Abstract

Monochromatic aberrations that exist in the human eye will cause differences in the appearance of the point-spread function (PSF) depending on whether there is positive or negative defocus. We establish whether it is possible to use these differences in the PSF to distinguish the direction of defocus. The monochromatic aberrations of eight subjects were measured with a Hartmann–Shack wave-front sensor. Subjects also performed a forced-choice psychophysical task in which they decided whether a blurred target was defocused in front of or behind the retina. The optical system for the psychophysical task was designed to isolate the blur due to monochromatic aberrations as the only odd-error cue to the direction of defocus. Shack–Hartmann measurements showed that monochromatic aberrations increase as the pupil size increases. On average, the correct/incorrect responses for discriminating differences in the PSF for different directions of defocus were 54/46 for a 1-mm pupil and 83/17 for a 5-mm pupil, representing more than an eight-fold increase in discriminability. This discriminability extended for large amounts of defocus and also for more complex targets, such as letters. Sensitivity to the differences in the PSF for different directions of defocus increased as monochromatic aberrations increased, particularly for the even-order aberrations, which give rise to an odd-error focus cue. It was found that the ability to discriminate PSFs for different directions of defocus varied among individuals but, in general, depended on the magnitude of monochromatic aberrations.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. F. Schaeffel, D. Troilo, J. Wallman, H. C. Howland, “Developing eyes that lack accommodation grow to compensate for imposed defocus,” Visual Neurosci. 4, 177–183 (1990).
    [CrossRef]
  14. T. Park, J. A. Winawer, J. Wallman, “In a matter of minutes the eye can know which way to grow,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 55 (2001).
  15. 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]
  16. W. N. Charman, J. Tucker, “Accommodation and color,” J. Opt. Soc. Am. 68, 459–471 (1978).
    [CrossRef] [PubMed]
  17. G. Walsh, W. N. Charman, “The effect of defocus on the contrast and phase of the retinal image of a sinusoidal grating,” Ophthalmic Physiol. Opt. 9, 398–404 (1989).
    [CrossRef] [PubMed]
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    [CrossRef]
  19. W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990).
  20. F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
    [CrossRef]
  21. M. C. W. Campbell, D. Priest, J. J. Hunter, “The importance of monochromatic aberrations to detecting defocus in retina images,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 98 (2001).

2001

T. Park, J. A. Winawer, J. Wallman, “In a matter of minutes the eye can know which way to grow,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 55 (2001).

M. C. W. Campbell, D. Priest, J. J. Hunter, “The importance of monochromatic aberrations to detecting defocus in retina images,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 98 (2001).

1998

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

R. A. Applegate, P. Artal, eds., feature topic, “Measurement and Correction of the Optical Aberrations of the Human eye,” J. Opt. Soc. Am. A 15, 2445–2596 (1998).
[CrossRef]

1997

P. B. Kruger, S. Mathews, M. Katz, K. R. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

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

1994

1993

C. F. Wildsoet, H. C. Howland, S. Falconer, K. Dick, “Chromatic aberration and accommodation:  their role in emmetropization in the chick,” Vision Res. 33, 1593–1603 (1993).
[CrossRef] [PubMed]

1990

F. Schaeffel, D. Troilo, J. Wallman, H. C. Howland, “Developing eyes that lack accommodation grow to compensate for imposed defocus,” Visual Neurosci. 4, 177–183 (1990).
[CrossRef]

1989

G. Walsh, W. N. Charman, “The effect of defocus on the contrast and phase of the retinal image of a sinusoidal grating,” Ophthalmic Physiol. Opt. 9, 398–404 (1989).
[CrossRef] [PubMed]

1988

F. Schaeffel, A. Glasser, H. C. Howland, “Accommodation, refractive error and eye growth in chickens,” Vision Res. 28, 639–657 (1988).
[CrossRef] [PubMed]

1986

P. B. Kruger, J. Pola, “Stimuli for accommodation: blur, chromatic aberration and size,” Vision Res. 26, 957–971 (1986).
[CrossRef]

1978

1977

1959

1951

E. F. Fincham, “The accommodation reflex and its stimulus,” Br. J. Ophthamol. 35, 381–393 (1951).
[CrossRef]

1801

T. Young, “On the mechanism of the eye,” Philos. Trans. R. Soc. London 91, 23–88 (1801).
[CrossRef]

Aggarwala, K. R.

P. B. Kruger, S. Mathews, M. Katz, K. R. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Bille, J. F.

Campbell, F. W.

Campbell, M. C. W.

M. C. W. Campbell, D. Priest, J. J. Hunter, “The importance of monochromatic aberrations to detecting defocus in retina images,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 98 (2001).

Charman, W. N.

G. Walsh, W. N. Charman, “The effect of defocus on the contrast and phase of the retinal image of a sinusoidal grating,” Ophthalmic Physiol. Opt. 9, 398–404 (1989).
[CrossRef] [PubMed]

W. N. Charman, J. Tucker, “Accommodation and color,” J. Opt. Soc. Am. 68, 459–471 (1978).
[CrossRef] [PubMed]

Dick, K.

C. F. Wildsoet, H. C. Howland, S. Falconer, K. Dick, “Chromatic aberration and accommodation:  their role in emmetropization in the chick,” Vision Res. 33, 1593–1603 (1993).
[CrossRef] [PubMed]

Falconer, S.

C. F. Wildsoet, H. C. Howland, S. Falconer, K. Dick, “Chromatic aberration and accommodation:  their role in emmetropization in the chick,” Vision Res. 33, 1593–1603 (1993).
[CrossRef] [PubMed]

Fincham, E. F.

E. F. Fincham, “The accommodation reflex and its stimulus,” Br. J. Ophthamol. 35, 381–393 (1951).
[CrossRef]

Glasser, A.

F. Schaeffel, A. Glasser, H. C. Howland, “Accommodation, refractive error and eye growth in chickens,” Vision Res. 28, 639–657 (1988).
[CrossRef] [PubMed]

Goelz, S.

Grimm, B.

Habak, C.

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

Helmholtz, H.

H. Helmholtz, Helmholtz’s Treatise on Physiological Optics, J. P. C. Southall, ed. (Optical Society of America, Rochester, N.Y., 1924).

Howland, B.

Howland, H. C.

C. F. Wildsoet, H. C. Howland, S. Falconer, K. Dick, “Chromatic aberration and accommodation:  their role in emmetropization in the chick,” Vision Res. 33, 1593–1603 (1993).
[CrossRef] [PubMed]

F. Schaeffel, D. Troilo, J. Wallman, H. C. Howland, “Developing eyes that lack accommodation grow to compensate for imposed defocus,” Visual Neurosci. 4, 177–183 (1990).
[CrossRef]

F. Schaeffel, A. Glasser, H. C. Howland, “Accommodation, refractive error and eye growth in chickens,” Vision Res. 28, 639–657 (1988).
[CrossRef] [PubMed]

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]

Hunter, J. J.

M. C. W. Campbell, D. Priest, J. J. Hunter, “The importance of monochromatic aberrations to detecting defocus in retina images,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 98 (2001).

Katz, M.

P. B. Kruger, S. Mathews, M. Katz, K. R. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Kruger, P. B.

P. B. Kruger, S. Mathews, M. Katz, K. R. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

P. B. Kruger, J. Pola, “Stimuli for accommodation: blur, chromatic aberration and size,” Vision Res. 26, 957–971 (1986).
[CrossRef]

Liang, J.

Losada, M. A.

R. Navarro, M. A. Losada, “On the true shape of the optical point spread function in the human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 66–69.

Mathews, S.

P. B. Kruger, S. Mathews, M. Katz, K. R. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Navarro, R.

R. Navarro, M. A. Losada, “On the true shape of the optical point spread function in the human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 66–69.

Nowbotsing, S.

P. B. Kruger, S. Mathews, M. Katz, K. R. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

Park, T.

T. Park, J. A. Winawer, J. Wallman, “In a matter of minutes the eye can know which way to grow,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 55 (2001).

Pola, J.

P. B. Kruger, J. Pola, “Stimuli for accommodation: blur, chromatic aberration and size,” Vision Res. 26, 957–971 (1986).
[CrossRef]

Priest, D.

M. C. W. Campbell, D. Priest, J. J. Hunter, “The importance of monochromatic aberrations to detecting defocus in retina images,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 98 (2001).

Schaeffel, F.

F. Schaeffel, D. Troilo, J. Wallman, H. C. Howland, “Developing eyes that lack accommodation grow to compensate for imposed defocus,” Visual Neurosci. 4, 177–183 (1990).
[CrossRef]

F. Schaeffel, A. Glasser, H. C. Howland, “Accommodation, refractive error and eye growth in chickens,” Vision Res. 28, 639–657 (1988).
[CrossRef] [PubMed]

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990).

Troilo, D.

F. Schaeffel, D. Troilo, J. Wallman, H. C. Howland, “Developing eyes that lack accommodation grow to compensate for imposed defocus,” Visual Neurosci. 4, 177–183 (1990).
[CrossRef]

Tscherning, M.

M. Tscherning, Physiologic Optics, C. Weiland, ed., 4th ed. (Keystone, Philadelphia, Pa., 1924).

Tucker, J.

Wallman, J.

T. Park, J. A. Winawer, J. Wallman, “In a matter of minutes the eye can know which way to grow,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 55 (2001).

F. Schaeffel, D. Troilo, J. Wallman, H. C. Howland, “Developing eyes that lack accommodation grow to compensate for imposed defocus,” Visual Neurosci. 4, 177–183 (1990).
[CrossRef]

Walsh, G.

G. Walsh, W. N. Charman, “The effect of defocus on the contrast and phase of the retinal image of a sinusoidal grating,” Ophthalmic Physiol. Opt. 9, 398–404 (1989).
[CrossRef] [PubMed]

Westheimer, G.

Wildsoet, C. F.

C. F. Wildsoet, H. C. Howland, S. Falconer, K. Dick, “Chromatic aberration and accommodation:  their role in emmetropization in the chick,” Vision Res. 33, 1593–1603 (1993).
[CrossRef] [PubMed]

Wilkinson, F.

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

Williams, D. R.

Wilson, H. R.

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

Winawer, J. A.

T. Park, J. A. Winawer, J. Wallman, “In a matter of minutes the eye can know which way to grow,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 55 (2001).

Young, T.

T. Young, “On the mechanism of the eye,” Philos. Trans. R. Soc. London 91, 23–88 (1801).
[CrossRef]

Br. J. Ophthamol.

E. F. Fincham, “The accommodation reflex and its stimulus,” Br. J. Ophthamol. 35, 381–393 (1951).
[CrossRef]

Invest. Ophthalmol. Visual Sci. Suppl.

T. Park, J. A. Winawer, J. Wallman, “In a matter of minutes the eye can know which way to grow,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 55 (2001).

M. C. W. Campbell, D. Priest, J. J. Hunter, “The importance of monochromatic aberrations to detecting defocus in retina images,” Invest. Ophthalmol. Visual Sci. Suppl. 42, 98 (2001).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Ophthalmic Physiol. Opt.

G. Walsh, W. N. Charman, “The effect of defocus on the contrast and phase of the retinal image of a sinusoidal grating,” Ophthalmic Physiol. Opt. 9, 398–404 (1989).
[CrossRef] [PubMed]

Philos. Trans. R. Soc. London

T. Young, “On the mechanism of the eye,” Philos. Trans. R. Soc. London 91, 23–88 (1801).
[CrossRef]

Vision Res.

P. B. Kruger, J. Pola, “Stimuli for accommodation: blur, chromatic aberration and size,” Vision Res. 26, 957–971 (1986).
[CrossRef]

P. B. Kruger, S. Mathews, M. Katz, K. R. Aggarwala, S. Nowbotsing, “Accommodation without feedback suggests directional signals specify ocular focus,” Vision Res. 37, 2511–2526 (1997).
[CrossRef] [PubMed]

F. Schaeffel, A. Glasser, H. C. Howland, “Accommodation, refractive error and eye growth in chickens,” Vision Res. 28, 639–657 (1988).
[CrossRef] [PubMed]

C. F. Wildsoet, H. C. Howland, S. Falconer, K. Dick, “Chromatic aberration and accommodation:  their role in emmetropization in the chick,” Vision Res. 33, 1593–1603 (1993).
[CrossRef] [PubMed]

F. Wilkinson, H. R. Wilson, C. Habak, “Detection and recognition of radial frequency patterns,” Vision Res. 38, 3555–3568 (1998).
[CrossRef]

Visual Neurosci.

F. Schaeffel, D. Troilo, J. Wallman, H. C. Howland, “Developing eyes that lack accommodation grow to compensate for imposed defocus,” Visual Neurosci. 4, 177–183 (1990).
[CrossRef]

Other

M. Tscherning, Physiologic Optics, C. Weiland, ed., 4th ed. (Keystone, Philadelphia, Pa., 1924).

R. Navarro, M. A. Losada, “On the true shape of the optical point spread function in the human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 66–69.

H. Helmholtz, Helmholtz’s Treatise on Physiological Optics, J. P. C. Southall, ed. (Optical Society of America, Rochester, N.Y., 1924).

W. J. Smith, Modern Optical Engineering, 2nd ed. (McGraw-Hill, New York, 1990).

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Figures (10)

Fig. 1
Fig. 1

Simulated PSFs for subject SN, based on his monochromatic aberrations, are shown for a 1-mm and 5-mm pupil. The RMS aberration for all terms except defocus is shown for both pupil sizes. The series of images simulates what this subject would perceive when looking at a point source. The amount of defocus that was used for the simulated defocus is listed below each PSF. The task of the subject was to distinguish between points that were defocused by the same amount but with opposite sign. With this figure it is possible to appreciate the difficulty of distinguishing the sign of defocus with a pupil size of 1 mm, but it is possible to distinguish shape differences with a 5-mm pupil.

Fig. 2
Fig. 2

Schematic of the apparatus. A Badal optometer combined with a telescope was used to present the point source. An adjustable iris diaphragm, ID, was placed at the focal point of a 20-D achromatic lens, L1. The iris diaphragm was also conjugate to the pupil of the subject’s eye through two 10-D achromatic lenses, L2 and L3. A neutral density filter, NDF, was placed in the path to control the luminance. The point target was defocused by changing the location of the spatial filter, SF, on an optical rail. The subject’s alignment was maintained by a bite bar.

Fig. 3
Fig. 3

RMS as a function of pupil size for eight subjects. The RMS was calculated from the wave aberration of the eye measured with the Shack–Hartmann wave-front sensor. A tenth-order Zernike polynomial was fitted to each pupil size (based on the original wave-front measurement above 6 mm) before calculation of the RMS. This was done so that we could remove the residual defocus term for each pupil size.

Fig. 4
Fig. 4

Complete data for one subject, SN. We plotted the percentage of stimuli that were selected as myopic for each blur condition. For a 1-mm pupil, SN had trouble deciding on the sign of the blur. As the pupil size increased, the aberrations increased and the ability to select the correct sign increased. The error bars are the standard deviations of each value computed from the three separate measurements.

Fig. 5
Fig. 5

Discriminability is defined as the fraction of times above chance levels that the subject chose the correct direction of the sign of defocus for a given amount of blur. Discriminability is plotted here for subject SN and is the best for the largest pupil diameter. Error bars are ±1 standard deviation.

Fig. 6
Fig. 6

Average discriminability calculated from all blur sizes on either side of best focus. The plot shows the average discriminability as a function of pupil size for all eight subjects in the experiment. The response varied between subjects, but in all cases the discriminability increased monotonically with pupil size.

Fig. 7
Fig. 7

Average discriminability for 20/20-sized letters rather than a point source. In this plot the average discriminability is calculated from all blur sizes on either side of best focus. The plot shows the average discriminability as a function of pupil size for all five subjects in the experiment. The response varied between subjects, but in all cases but one (GQ) the discriminability increased monotonically with pupil size.

Fig. 8
Fig. 8

Discriminability versus RMS wave aberration. The discriminability increases with wave-front error but is weakly dependent on this linear relationship. The relationship between aberrations and discriminability is more complicated. The vertical dashed line indicates the RMS values below which the optics are considered to be diffraction limited.

Fig. 9
Fig. 9

PSFs for subject SN with -0.5 and +0.5 D of defocus, calculated with (a) even-order aberrations, which give rise to an odd-error focus cue, and (b) odd-order aberrations, which give rise to an even-error focus cue (or no focus cue).

Fig. 10
Fig. 10

Discriminability versus RMS aberrations for the even-order aberrations. The even-order aberrations give rise to an odd-error focus cue, and therefore the discriminability is more dependent on these terms. The vertical dashed line indicates the RMS value below which the optics are considered to be diffraction limited for 632-nm light.

Tables (1)

Tables Icon

Table 1 Summary of Discriminability Values of six Subjects for a 5-mm Pupil over an Extended Dioptric Range

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