Abstract

Previous optical modeling of the human eye with large pupils has predicted a larger impact of defocus on the human contrast sensitivity function and modulation transfer function than is observed experimentally. Theory predicts that aberrations and the Stiles–Crawford effect (SCE) should both lead to increased depth of focus, resulting in higher contrast sensitivities and veridical (not phase-reversed) perception over a larger range of spatial frequencies in defocused retinal images. Using a wave optics model, we examine these predictions quantitatively and compare them with psychophysical experiments that measure the effect of defocus on contrast sensitivity and perceived phase reversals. We find that SCE apodization has its biggest effect on defocused image quality when defocus and spherical aberration have the same sign. A model including typical amounts of spherical aberration and pupil apodization provides a dramatically improved prediction of the effects of defocus on contrast sensitivity with large pupils. The SCE can significantly improve defocused image quality and defocused vision, particularly for tasks that require veridical phase perception.

© 1999 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1998 (4)

1997 (2)

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

J. Liang, D. R. Williams, “Aberrations and retinal image quality of the normal eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
[CrossRef]

1996 (1)

R. L. Woods, A. Bradley, D. A. Atchison, “Consequences of monocular diplopia for the contrast sensitivity function,” Vision Res. 36, 3587–3596 (1996).
[CrossRef] [PubMed]

1995 (1)

A. Plakisti, W. N. Charman, “Comparison of the depth of focus with the naked eye and with three types of presbyopic contact lens correction,” J. Br. Contact Lens Assoc. 18, 119–125 (1995).
[CrossRef]

1994 (1)

J. Rovamo, J. Mustonen, R. Nasanen, “Two simple psychophysical methods for determining the optical modulation transfer function of the human eye,” Vision Res. 34, 2493–2502 (1994).
[CrossRef] [PubMed]

1993 (3)

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

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

A. Bradley, H. A. Rahman, P. S. Soni, X. Zhang, “Effects of target distance and pupil size on letter contrast sensitivity with simultaneous vision bifocal contact lenses,” Optom. Vision Sci. 70, 476–481 (1993).
[CrossRef]

1992 (1)

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

1990 (2)

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

F. Thorn, F. Schwartz, “Effects of dioptric blur on Snellen and grating acuity,” Optom. Vision Sci. 67, 3–7 (1990).
[CrossRef]

1989 (1)

1987 (3)

1984 (2)

1982 (1)

G. Smith, “Ocular defocus, spurious resolution and contrast reversal,” Ophthalmic Physiol. Opt. 2, 5–23 (1982).
[PubMed]

1980 (2)

1979 (1)

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

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 (2)

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

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 67, 1508–1518 (1977).
[CrossRef] [PubMed]

1975 (1)

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

1974 (2)

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

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

1971 (1)

1967 (1)

1965 (3)

1964 (1)

P. Jacquinot, B. Roizen-Dossier, “Apodization,” Prog. Opt. 3, 31–184 (1964).

1961 (1)

H. S. Smirnov, “Measurement of wave aberration in the human eye,” Biophysics 6, 687–703 (1961).

1957 (1)

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

1955 (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Applegate, R. A.

Artal, P.

Atchison, D. A.

Banks, M. S.

M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[CrossRef] [PubMed]

Bennet, P. J.

M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[CrossRef] [PubMed]

Berrio, E.

Bour, L. J.

Bradley, A.

D. A. Atchison, R. L. Woods, A. Bradley, “Predicting the effects of optical defocus on human contrast sensitivity,” J. Opt. Soc. Am. A 15, 2536–2544 (1998).
[CrossRef]

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

R. L. Woods, A. Bradley, D. A. Atchison, “Consequences of monocular diplopia for the contrast sensitivity function,” Vision Res. 36, 3587–3596 (1996).
[CrossRef] [PubMed]

A. Bradley, H. A. Rahman, P. S. Soni, X. Zhang, “Effects of target distance and pupil size on letter contrast sensitivity with simultaneous vision bifocal contact lenses,” Optom. Vision Sci. 70, 476–481 (1993).
[CrossRef]

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

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Campbell, F. W.

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 4, 851–863 (1987).
[CrossRef] [PubMed]

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

D. G. Green, F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,” J. Opt. Soc. Am. 55, 1154–1157 (1965).
[CrossRef]

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

Carroll, J. P.

Charman, W. N.

A. Plakisti, W. N. Charman, “Comparison of the depth of focus with the naked eye and with three types of presbyopic contact lens correction,” J. Br. Contact Lens Assoc. 18, 119–125 (1995).
[CrossRef]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

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 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 human eye for Snellen letters,” Am. J. Optom. Physiol. Opt. 52, 3–21 (1975).
[CrossRef] [PubMed]

Geisler, W. S.

M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[CrossRef] [PubMed]

Green, D. G.

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

D. G. Green, F. W. Campbell, “Effect of focus on the visual response to a sinusoidally modulated spatial stimulus,” J. Opt. Soc. Am. 55, 1154–1157 (1965).
[CrossRef]

Gubisch, R. W.

Hopkins, H. H.

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–103 (1955).
[CrossRef]

Howarth, P. A.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Howland, B.

Howland, H. C.

Iglesias, I.

Jacquinot, P.

P. Jacquinot, B. Roizen-Dossier, “Apodization,” Prog. Opt. 3, 31–184 (1964).

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).

Joblin, A.

Krakau, C. E. T.

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

Lakshminarayanan, V.

Legge, G. E.

Liang, J.

Martin, L. C.

L. C. Martin, Technical Optics: A Revised and Enlarged Edition of “An Introduction to Applied Optics” (Pitman, London, 1961), Vol. 2.

Metcalf, H.

Mino, M.

Mullen, K. T.

Mustonen, J.

J. Rovamo, J. Mustonen, R. Nasanen, “Two simple psychophysical methods for determining the optical modulation transfer function of the human eye,” Vision Res. 34, 2493–2502 (1994).
[CrossRef] [PubMed]

Nasanen, R.

J. Rovamo, J. Mustonen, R. Nasanen, “Two simple psychophysical methods for determining the optical modulation transfer function of the human eye,” Vision Res. 34, 2493–2502 (1994).
[CrossRef] [PubMed]

Okano, Y.

Olsen, T.

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

Plakisti, A.

A. Plakisti, W. N. Charman, “Comparison of the depth of focus with the naked eye and with three types of presbyopic contact lens correction,” J. Br. Contact Lens Assoc. 18, 119–125 (1995).
[CrossRef]

Rahman, H. A.

A. Bradley, H. A. Rahman, P. S. Soni, X. Zhang, “Effects of target distance and pupil size on letter contrast sensitivity with simultaneous vision bifocal contact lenses,” Optom. Vision Sci. 70, 476–481 (1993).
[CrossRef]

Roizen-Dossier, B.

P. Jacquinot, B. Roizen-Dossier, “Apodization,” Prog. Opt. 3, 31–184 (1964).

Rovamo, J.

J. Rovamo, J. Mustonen, R. Nasanen, “Two simple psychophysical methods for determining the optical modulation transfer function of the human eye,” Vision Res. 34, 2493–2502 (1994).
[CrossRef] [PubMed]

Schwartz, F.

F. Thorn, F. Schwartz, “Effects of dioptric blur on Snellen and grating acuity,” Optom. Vision Sci. 67, 3–7 (1990).
[CrossRef]

Smirnov, H. S.

H. S. Smirnov, “Measurement of wave aberration in the human eye,” Biophysics 6, 687–703 (1961).

Smith, G.

Soni, P. S.

A. Bradley, H. A. Rahman, P. S. Soni, X. Zhang, “Effects of target distance and pupil size on letter contrast sensitivity with simultaneous vision bifocal contact lenses,” Optom. Vision Sci. 70, 476–481 (1993).
[CrossRef]

Still, D. L.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

Thibos, L. N.

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

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

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[CrossRef] [PubMed]

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]

Thorn, F.

F. Thorn, F. Schwartz, “Effects of dioptric blur on Snellen and grating acuity,” Optom. Vision Sci. 67, 3–7 (1990).
[CrossRef]

Tucker, J.

J. Tucker, W. N. Charman, “The depth-of-focus of the human 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]

Walsh, 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 depth of focus of the human eye for Snellen letters,” Opt. Acta 24, 1211–1216 (1977).
[CrossRef]

Williams, D. R.

Woo, G. C.

Woods, R. L.

D. A. Atchison, R. L. Woods, A. Bradley, “Predicting the effects of optical defocus on human contrast sensitivity,” J. Opt. Soc. Am. A 15, 2536–2544 (1998).
[CrossRef]

R. L. Woods, A. Bradley, D. A. Atchison, “Consequences of monocular diplopia for the contrast sensitivity function,” Vision Res. 36, 3587–3596 (1996).
[CrossRef] [PubMed]

Ye, M.

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

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

Zhang, X.

L. N. Thibos, M. Ye, X. Zhang, A. Bradley, “Spherical aberration of the reduced schematic eye with elliptical refracting surface,” Optom. Vision Sci. 74, 548–556 (1997).
[CrossRef]

A. Bradley, H. A. Rahman, P. S. Soni, X. Zhang, “Effects of target distance and pupil size on letter contrast sensitivity with simultaneous vision bifocal contact lenses,” Optom. Vision Sci. 70, 476–481 (1993).
[CrossRef]

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

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[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 human 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).

Biophysics (1)

H. S. Smirnov, “Measurement of wave aberration in the human eye,” Biophysics 6, 687–703 (1961).

Br. J. Physiol. Opt. (2)

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

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).

J. Br. Contact Lens Assoc. (1)

A. Plakisti, W. N. Charman, “Comparison of the depth of focus with the naked eye and with three types of presbyopic contact lens correction,” J. Br. Contact Lens Assoc. 18, 119–125 (1995).
[CrossRef]

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (10)

J. Liang, D. R. Williams, “Aberrations and retinal image quality of the normal eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
[CrossRef]

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

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 4, 851–863 (1987).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Modulation transferred to the image of a 2.7-c/deg grating plotted as a function of defocus from the paraxial focus for a model eye with an 8-mm entrance pupil and 580-nm light. Solid and dashed curves describe image modulation for an aberration-free eye and one with +1.5 D of spherical aberration, respectively. Thin curves are for uniform pupils (no SCE), and thick curves are for eyes with SCE apodization. All curves are least-squares fits to the computed data.

Fig. 2
Fig. 2

MTF’s for the four conditions shown in Fig. 1: no spherical aberration or SCE (thin solid curve), spherical aberration (+1.5 D) but no SCE (thin dashed curve), no aberration with SCE (thick solid curve), and spherical aberration with SCE (thick dashed curve). All data are calculated for 580-nm light, an 8-mm entrance pupil, and +2 D of defocus.

Fig. 3
Fig. 3

MTF’s computed for the aberration-free uniform-pupil model (dashed curves) and for the aberrated and apodized model (solid curves) for 556-nm light. Each plot contains the reference MTF for the focused but aberrated and apodized eye with a 2-mm pupil (top line). Pupil size and level of defocus are given in each plot for the defocused MTF’s.

Fig. 4
Fig. 4

CSF’s (A) and phase perception (B) are plotted for a model eye with a 2-mm-diameter entrance pupil, 0.15 D of spherical aberration, and a SCE with a ρ10=0.046 for an object located 5° from the optical axis (lines). Experimentally measured focused (open circles) and +4 D defocused (filled circles) CSF’s are shown in plot A. Error bars represent ±1 standard deviation. It is not possible to measure CS less than 1.0; therefore, although the calculations can predict CS of less than 1.0 [see Eq. (3)], in effect the model predicts no measurable CS at these frequencies. Plot B shows the percentage of correct phase choices with +4 D of defocus (filled circles).

Fig. 5
Fig. 5

CSF’s (A) and phase perception (B) predictions (lines) are shown for a 7-mm entrance pupil and +2 D of defocus, +1.25 D of LSA, a 5° eccentric target, and an apodized (ρ10=0.046) pupil. The best-focus reference CSF obtained with the 2-mm pupil is denoted with open circles, and the +2-D defocused CSF obtained with a 7-mm pupil is denoted with filled circles (plot A). Plot B shows the predicted (line) and experimentally measured (filled circles) phase perception data.

Fig. 6
Fig. 6

Same as Fig. 5, but for +3 D of defocus.

Equations (3)

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P(x, y)=A(x, y)exp[iW(x, y)],
A(x, y)=exp(-ρR2).
MTFaMTFb=CSFaCSFb,

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