Abstract

The Stiles–Crawford effect is often invoked by vision scientists when predictions of the effects of aberrations and defocus on spatial visual performance are not borne out experimentally. Modeling the Stiles–Crawford effect as an apodization, we investigated the expected influence that it would have on spatial visual performance in the presence of 1-diopter primary spherical aberration at the edge of a 6-mm-diameter centered pupil. The changes in refraction produced by a high Stiles–Crawford effect, according to various criteria, were small at approximately 0.10 diopter. The Stiles–Crawford effect has only a small capability to compensate for defocus and spherical aberration. These results indicate that the Stiles–Crawford effect has little influence on spatial visual performance in the case of centered pupils. We suggest that the faith that has often been placed in the Stiles–Crawford effect to account for discrepancies between experimental results and expected results is not justified, at least for well-centered pupils and Stiles–Crawford effects.

© 1998 Optical Society of America

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References

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    [CrossRef]
  2. 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]
  3. J. M. Enoch, V. Lakshminarayanan, “Retinal fiber optics,” in Visual Optics and Instrumentation, W. N. Charman, ed., Vol. 1 of Vision and Visual Dysfunction (Macmillan, London, 1991), pp. 280–309.
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. J. Tucker, W. N. Charman, “The depth-of-focus of the eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
    [CrossRef] [PubMed]
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    [CrossRef]
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  10. 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]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. G. Smith, D. A. Atchison, in The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), Chaps. 33 and 35.
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    [CrossRef] [PubMed]
  26. J. Macdonald, “The calculation of the optical transfer function,” Opt. Acta 18, 269–290 (1971).
    [CrossRef]
  27. G. Smith, “The spherical aberration of aphakic eyes cor-rected with intra-ocular lenses,” Clin. Exp. Optom. 75, 27–34 (1992).
    [CrossRef]
  28. F. W. Campbell, D. G. Green, “Optical and retinal fac-tors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  29. N. C. Strang, D. A. Atchison, R. L. Woods, “Predicting variations in visual performance caused by optical defects. 2,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 60–63.

1996 (1)

H. L. Liou, N. A. Brennan, “The prediction of spherical aberration with schematic eyes,” Ophthalmic Physiol. Opt. 16, 348–354 (1996).
[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]

G. Smith, “The spherical aberration of aphakic eyes cor-rected with intra-ocular lenses,” Clin. Exp. Optom. 75, 27–34 (1992).
[CrossRef]

1989 (1)

1988 (1)

1984 (1)

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

1980 (1)

1978 (1)

W. N. Charman, J. A. M. Jennings, H. Whitefoot, “The refraction of the eye in relation to spherical aberration and pupil size,” Br. J. Physiol. Opt. 32, 78–93 (1978).

1977 (1)

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-focus of the human eye for Snellen letters,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

1975 (1)

J. Tucker, W. N. Charman, “The depth-of-focus of the eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [PubMed]

1974 (2)

C. E. T. Krakau, “On the Stiles–Crawford phenomenon and resolution power,” Acta Ophthalmol. 52, 581–583 (1974).
[CrossRef]

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

1971 (2)

1965 (2)

H. Metcalf, “Stiles–Crawford apodization,” J. Opt. Soc. Am. 55, 72–74 (1965).
[CrossRef]

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

1962 (2)

1959 (1)

1958 (1)

1957 (1)

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[CrossRef]

1933 (1)

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Applegate, R. A.

Artal, P.

Atchison, D. A.

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

N. C. Strang, D. A. Atchison, R. L. Woods, “Predicting variations in visual performance caused by optical defects. 2,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 60–63.

G. Smith, D. A. Atchison, in The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), Chaps. 33 and 35.

Bescós, J.

Bradley, A.

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]

A. Bradley, L. N. Thibos, “Modeling off-axis vision. I: The optical effects of decentering visual targets or the eye’s entrance pupil,” in Vision Models for Target Detection and Recognition, E. Peli, ed. (World Scientific, Singapore, 1995), Chap. 12, pp. 313–337.

Brennan, N. A.

H. L. Liou, N. A. Brennan, “The prediction of spherical aberration with schematic eyes,” Ophthalmic Physiol. Opt. 16, 348–354 (1996).
[CrossRef] [PubMed]

Campbell, F. W.

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

G. Westheimer, F. W. Campbell, “Light distribution in the image formed by the living human eye,” J. Opt. Soc. Am. 52, 1040–1045 (1962).
[CrossRef] [PubMed]

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[CrossRef]

Carroll, J. P.

Charman, W. N.

W. N. Charman, J. A. M. Jennings, H. Whitefoot, “The refraction of the eye in relation to spherical aberration and pupil size,” Br. J. Physiol. Opt. 32, 78–93 (1978).

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-focus of the human eye for Snellen letters,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

J. Tucker, W. N. Charman, “The depth-of-focus of the eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [PubMed]

Crawford, B. H.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Enoch, J. M.

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] [PubMed]

J. M. Enoch, V. Lakshminarayanan, “Retinal fiber optics,” in Visual Optics and Instrumentation, W. N. Charman, ed., Vol. 1 of Vision and Visual Dysfunction (Macmillan, London, 1991), pp. 280–309.

Green, D. G.

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

Jennings, J. A. M.

W. N. Charman, J. A. M. Jennings, H. Whitefoot, “The refraction of the eye in relation to spherical aberration and pupil size,” Br. J. Physiol. Opt. 32, 78–93 (1978).

Krakau, C. E. T.

C. E. T. Krakau, “On the Stiles–Crawford phenomenon and resolution power,” Acta Ophthalmol. 52, 581–583 (1974).
[CrossRef]

Krauskopf, J.

Lakshminarayanan, V.

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]

J. M. Enoch, V. Lakshminarayanan, “Retinal fiber optics,” in Visual Optics and Instrumentation, W. N. Charman, ed., Vol. 1 of Vision and Visual Dysfunction (Macmillan, London, 1991), pp. 280–309.

Liou, H. L.

H. L. Liou, N. A. Brennan, “The prediction of spherical aberration with schematic eyes,” Ophthalmic Physiol. Opt. 16, 348–354 (1996).
[CrossRef] [PubMed]

Macdonald, J.

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

Martin, L. C.

L. C. Martin, Technical Optics, 2nd ed. (Pitman, London, 1961), Vol. 2.

Metcalf, H.

Mino, M.

Navarro, R.

Okano, Y.

Olsen, T.

T. Olsen, “On the Stiles–Crawford effect and ocular imagery,” Acta Ophthalmol. 71, 85–88 (1993).
[CrossRef]

Santamari´a, J.

Smith, G.

G. Smith, “The spherical aberration of aphakic eyes cor-rected with intra-ocular lenses,” Clin. Exp. Optom. 75, 27–34 (1992).
[CrossRef]

G. Smith, D. A. Atchison, in The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), Chaps. 33 and 35.

Stiles, W. S.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Strang, N. C.

N. C. Strang, D. A. Atchison, R. L. Woods, “Predicting variations in visual performance caused by optical defects. 2,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 60–63.

Thibos, L. N.

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]

A. Bradley, L. N. Thibos, “Modeling off-axis vision. I: The optical effects of decentering visual targets or the eye’s entrance pupil,” in Vision Models for Target Detection and Recognition, E. Peli, ed. (World Scientific, Singapore, 1995), Chap. 12, pp. 313–337.

Tucker, J.

J. Tucker, W. N. Charman, “The depth-of-focus of the eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [PubMed]

van Meeteren, A.

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

Westheimer, G.

Whitefoot, H.

W. N. Charman, J. A. M. Jennings, H. Whitefoot, “The refraction of the eye in relation to spherical aberration and pupil size,” Br. J. Physiol. Opt. 32, 78–93 (1978).

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-focus of the human eye for Snellen letters,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

Woods, R. L.

N. C. Strang, D. A. Atchison, R. L. Woods, “Predicting variations in visual performance caused by optical defects. 2,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 60–63.

Ye, M.

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]

Zhang, X.

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]

Acta Ophthalmol. (2)

C. E. T. Krakau, “On the Stiles–Crawford phenomenon and resolution power,” Acta Ophthalmol. 52, 581–583 (1974).
[CrossRef]

T. Olsen, “On the Stiles–Crawford effect and ocular imagery,” Acta Ophthalmol. 71, 85–88 (1993).
[CrossRef]

Am. J. Optom. Physiol. Opt. (1)

J. Tucker, W. N. Charman, “The depth-of-focus of the eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [PubMed]

Appl. Opt. (1)

Aust. J. Optom. (1)

D. A. Atchison, “Visual optics in man,” Aust. J. Optom. 67, 141–150 (1984).

Br. J. Physiol. Opt. (1)

W. N. Charman, J. A. M. Jennings, H. Whitefoot, “The refraction of the eye in relation to spherical aberration and pupil size,” Br. J. Physiol. Opt. 32, 78–93 (1978).

Clin. Exp. Optom. (1)

G. Smith, “The spherical aberration of aphakic eyes cor-rected with intra-ocular lenses,” Clin. Exp. Optom. 75, 27–34 (1992).
[CrossRef]

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (3)

J. Physiol. (London) (1)

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

Ophthalmic Physiol. Opt. (1)

H. L. Liou, N. A. Brennan, “The prediction of spherical aberration with schematic eyes,” Ophthalmic Physiol. Opt. 16, 348–354 (1996).
[CrossRef] [PubMed]

Opt. Acta (4)

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

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-focus of the human eye for Snellen letters,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
[CrossRef]

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Vision Res. (1)

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]

Other (5)

J. M. Enoch, V. Lakshminarayanan, “Retinal fiber optics,” in Visual Optics and Instrumentation, W. N. Charman, ed., Vol. 1 of Vision and Visual Dysfunction (Macmillan, London, 1991), pp. 280–309.

L. C. Martin, Technical Optics, 2nd ed. (Pitman, London, 1961), Vol. 2.

A. Bradley, L. N. Thibos, “Modeling off-axis vision. I: The optical effects of decentering visual targets or the eye’s entrance pupil,” in Vision Models for Target Detection and Recognition, E. Peli, ed. (World Scientific, Singapore, 1995), Chap. 12, pp. 313–337.

N. C. Strang, D. A. Atchison, R. L. Woods, “Predicting variations in visual performance caused by optical defects. 2,” in Vision Science and Its Applications, Vol. 1 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 60–63.

G. Smith, D. A. Atchison, in The Eye and Visual Optical Instruments (Cambridge U. Press, New York, 1997), Chaps. 33 and 35.

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Figures (8)

Fig. 1
Fig. 1

Refraction (defocus) that produces the maximum modulation transfer for various spatial frequencies in the presence of 1-D spherical aberration at the edge of a 6-mm-diameter pupil. This is shown for no Stiles–Crawford effect (pe=0 mm-2) and for Stiles–Crawford effect (pe=0.17 mm-2). The arrows indicate refraction for 20 cycles per degree (c/deg).

Fig. 2
Fig. 2

Strehl intensity ratio as a function of refraction (defocus) for various levels of defocus in the presence of 1-D spherical aberration at the edge of a 6-mm-diameter pupil. This is shown for no Stiles–Crawford effect (pe=0 mm-2) and for Stiles–Crawford effect (pe=0.17 mm-2). The arrows indicate certain peaks.

Fig. 3
Fig. 3

MTF’s for in-focus optics, with and without 1-D primary spherical aberration at the edge of a 6-mm-diameter pupil. This is shown for no Stiles–Crawford effect (pe=0 mm-2) and for Stiles–Crawford effect (pe=0.17 mm-2).

Fig. 4
Fig. 4

Point-spread functions for in-focus optics, with and without 1-D primary spherical aberration at the edge of a 6-mm-diameter pupil. This is shown for no Stiles–Crawford effect (pe=0 mm-2) and for Stiles–Crawford effect (pe=0.17 mm-2). The point-spread functions have been normalized to the peak of the relevant in-focus and aberration-free, but Stiles–Crawford-influenced, point-spread function.

Fig. 5
Fig. 5

Modulation transfer as a function of defocus for various spatial frequencies when there is no aberration. This is shown for no Stiles–Crawford effect (pe=0 mm-2) and for Stiles–Crawford effect (pe=0.17 mm-2).

Fig. 6
Fig. 6

Modulation transfer as a function of defocus for various spatial frequencies when there is +1-D primary spherical aberration at the edge of a 6-mm-diameter pupil. This is shown for no Stiles–Crawford effect (pe=0 mm-2) and for Stiles–Crawford effect (pe=0.17 mm-2).

Fig. 7
Fig. 7

MTF’s for -2-D defocus combined with 1-D primary spherical aberration at the edge of a 6-mm-diameter pupil. This is shown for no Stiles–Crawford effect (pe=0 mm-2) and for Stiles–Crawford effect (pe=0.17 mm-2). The -2-D defocus is relative to the defocus that gives the maximum modulation transfer at 20 c/deg; the actual levels are -2.33 D (pe=0 mm-2) and -2.28 D (pe=0.17 mm-2).

Fig. 8
Fig. 8

MTF’s for +2-D defocus combined with 1-D primary spherical aberration at the edge of a 6-mm-diameter pupil. This is shown for no Stiles–Crawford effect (pe=0 mm-2) and for Stiles–Crawford effect (pe=0.17 mm-2). The +2-D defocus is relative to the defocus that gives the maximum modulation transfer at 20 c/deg; the actual levels are +1.67 D (pe=0 mm-2) and +1.72 D (pe=0.17 mm-2).

Equations (26)

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

10-p10R2,
exp(-peR2),
p10=pe/ln(10).
R=0ρ2π exp(-peR2)RdR/(πρ2)=[1-exp(-peρ2)]/(peρ2).
ρeff={[1-exp(-peρ2)]/pe}1/2.
Deff=2{[1-exp(-peD2/4)]/pe}1/2.
f(X, Y)=A(X, Y)exp[i2πW(X, Y)/λ].
A(X, Y)=exp[-(pe/2)(X2+Y2)]=exp[-(pe/2)R2].
T(X, Y)=1-r2,
RE=-2w40(ρ)R2/ρ4,
W40=w40/ρ4
RE(R)=-2W40R2.
RE(ρ)=-2W40ρ2.
LSA(ρ)=4W40ρ2.
RE(ρ)=-LSA(ρ)/2.
RE(ρ)=-(2/3)LSA(ρ).
W(R)=W20R2+W40R4,
var(W)=var(W20R2+W40R4)=var(W20R2)+var(W40R4)+2 Cov(W20R2, W40R4)=W202 var(R2)+W402 var(R4)+2W20W40[E(R6)-E(R2)E(R4)],
var(W)=AW202+BW20W40+C(W40)2,
A=var(R2),
B=2 Cov(R2, R4)=2[E(R6)-E(R2)E(R4)],
C=var(R4).
d var(W)/dW20=2AW20+BW40=0,
W20=-BW40/2A=-W40 Cov(R2, R4)/var(R2).
E(Rn)=R=0ρ2πR exp(-peR2)RndR/R=0ρ2πR exp(-peR2)dR,
RE=2W20.

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