Abstract

The modulation transfer function (MTF) of human eyes for different pupil sizes was measured in a group of normal young subjects by use of a double-pass method. Measurements were carried out in the fovea, with monochromatic red light, paralyzed accommodation, artificial pupils, and optimum spherical refraction in each subject. For each pupil size both the averaged MTF and the intersubject variability were calculated. MTF’s were approximated by the sum of two exponential functions. This three-parameter function provides a better approximation to our ocular MTF’s than do most of the previous parametric models (usually one exponential), especially at intermediate and high spatial frequencies. Further curve fitting of the parameters allowed us to obtain a general expression for the mean MTF as a function of both pupil diameter and normalized spatial frequency. This equation summarizes our estimates of the average monochromatic retinal image quality of the human eye for any pupil diameter with good accuracy and in a compact way, which allows one to incorporate the eye’s image quality easily in any particular study.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. N. Charman, “Optics of the human eye,” in Visual Optics and Instrumentation, Vol. 1 of Vision and Visual Dysfunction, J. R. Cronly-Dillon, ed. (Macmillan, London, 1991), pp. 1–26.
  2. P. Artal, R. Navarro, “Simultaneous measurement of two-point-spread functions at different locations across the human fovea,” Appl. Opt. 31, 3646–3656 (1992).
    [CrossRef] [PubMed]
  3. P. Artal, R. Navarro, D. H. Brainard, S. J. Galvin, D. R. Williams, “Off-axis optical quality of the eye and retinal sampling,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 33, 3241 (1992).
  4. F. W. Campbell, R. W. Gubisch, “Optical image quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).
  5. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the eye,” J. Opt. Soc. Am. A 1, 321–328 (1984).
    [CrossRef]
  6. J. Santamaría, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
    [CrossRef]
  7. M. F. Flamant, “Etude de la repartition de la lumière dans l’image retinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).
  8. H. Kreuger, E. A. Moser, “On the approximation of the modulation transfer function (MTF) by analytical functions,” Vision Res. 13, 493–494 (1973).
    [CrossRef]
  9. R. J. Deeley, N. Drasdo, W. N. Charman, “A simple parametric model of the human ocular modulation transfer function,” Ophthalmol. Physiol. Opt. 11, 91–93 (1991).
    [CrossRef]
  10. R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
    [CrossRef] [PubMed]
  11. G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
    [CrossRef] [PubMed]
  12. A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic method for the dynamic study of image formation by the human eye. Microfluctuations of accommodation,” J. Opt. 12, 123–128 (1981).
    [CrossRef]
  13. P. Artal, M. Ferro, I. Miranda, R. Navarro, “Effects of aging in retinal image quality,” J. Opt. Soc. Am. A 10, 1657–1663 (1993).
    [CrossRef]
  14. P. Artal, “Calculations of two-dimensional foveal retinal images in real eyes,” J. Opt. Soc. Am. A 7, 1374–1381 (1990).
    [CrossRef]

1993 (2)

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[CrossRef] [PubMed]

P. Artal, M. Ferro, I. Miranda, R. Navarro, “Effects of aging in retinal image quality,” J. Opt. Soc. Am. A 10, 1657–1663 (1993).
[CrossRef]

1992 (2)

P. Artal, R. Navarro, “Simultaneous measurement of two-point-spread functions at different locations across the human fovea,” Appl. Opt. 31, 3646–3656 (1992).
[CrossRef] [PubMed]

P. Artal, R. Navarro, D. H. Brainard, S. J. Galvin, D. R. Williams, “Off-axis optical quality of the eye and retinal sampling,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 33, 3241 (1992).

1991 (1)

R. J. Deeley, N. Drasdo, W. N. Charman, “A simple parametric model of the human ocular modulation transfer function,” Ophthalmol. Physiol. Opt. 11, 91–93 (1991).
[CrossRef]

1990 (1)

1988 (1)

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

1987 (1)

1984 (1)

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the eye,” J. Opt. Soc. Am. A 1, 321–328 (1984).
[CrossRef]

1981 (1)

A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic method for the dynamic study of image formation by the human eye. Microfluctuations of accommodation,” J. Opt. 12, 123–128 (1981).
[CrossRef]

1973 (1)

H. Kreuger, E. A. Moser, “On the approximation of the modulation transfer function (MTF) by analytical functions,” Vision Res. 13, 493–494 (1973).
[CrossRef]

1966 (1)

F. W. Campbell, R. W. Gubisch, “Optical image quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

1955 (1)

M. F. Flamant, “Etude de la repartition de la lumière dans l’image retinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).

Arnulf, A.

A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic method for the dynamic study of image formation by the human eye. Microfluctuations of accommodation,” J. Opt. 12, 123–128 (1981).
[CrossRef]

Artal, P.

Bescós, J.

J. Santamaría, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
[CrossRef]

A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic method for the dynamic study of image formation by the human eye. Microfluctuations of accommodation,” J. Opt. 12, 123–128 (1981).
[CrossRef]

Brainard, D. H.

P. Artal, R. Navarro, D. H. Brainard, S. J. Galvin, D. R. Williams, “Off-axis optical quality of the eye and retinal sampling,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 33, 3241 (1992).

Campbell, F. W.

F. W. Campbell, R. W. Gubisch, “Optical image quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

Charman, W. N.

R. J. Deeley, N. Drasdo, W. N. Charman, “A simple parametric model of the human ocular modulation transfer function,” Ophthalmol. Physiol. Opt. 11, 91–93 (1991).
[CrossRef]

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the eye,” J. Opt. Soc. Am. A 1, 321–328 (1984).
[CrossRef]

W. N. Charman, “Optics of the human eye,” in Visual Optics and Instrumentation, Vol. 1 of Vision and Visual Dysfunction, J. R. Cronly-Dillon, ed. (Macmillan, London, 1991), pp. 1–26.

Deeley, R. J.

R. J. Deeley, N. Drasdo, W. N. Charman, “A simple parametric model of the human ocular modulation transfer function,” Ophthalmol. Physiol. Opt. 11, 91–93 (1991).
[CrossRef]

Drasdo, N.

R. J. Deeley, N. Drasdo, W. N. Charman, “A simple parametric model of the human ocular modulation transfer function,” Ophthalmol. Physiol. Opt. 11, 91–93 (1991).
[CrossRef]

Ferro, M.

P. Artal, M. Ferro, I. Miranda, R. Navarro, “Effects of aging in retinal image quality,” J. Opt. Soc. Am. A 10, 1657–1663 (1993).
[CrossRef]

Flamant, M. F.

M. F. Flamant, “Etude de la repartition de la lumière dans l’image retinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).

Galvin, S. J.

P. Artal, R. Navarro, D. H. Brainard, S. J. Galvin, D. R. Williams, “Off-axis optical quality of the eye and retinal sampling,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 33, 3241 (1992).

Gubisch, R. W.

F. W. Campbell, R. W. Gubisch, “Optical image quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

Howland, H. C.

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the eye,” J. Opt. Soc. Am. A 1, 321–328 (1984).
[CrossRef]

Kreuger, H.

H. Kreuger, E. A. Moser, “On the approximation of the modulation transfer function (MTF) by analytical functions,” Vision Res. 13, 493–494 (1973).
[CrossRef]

Miranda, I.

P. Artal, M. Ferro, I. Miranda, R. Navarro, “Effects of aging in retinal image quality,” J. Opt. Soc. Am. A 10, 1657–1663 (1993).
[CrossRef]

Moser, E. A.

H. Kreuger, E. A. Moser, “On the approximation of the modulation transfer function (MTF) by analytical functions,” Vision Res. 13, 493–494 (1973).
[CrossRef]

Navarro, R.

P. Artal, M. Ferro, I. Miranda, R. Navarro, “Effects of aging in retinal image quality,” J. Opt. Soc. Am. A 10, 1657–1663 (1993).
[CrossRef]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[CrossRef] [PubMed]

P. Artal, R. Navarro, “Simultaneous measurement of two-point-spread functions at different locations across the human fovea,” Appl. Opt. 31, 3646–3656 (1992).
[CrossRef] [PubMed]

P. Artal, R. Navarro, D. H. Brainard, S. J. Galvin, D. R. Williams, “Off-axis optical quality of the eye and retinal sampling,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 33, 3241 (1992).

Santamaría, J.

J. Santamaría, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
[CrossRef]

A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic method for the dynamic study of image formation by the human eye. Microfluctuations of accommodation,” J. Opt. 12, 123–128 (1981).
[CrossRef]

Walsh, G.

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the eye,” J. Opt. Soc. Am. A 1, 321–328 (1984).
[CrossRef]

Williams, D. R.

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[CrossRef] [PubMed]

P. Artal, R. Navarro, D. H. Brainard, S. J. Galvin, D. R. Williams, “Off-axis optical quality of the eye and retinal sampling,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 33, 3241 (1992).

Appl. Opt. (1)

Invest. Ophthalmol. Vis. Sci. (Suppl.) (1)

P. Artal, R. Navarro, D. H. Brainard, S. J. Galvin, D. R. Williams, “Off-axis optical quality of the eye and retinal sampling,” Invest. Ophthalmol. Vis. Sci. (Suppl.) 33, 3241 (1992).

J. Opt. (1)

A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic method for the dynamic study of image formation by the human eye. Microfluctuations of accommodation,” J. Opt. 12, 123–128 (1981).
[CrossRef]

J. Opt. Soc. Am. A (5)

J. Physiol. (London) (1)

F. W. Campbell, R. W. Gubisch, “Optical image quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

Ophthalmol. Physiol. Opt. (1)

R. J. Deeley, N. Drasdo, W. N. Charman, “A simple parametric model of the human ocular modulation transfer function,” Ophthalmol. Physiol. Opt. 11, 91–93 (1991).
[CrossRef]

Rev. Opt. (1)

M. F. Flamant, “Etude de la repartition de la lumière dans l’image retinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).

Vision Res. (2)

H. Kreuger, E. A. Moser, “On the approximation of the modulation transfer function (MTF) by analytical functions,” Vision Res. 13, 493–494 (1973).
[CrossRef]

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

Other (1)

W. N. Charman, “Optics of the human eye,” in Visual Optics and Instrumentation, Vol. 1 of Vision and Visual Dysfunction, J. R. Cronly-Dillon, ed. (Macmillan, London, 1991), pp. 1–26.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Average MTF’s for a group of normal young subjects for three pupil diameters. Error bars represent intersubject variability in the modulation transfer.

Fig. 2
Fig. 2

Standard deviation in the modulation as a function of spatial frequency for the pupil diameters considered in Fig. 1.

Fig. 3
Fig. 3

Average MTF’s for four pupil diameters (symbols) and the analytical approximations (curves).

Fig. 4
Fig. 4

Average MTF’s for six pupil diameters represented in a normalized spatial-frequency scale. (The solid curve corresponds to the diffraction-limited MTF.)

Fig. 5
Fig. 5

Comparison of different MTF’s for 4-mm-diameter pupil: diffraction limit; best section of the MTF computed from the wave aberration for one subject14; 5-mm-diameter pupil data obtained by an aberroscope method5; double-pass polychromatic MTF4; average MTF and error bars (2 SD) obtained in the present study; double-pass monochromatic MTF obtained with natural pupil and accommodation.10

Tables (2)

Tables Icon

Table 1 Analytical Expression for the Mean MTF for Each Pupil Sizea

Tables Icon

Table 2 Analytical Expression for the Mean MTF for Each Pupil Sizea

Equations (2)

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

MTF ( u ) = ( 1 - C ) exp ( - A u ) + C exp ( - B u ) ,
MTF ( u 0 , p ) = ( 1 - C 1 + C 2 p ) exp [ - A 1 exp ( A 2 p ) u 0 ] + ( C 1 - C 2 p ) exp [ - B 1 exp ( B 2 p ) u 0 ] ,

Metrics