]

C. Cui, V. Lakshminarayanan, “Choice of reference axis in ocular wave-front aberration measurement,” J. Opt. Soc. Am. A 15, 2488–2496 (1998).
[CrossRef]

J. C. He, S. Marcos, R. H. Webb, S. A. Burns, “Measurement of the wave-front aberration by a fast psychophysical procedure,” J. Opt. Soc. Am. A 15, 2449–2456 (1998).
[CrossRef]

R. A. Applegate, V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993).
[CrossRef] [PubMed]

D. A. Atchison, A. Joblin, G. Smith, “Influence of Stiles–Crawford effect apodization on spatial visual performance,” J. Opt. Soc. Am. A 15, 2545–2551 (1998).
[CrossRef]

L. N. Thibos, “Calculation of the influence of lateral chromatic aberration on image quality across the visual field,” J. Opt. Soc. Am. A 4, 1673–1680 (1987).
[CrossRef] [PubMed]

J. C. He, S. Marcos, S. A. Burns, “Comparison of cone directionality determined by psychophysical and reflectometric techniques,” J. Opt. Soc. Am. A 16, 2363–2369 (1999).
[CrossRef]

Y. U. Ogboso, H. E. Bedell, “Magnitude of lateral chromatic aberration across the retina of the human eye,” J. Opt. Soc. Am. A 4, 1666–1672 (1987).
[CrossRef] [PubMed]

M. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
[CrossRef]

J. Physiol. (London) (2)

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).

D. G. Green, “Visual resolution when light enters the pupil through different parts of the pupil,” J. Physiol. (London) 190, 580–593 (1967).

Ophthalmic Physiol. Opt. (1)

D. A. Atchison, D. H. Scott, G. Smith, “Pupil photometric efficiency and effective centre,” Ophthalmic Physiol. Opt. 20, 501–503 (2000).
[CrossRef] [PubMed]

Opt. Acta (2)

J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta 8, 329–358 (1961).
[CrossRef]

J. Macdonald, “The calculation of the optical transfer function,” Opt. Acta 18, 269–290 (1971).
[CrossRef]

Optom. Vision Sci. (1)

L. N. Thibos, A. Bradley, X. Zhang, “Effect of ocular chromatic aberration on monocular visual performance,” Optom. Vision Sci. 68, 599–607 (1991).
[CrossRef]

Philos. Trans. R. Soc. London, Ser. B (1)

H. Hartridge, “The visual perception of fine detail,” Philos. Trans. R. Soc. London, Ser. B 232, 517–671 (1947).
[CrossRef]

Proc. R. Soc. London, Ser. B (2)

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new colour effect,” Proc. R. Soc. London, Ser. B 123, 90–118 (1937).
[CrossRef]

W. S. Stiles, “The directional sensitivity of the retina and the spectral sensitivities of the rods and cones,” Proc. R. Soc. London, Ser. B 127, 64–105 (1939).
[CrossRef]

Vision Res. (12)

B. N. Kishto, “The colour stereoscopic effect,” Vision Res. 5, 313–329 (1965).
[CrossRef]

L. N. Thibos, A. Bradley, D. L. Still, X. Xhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1988).
[CrossRef]

P. Simonet, M. C. W. Campbell, “The optical transverse chromatic aberration on the fovea of the human eye,” Vision Res. 30, 187–206 (1988).
[CrossRef]

S. Marcos, S. A. Burns, E. Moreno-Burriuso, R. Navarro, “A new approach to the study of ocular chromatic aberrations,” Vision Res. 39, 4309–4323 (1999).
[CrossRef]

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupils,” Vision Res. 23, 573–579 (1993).
[CrossRef]

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

M. Ye, A. Bradley, L. N. Thibos, X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2128 (1992).
[CrossRef] [PubMed]

B. Winn, A. Bradley, N. C. Strang, P. V. McGraw, L. N. Thibos, “Reversals of the colour-depth illusion explained by ocular chromatic aberration,” Vision Res. 35, 2675–2684 (1995).
[CrossRef] [PubMed]

R. J. Watt, M. J. Morgan, “Mechanisms responsible for the assessment of visual location: theory and evidence,” Vision Res. 23, 97–109 (1983).
[CrossRef] [PubMed]

A. Toet, C. S. Smit, B. Nienhuis, J. J. Koenderink, “The visual assessment of the spatial location of a bright bar,” Vision Res. 30, 721–737 (1988).
[CrossRef]

D. Whitaker, P. V. McGraw, I. Pacey, B. T. Barrett, “Centroid analysis predicts visual localization of first- and second-order stimuli,” Vision Res. 36, 2597–2970 (1996).
[CrossRef]

D. Whitaker, P. V. McGraw, “The effect of suprathreshold contrast on stimulus centroid and its implications for the perceived location of objects,” Vision Res. 38, 3591–3599 (1998).
[CrossRef]

Other (16)

W. Wijngaard, J. van Kruysbergen, “The function of the non-guided light in some explanations of the Stiles-Crawford effects,” in Photoreceptor Optics, A. H. Snyder, R. Menzel, eds. (Springer–Verlag, New York, 1975), pp. 175–183.

M. C. Rynders, “The Stiles–Crawford effect and an experimental determination of its impact on vision,” unpublished Ph.D. thesis (available from School of Optometry, Indiana University, Bloomington, Ind., 1994).

M. C. Rynders, L. N. Thibos, A. Bradley, N. Lopéz-Gil, “Apodization neutralization: a new technique for investigating the impact of the Stiles–Crawford effect on visual function,” in Basic and Clinical Applications of Visual Science, The Professor Jay M. Enoch Festschift Volume. V. Lakshminarayanan, ed. Doc. Ophthalmol. Proc. Series60, 57–61 (1997).
[CrossRef]

A. Bradley, L. N. Thibos, “Modelling off-axis vision-I: The optical effects of decentring visual targets or the eye’s entrance pupil,” in Vision Models for Target Decentration and Recognition, E. Peli, ed. (World Scientific, Singapore (1995)), Chap. 12, pp. 313–317.

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth–Heinemann, Stoneham, Mass., 2000), p. 41.

For a 6-mm-diameter pupil, there are 0.049 and 0.019 waves-squared variance for wavelengths of 433 and 622 nm, respectively, owing to residual spherical aberration.

G. Smith, D. A. Atchison, The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), pp. 118–121.

For a 6-mm diameter pupil at 589 nm, the total variance is 1.46 waves squared. The primary aberration term by itself would produce 1.87 waves-squared variance.

D. A. Atchison, G. Smith, Optics of the Human Eye (Butterworth–Heinemann, Stoneham, Mass., 2000), pp. 143–145.

Applegate and Lakshminarayanan21used the equation SCE=10-p10(X2+Y2).Their means and standard deviations for p10were horizontal meridian 0.048±0.013 mm-2,vertical meridian 0.053±0.012 mm-2.Converting to a natural logarithm base gives approximate mean and 97.5% upper limit to peof 0.12 and 0.17 mm-2, respectively, in Eq. (4).

This procedure was given to us by D. Robert Iskander, School of Multimedia and Telecommunications, Gold Coast Campus, Griffith University, PMB 50, Gold Coast Mail Centre, Queensland 9726, Australia.

D. A. Atchison, D. H. Scott, M. J. Cox, “Mathematical treatment of ocular aberrations: a user’s guide,” in Vision Sciences and Its Applications, V. Lakshminarayanan, ed., Vol. 35 of OSA Trends In Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 110–130.

Susana Marcos provided the aberration polynomial coefficients (Instituto de Optica, Consejo Superior de Investigaciones Científicas, Serrano 121, Madrid, 28006 Spain).

C. J. Dunnewold, “On the Campbell and Stiles–Crawford effects and their clinical importance,” Ph.D. dissertation (Rijksuniversiteit te Utrecht, Utrecht, The Netherlands, 1964), pp. 1–84.

Standard deviations of the peak of the SCE from Fig. 45 of Dunnewold23were determined by Applegate and Lakshminarayanan.21

S. A. Burns, S. Marcos, “Evaluating the role of cone directionality in image formation,” in Digest of Topical Meeting on Vision Science and Its Applications (Optical Society of America, Washington D.C., 2000), pp. 7–10.

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Figures (12)

Fig. 1
Fig. 1

Three-dimensional wave-aberration maps of three subjects for a 6-mm-diameter pupil and 550 nm. (a) Subject A’s map is dominated by spherical aberration (correction -0.08 DS/-0.23DC×61). (b) Subject B’s map is dominated by astigmatism and some vertical coma (correction plano/-0.58×179). (c) Subject C was poorly corrected, but there is also significant positive horizontal coma and positive spherical aberration (correction +1.39DS/-0.61DC×177).

Fig. 2
Fig. 2

Monochromatic (589 nm) MTFs of the model eye with spherical aberration with a 2-mm-diameter pupil in the presence of 0-, 1-, and 2.5-mm horizontal pupil decentrations. Target orientations are horizontal and vertical. There is no SCE (pe=0). A small change in axial length from the paraxial length has been made so that the modulation transfer is a maximum at 20 cycles/deg in the centered condition.

Fig. 3
Fig. 3

MTF’s of the model eye with spherical aberration with a 5-mm-diameter pupil in the presence of 0-, 1-, and 2-mm horizontal pupil decentration. Other details are as for Fig. 2.

Fig. 4
Fig. 4

MTF’s of the model eye with spherical aberration and a 2-mm-diameter pupil, with 0- and +2.5-mm horizontal pupil decentration, both with and without the SCE (pe=0 and 0.12 mm-2, respectively). Wavelength is 589 nm. Target orientations are vertical and horizontal. The SCE has been shifted by 0, -2, and +2 mm horizontally relative to the centered pupil. Small changes in axial length from the paraxial length have been made so that the modulation transfer is a maximum at 20 cycles/deg in the centered condition. The neural contrast threshold from one subject28 is also shown.

Fig. 5
Fig. 5

MTF’s of the model eye with spherical aberration and a 5-mm-diameter pupil with 0- and +1-mm horizontal pupil decentration. Other details are as for Fig. 4.

Fig. 6
Fig. 6

MTF’s of the model eye based on the wave-aberration function of subject B and a 2-mm-diameter pupil with 0 and +2.5-mm vertical pupil decentration. Wavelength is 589 nm. Target orientations are horizontal and vertical. Results for 0-mm decentration are shown without the SCE operating. Results for +2.5-mm decentration are shown with the SCE (pe=0.12 mm-2), shifted by both -2 mm and +2 mm vertically.

Fig. 7
Fig. 7

MTF’s of a model eye based on the wave-aberration function of subject B and a 5-mm-diameter pupil with 0- and +1-mm vertical pupil decentration. Wavelength is 589 nm. Target orientations are horizontal and vertical. Results are shown with the SCE (pe=0.12 mm-2), shifted by both -2 and +2 mm vertically.

Fig. 8
Fig. 8

Monochromatic (433 nm) line-spread intensity distributions of the model eye are shown for a 5-mm diameter and +1-mm horizontal pupil decentration. Results are shown both without and with the SCE (pe=0 and 0.12 mm-2, respectively). The SCE is decentered horizontally by -2 mm, 0, and +2 mm relative to the centered pupil. All distributions have been normalized to the peak intensity of the distribution without the SCE. Spherical aberration is present. Chief ray position and distribution centroids are marked.

Fig. 9
Fig. 9

Theoretical estimates of subjective TCA as a function of pupil diameter for 0, +1-, +2-, and +3-mm horizontal decentrations. These are shown both without and with the SCE (pe=0 and 0.12 mm-2, respectively). The SCE is decentered by -2, 0, and +2 mm relative to the centered pupil. Results are shown for two criteria: the centroid of the line-spread function (symbols) and the aberrations based on the SCE-weighted effective pupil center (curves). Spherical aberration is present.

Fig. 10
Fig. 10

Theoretical estimates of subjective TCA as a function of horizontal pupil decentration for a 5-mm-diameter pupil. These are shown both without (solid line) and with the SCE (pe=0 and 0.12 mm-2, respectively). The SCE is decentered by -2, -1, 0, +1, and +2 mm horizontally relative to the centered pupil. The curves give the aberrations based on the SCE-weighted effective pupil center of the purely theoretical model eye with spherical aberration, and the circles give the aberrations based on the centroid of the line-spread function of the model eye with subject A’s aberrations.

Fig. 11
Fig. 11

Subjective TCA as a function of pupil size for two experimental studies. Different symbols are used for different subjects and conditions. a) Ye et al.6 Determined from chromostereopsis results. 2-mm-decentration results are from their Table 1, wavelengths 433 and 622 nm. 1-mm-decentration results are from their Fig. 5, wavelengths 433 and 589 nm. Results are averages of nasal and temporal decentrations. b) Rynders et al.8,9 Determined by the slope fitted to curves of subjective transverse chromatic aberration versus pupil decentration. Wavelengths 447 and 650 nm.

Fig. 12
Fig. 12

Estimates of subjective TCA as a function of horizontal-pupil decentration for a 5-mm pupil diameter. These are based on the wave-aberration coefficients for subject SB’s right eye in experiment 2 of Marcos et al.22,30 These are shown with the SCE operating (pe=0.12 mm-2). The SCE is decentered horizontally by -2, 0, and +2 mm relative to the centered pupil. Also shown are TCA’s obtained from raytracing: The solid curve shows the TCA when aberrations for red (601 nm) are set to be the same as those for blue (473 nm), and the dotted curve shows the TCA when this change is not made for the red.

Tables (1)

Tables Icon

Table 1 Aberrations Induced by Pupil Decentration

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

Z=cρ21+[1-(1+Q)cρ2]1/2+Aρ4+Bρ6+Cρ8+Dρ10+,
Q=-1/n2=-0.5628,
W(X, Y)=W2,0(X2+Y2)+W4,0(X2+Y2)2+W6,0(X2+Y2)3+W8,0(X2+Y2)4+W10,0(X2+Y2)5,
SCE=exp{-pe[(X-xsc)2+(Y-ysc)2]},
f(X, Y)=A(X, Y)S(X, Y)exp[i2πW(X, Y)/λ],
A(X, Y)=exp{-(pe/2)[(X-xsc)2+(Y-ysc)2]}.
S(X, Y)=1for(X-x0)2+(Y-y0)2Rp2,
S(X, Y)=0for(X-x0)2+(Y-y0)2>Rp2.
x¯=x0-RPx0+RP-Rp2-(X-x0)2+Rp2-(X-x0)2 X exp[-pe(X2+Y2)]dYdXx0-RPx0+RP-Rp2-(X-x0)2+Rp2-(X-x0)2 exp[-pe(X2+Y2)]dYdX.
x¯=x0-RPx0+RP-Rp2-(X-x0)2+Rp2-(X-x0)2X exp{-pe[(X-xsc)2+Y2]}dYdXx0-RPx0+RP-Rp2-(X-x0)2+Rp2-(X-x0)2 exp{-pe[(X-xsc)2+Y2]}dYdX.
sTA(x0)=TA(x¯).
sTCA(x0)=TA(x¯)433-TA(x¯)622.
W=W4,0[(X-x0)2+Y2]2,
W=W4,0(x04-4x03X+6x02X2+2x02Y2-4x0X3-4x0XY2+X4+2X2Y2+Y4).

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