Abstract

We determined the foveal optical modulation transfer functions of the human eye (O) for pupil sizes of 1–8 mm by using two simple psychophysical techniques. O as a function of spatial frequency f could be described by exp[-(f/fc)n] at any pupil size in our data as well as in the data available in the literature [J. Physiol. (London) 186, 558 (1966); Opt. Acta 21, 395 (1974); Vision Res. 33, 15 (1993); J. Opt. Soc. Am. A 11, 246 (1994)]. When all these estimates of fc and n were pooled the parameters were found to depend on the pupil diameter as fc=16.6-1.49p and n=exp(0.840/p-0.318). This result indicates that at 1 mm O(f) is close to the diffraction-limited system.

© 1998 Optical Society of America

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  1. F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 558–578 (1966).
  2. P. Artal, R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11, 246–249 (1994).
    [CrossRef]
  3. J. Krauskopf, “Light distribution in human retinal images,” J. Opt. Soc. Am. A 52, 1046–1050 (1962).
    [CrossRef]
  4. J. A. M. Jennings, W. N. Charman, “Off-axis image quality on the human eye,” Vision Res. 21, 445–455 (1981).
    [CrossRef]
  5. P. Artal, “Calculations of two-dimensional foveal images in real eyes,” J. Opt. Soc. Am. A 7, 1374–1381 (1990).
    [CrossRef] [PubMed]
  6. J. K. Ijspeert, T. J. P. P. van den Berg, H. Spekreijse, “An improved mathematical description of the foveal visual point spread function with parameters for age, pupil size and pigmentation,” Vision Res. 33, 15–20 (1993).
    [CrossRef] [PubMed]
  7. G. Westheimer, “Modulation thresholds for sinusoidal light distributions on the retina,” J. Physiol. (London) 152, 67–74 (1960).
  8. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  9. L. J. Bour, “MTF of the defocused optical system of the human eye for incoherent monochromatic light,” J. Opt. Soc. Am. A 70, 321–328 (1980).
    [CrossRef]
  10. F. Berny, S. Slansky, “Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. H. Dickson, ed. (Oriel, Birmingham, UK, 1969).
  11. 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]
  12. 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]
  13. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 6, 766–795 (1962).
  14. M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
    [CrossRef] [PubMed]
  15. A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
    [CrossRef]
  16. J. Rovamo, J. Mustonen, R. Näsänen, “Two simple psychophysical methods for determining the optical modulation transfer function of the human eye,” Vision Res. 34, 2493–2502 (1994).
    [CrossRef] [PubMed]
  17. F. L. van Nes, J. J. Koenderink, H. Nas, M. A. Bouman, “Spatiotemporal modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 1082–1088 (1967).
    [CrossRef] [PubMed]
  18. J. K. Mustonen, J. M. Rovamo, R. Näsänen, “The effects of grating area and spatial frequency on contrast sensitivity as a function of light level,” Vision Res. 33, 2065–2072 (1993).
    [CrossRef] [PubMed]
  19. J. Rovamo, J. Mustonen, R. Näsänen, “Neural modulation transfer function of the human visual system at various eccentricities,” Vision Res. 35, 767–774 (1995).
    [CrossRef] [PubMed]
  20. M. S. Banks, W. S. Geisler, P. J. Bennett, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
    [CrossRef] [PubMed]
  21. W. P. Tanner, T. G. Birdsall, “Definitions of d′ and n as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
    [CrossRef]
  22. J. W. Coltman, A. E. Anderson, “Noise limitations to resolving power in electronic imaging,” Proc. IRE 48, 858–865 (1960).
    [CrossRef]
  23. J. Rovamo, R. Franssila, R. Näsänen, “Contrast sensitivity as a function of spatial frequency, viewing distance and eccentricity with and without spatial noise,” Vision Res. 32, 1123–1129 (1992).
    [CrossRef]
  24. R. Näsänen, H. Kukkonen, J. Rovamo, “Spatial intergration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
    [CrossRef]
  25. R. L. Savoy, J. J. McCann, “Visibility of low-spatial-frequency sine-wave targets: dependence on number of cycles,” J. Opt. Soc. Am. 65, 343–350 (1975).
    [CrossRef] [PubMed]
  26. J. J. McCann, “Visibility of gradients and low spatial frequency sinusoids: evidence for a distance constancy mechanism,” Photograph. Sci. Eng. 22, 64–68 (1978).
  27. J. Rovamo, O. Luntinen, R. Näsänen, “Modelling the dependence of contrast sensitivity on grating area and spatial frequency,” Vision Res. 33, 2773–2788 (1993).
    [CrossRef] [PubMed]
  28. J. Rovamo, J. Mustonen, R. Näsänen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
    [CrossRef] [PubMed]
  29. N. S. Graham, D. C. Hood, “Quantal noise and decision rules in dynamic models of light adaptation,” Vision Res. 32, 779–787 (1992).
    [CrossRef] [PubMed]
  30. D. R. Williams, D. H. Brainard, M. J. McMahon, R. Navarro, “Double-pass and interferometric measures of the optical quality of the eye,” J. Opt. Soc. Am. A 11, 3123–3135 (1994).
    [CrossRef]
  31. J. Rovamo, H. Kukkonen, K. Tiippana, R. Näsänen, “Effects of luminance and exposure time on contrast sensitivity in spatial noise,” Vision Res. 33, 1123–1129 (1993).
    [CrossRef] [PubMed]
  32. D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
    [CrossRef] [PubMed]
  33. J. Rovamo, H. Kukkonen, “The effect of noise check size and shape on grating detectability,” Vision Res. 36, 271–279 (1996).
    [CrossRef] [PubMed]
  34. G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psychol. 18, 1–10 (1965).
    [CrossRef] [PubMed]
  35. C. B. Johnson, “Circular aperture diffraction limited MTF: approximate expressions,” Appl. Opt. 11, 1875–1876 (1972).
    [CrossRef]
  36. J. A. M. Jennings, W. N. Charman, “An analytical approximation for the modulation transfer function of the eye,” Br. J. Physiol. Opt. 29, 64–72 (1974).
    [PubMed]
  37. J. A. M. Jennings, W. N. Charman, “Analytic approximation of the off-axis modulation transfer function of the eye,” Vision Res. 37, 697–704 (1997).
    [CrossRef] [PubMed]
  38. R. J. Deeley, N. Drasdo, W. N. Charman, “A simple parametric model of the human ocular modulation transfer function,” Ophthalmic Physiol. Opt. 11, 91–93 (1991).
    [CrossRef] [PubMed]
  39. T. J. T. P. van den Berg, J. K. Ijspeert, H. Spekreijse, “Discrepancies in high frequency optical modulation transfer of the human eye, reply to Drasdo, Thompson and Charman (1994),” Vision Res. 34, 1251–1253 (1994).
    [CrossRef]
  40. S. Polyak, The Vertebrate Visual System (Chicago U. Press, Chicago, Ill., 1957).
  41. J. Rovamo, A. Raninen, S. Lukkarinen, K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767–3774 (1996).
    [CrossRef] [PubMed]
  42. F. L. van Nes, M. A. Bouman, “Spatial modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 401–406 (1967).
    [CrossRef]
  43. D. R. Williams, “Visibility of interference fringes near the resolution limit,” J. Opt. Soc. Am. A 2, 1087–1093 (1985).
    [CrossRef] [PubMed]
  44. M. I. Kankaanpää, J. M. Rovamo, J. Hallikainen, “Neural modulation transfer function for equiluminous chromatic gratings,” Perception Suppl. 25, 78 (1996).
  45. R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1990).
  46. J. Tucker, W. N. Charman, P. A. Ward, “Modulation dependence on the accommodation response to sinusoidal gratings,” Vision Res. 26, 1693–1707 (1986).
    [CrossRef]
  47. D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
    [CrossRef] [PubMed]
  48. 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]

1997 (1)

J. A. M. Jennings, W. N. Charman, “Analytic approximation of the off-axis modulation transfer function of the eye,” Vision Res. 37, 697–704 (1997).
[CrossRef] [PubMed]

1996 (3)

J. Rovamo, H. Kukkonen, “The effect of noise check size and shape on grating detectability,” Vision Res. 36, 271–279 (1996).
[CrossRef] [PubMed]

J. Rovamo, A. Raninen, S. Lukkarinen, K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767–3774 (1996).
[CrossRef] [PubMed]

M. I. Kankaanpää, J. M. Rovamo, J. Hallikainen, “Neural modulation transfer function for equiluminous chromatic gratings,” Perception Suppl. 25, 78 (1996).

1995 (2)

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

J. Rovamo, J. Mustonen, R. Näsänen, “Neural modulation transfer function of the human visual system at various eccentricities,” Vision Res. 35, 767–774 (1995).
[CrossRef] [PubMed]

1994 (5)

P. Artal, R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11, 246–249 (1994).
[CrossRef]

D. R. Williams, D. H. Brainard, M. J. McMahon, R. Navarro, “Double-pass and interferometric measures of the optical quality of the eye,” J. Opt. Soc. Am. A 11, 3123–3135 (1994).
[CrossRef]

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

J. Rovamo, J. Mustonen, R. Näsänen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

T. J. T. P. van den Berg, J. K. Ijspeert, H. Spekreijse, “Discrepancies in high frequency optical modulation transfer of the human eye, reply to Drasdo, Thompson and Charman (1994),” Vision Res. 34, 1251–1253 (1994).
[CrossRef]

1993 (5)

J. Rovamo, H. Kukkonen, K. Tiippana, R. Näsänen, “Effects of luminance and exposure time on contrast sensitivity in spatial noise,” Vision Res. 33, 1123–1129 (1993).
[CrossRef] [PubMed]

J. Rovamo, O. Luntinen, R. Näsänen, “Modelling the dependence of contrast sensitivity on grating area and spatial frequency,” Vision Res. 33, 2773–2788 (1993).
[CrossRef] [PubMed]

R. Näsänen, H. Kukkonen, J. Rovamo, “Spatial intergration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef]

J. K. Ijspeert, T. J. P. P. van den Berg, H. Spekreijse, “An improved mathematical description of the foveal visual point spread function with parameters for age, pupil size and pigmentation,” Vision Res. 33, 15–20 (1993).
[CrossRef] [PubMed]

J. K. Mustonen, J. M. Rovamo, R. Näsänen, “The effects of grating area and spatial frequency on contrast sensitivity as a function of light level,” Vision Res. 33, 2065–2072 (1993).
[CrossRef] [PubMed]

1992 (2)

J. Rovamo, R. Franssila, R. Näsänen, “Contrast sensitivity as a function of spatial frequency, viewing distance and eccentricity with and without spatial noise,” Vision Res. 32, 1123–1129 (1992).
[CrossRef]

N. S. Graham, D. C. Hood, “Quantal noise and decision rules in dynamic models of light adaptation,” Vision Res. 32, 779–787 (1992).
[CrossRef] [PubMed]

1991 (2)

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

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

1990 (2)

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef] [PubMed]

P. Artal, “Calculations of two-dimensional foveal images in real eyes,” J. Opt. Soc. Am. A 7, 1374–1381 (1990).
[CrossRef] [PubMed]

1987 (1)

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

1986 (1)

J. Tucker, W. N. Charman, P. A. Ward, “Modulation dependence on the accommodation response to sinusoidal gratings,” Vision Res. 26, 1693–1707 (1986).
[CrossRef]

1985 (1)

1984 (1)

1981 (1)

J. A. M. Jennings, W. N. Charman, “Off-axis image quality on the human eye,” Vision Res. 21, 445–455 (1981).
[CrossRef]

1980 (1)

L. J. Bour, “MTF of the defocused optical system of the human eye for incoherent monochromatic light,” J. Opt. Soc. Am. A 70, 321–328 (1980).
[CrossRef]

1978 (1)

J. J. McCann, “Visibility of gradients and low spatial frequency sinusoids: evidence for a distance constancy mechanism,” Photograph. Sci. Eng. 22, 64–68 (1978).

1977 (1)

1975 (1)

1974 (2)

J. A. M. Jennings, W. N. Charman, “An analytical approximation for the modulation transfer function of the eye,” Br. J. Physiol. Opt. 29, 64–72 (1974).
[PubMed]

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

1972 (1)

1967 (2)

1966 (1)

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

1965 (3)

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

G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psychol. 18, 1–10 (1965).
[CrossRef] [PubMed]

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]

1962 (2)

J. Krauskopf, “Light distribution in human retinal images,” J. Opt. Soc. Am. A 52, 1046–1050 (1962).
[CrossRef]

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 6, 766–795 (1962).

1960 (2)

J. W. Coltman, A. E. Anderson, “Noise limitations to resolving power in electronic imaging,” Proc. IRE 48, 858–865 (1960).
[CrossRef]

G. Westheimer, “Modulation thresholds for sinusoidal light distributions on the retina,” J. Physiol. (London) 152, 67–74 (1960).

1958 (1)

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and n as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Anderson, A. E.

J. W. Coltman, A. E. Anderson, “Noise limitations to resolving power in electronic imaging,” Proc. IRE 48, 858–865 (1960).
[CrossRef]

Artal, P.

Atchison, D. A.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Banks, M. S.

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

Bennett, P. J.

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

Berny, F.

F. Berny, S. Slansky, “Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. H. Dickson, ed. (Oriel, Birmingham, UK, 1969).

Birdsall, T. G.

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and n as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Bouman, M. A.

Bour, L. J.

L. J. Bour, “MTF of the defocused optical system of the human eye for incoherent monochromatic light,” J. Opt. Soc. Am. A 70, 321–328 (1980).
[CrossRef]

Brainard, D. H.

Campbell, F. W.

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

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]

Campbell, M. C. W.

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef] [PubMed]

Charman, W. N.

J. A. M. Jennings, W. N. Charman, “Analytic approximation of the off-axis modulation transfer function of the eye,” Vision Res. 37, 697–704 (1997).
[CrossRef] [PubMed]

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

J. Tucker, W. N. Charman, P. A. Ward, “Modulation dependence on the accommodation response to sinusoidal gratings,” Vision Res. 26, 1693–1707 (1986).
[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]

J. A. M. Jennings, W. N. Charman, “Off-axis image quality on the human eye,” Vision Res. 21, 445–455 (1981).
[CrossRef]

J. A. M. Jennings, W. N. Charman, “An analytical approximation for the modulation transfer function of the eye,” Br. J. Physiol. Opt. 29, 64–72 (1974).
[PubMed]

Christensen, J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Collins, M. J.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Coltman, J. W.

J. W. Coltman, A. E. Anderson, “Noise limitations to resolving power in electronic imaging,” Proc. IRE 48, 858–865 (1960).
[CrossRef]

De Valois, K. K.

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1990).

De Valois, R. L.

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1990).

Deeley, R. J.

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

Donner, K.

J. Rovamo, A. Raninen, S. Lukkarinen, K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767–3774 (1996).
[CrossRef] [PubMed]

Drasdo, N.

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

Franssila, R.

J. Rovamo, R. Franssila, R. Näsänen, “Contrast sensitivity as a function of spatial frequency, viewing distance and eccentricity with and without spatial noise,” Vision Res. 32, 1123–1129 (1992).
[CrossRef]

Geisler, W. S.

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

Graham, N. S.

N. S. Graham, D. C. Hood, “Quantal noise and decision rules in dynamic models of light adaptation,” Vision Res. 32, 779–787 (1992).
[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.

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

Hallikainen, J.

M. I. Kankaanpää, J. M. Rovamo, J. Hallikainen, “Neural modulation transfer function for equiluminous chromatic gratings,” Perception Suppl. 25, 78 (1996).

Harrison, E. M.

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef] [PubMed]

Hood, D. C.

N. S. Graham, D. C. Hood, “Quantal noise and decision rules in dynamic models of light adaptation,” Vision Res. 32, 779–787 (1992).
[CrossRef] [PubMed]

Howland, B.

Howland, H. C.

Ijspeert, J. K.

T. J. T. P. van den Berg, J. K. Ijspeert, H. Spekreijse, “Discrepancies in high frequency optical modulation transfer of the human eye, reply to Drasdo, Thompson and Charman (1994),” Vision Res. 34, 1251–1253 (1994).
[CrossRef]

J. K. Ijspeert, T. J. P. P. van den Berg, H. Spekreijse, “An improved mathematical description of the foveal visual point spread function with parameters for age, pupil size and pigmentation,” Vision Res. 33, 15–20 (1993).
[CrossRef] [PubMed]

Jennings, J. A. M.

J. A. M. Jennings, W. N. Charman, “Analytic approximation of the off-axis modulation transfer function of the eye,” Vision Res. 37, 697–704 (1997).
[CrossRef] [PubMed]

J. A. M. Jennings, W. N. Charman, “Off-axis image quality on the human eye,” Vision Res. 21, 445–455 (1981).
[CrossRef]

J. A. M. Jennings, W. N. Charman, “An analytical approximation for the modulation transfer function of the eye,” Br. J. Physiol. Opt. 29, 64–72 (1974).
[PubMed]

Johnson, C. B.

Kankaanpää, M. I.

M. I. Kankaanpää, J. M. Rovamo, J. Hallikainen, “Neural modulation transfer function for equiluminous chromatic gratings,” Perception Suppl. 25, 78 (1996).

Koenderink, J. J.

Krauskopf, J.

J. Krauskopf, “Light distribution in human retinal images,” J. Opt. Soc. Am. A 52, 1046–1050 (1962).
[CrossRef]

Kukkonen, H.

J. Rovamo, H. Kukkonen, “The effect of noise check size and shape on grating detectability,” Vision Res. 36, 271–279 (1996).
[CrossRef] [PubMed]

J. Rovamo, H. Kukkonen, K. Tiippana, R. Näsänen, “Effects of luminance and exposure time on contrast sensitivity in spatial noise,” Vision Res. 33, 1123–1129 (1993).
[CrossRef] [PubMed]

R. Näsänen, H. Kukkonen, J. Rovamo, “Spatial intergration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef]

Levitt, H.

G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psychol. 18, 1–10 (1965).
[CrossRef] [PubMed]

Lukkarinen, S.

J. Rovamo, A. Raninen, S. Lukkarinen, K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767–3774 (1996).
[CrossRef] [PubMed]

Luntinen, O.

J. Rovamo, O. Luntinen, R. Näsänen, “Modelling the dependence of contrast sensitivity on grating area and spatial frequency,” Vision Res. 33, 2773–2788 (1993).
[CrossRef] [PubMed]

McCann, J. J.

J. J. McCann, “Visibility of gradients and low spatial frequency sinusoids: evidence for a distance constancy mechanism,” Photograph. Sci. Eng. 22, 64–68 (1978).

R. L. Savoy, J. J. McCann, “Visibility of low-spatial-frequency sine-wave targets: dependence on number of cycles,” J. Opt. Soc. Am. 65, 343–350 (1975).
[CrossRef] [PubMed]

McMahon, M. J.

Mustonen, J.

J. Rovamo, J. Mustonen, R. Näsänen, “Neural modulation transfer function of the human visual system at various eccentricities,” Vision Res. 35, 767–774 (1995).
[CrossRef] [PubMed]

J. Rovamo, J. Mustonen, R. Näsänen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

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

Mustonen, J. K.

J. K. Mustonen, J. M. Rovamo, R. Näsänen, “The effects of grating area and spatial frequency on contrast sensitivity as a function of light level,” Vision Res. 33, 2065–2072 (1993).
[CrossRef] [PubMed]

Nas, H.

Näsänen, R.

J. Rovamo, J. Mustonen, R. Näsänen, “Neural modulation transfer function of the human visual system at various eccentricities,” Vision Res. 35, 767–774 (1995).
[CrossRef] [PubMed]

J. Rovamo, J. Mustonen, R. Näsänen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

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

J. Rovamo, O. Luntinen, R. Näsänen, “Modelling the dependence of contrast sensitivity on grating area and spatial frequency,” Vision Res. 33, 2773–2788 (1993).
[CrossRef] [PubMed]

R. Näsänen, H. Kukkonen, J. Rovamo, “Spatial intergration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef]

J. K. Mustonen, J. M. Rovamo, R. Näsänen, “The effects of grating area and spatial frequency on contrast sensitivity as a function of light level,” Vision Res. 33, 2065–2072 (1993).
[CrossRef] [PubMed]

J. Rovamo, H. Kukkonen, K. Tiippana, R. Näsänen, “Effects of luminance and exposure time on contrast sensitivity in spatial noise,” Vision Res. 33, 1123–1129 (1993).
[CrossRef] [PubMed]

J. Rovamo, R. Franssila, R. Näsänen, “Contrast sensitivity as a function of spatial frequency, viewing distance and eccentricity with and without spatial noise,” Vision Res. 32, 1123–1129 (1992).
[CrossRef]

Navarro, R.

Pelli, D. G.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

Polyak, S.

S. Polyak, The Vertebrate Visual System (Chicago U. Press, Chicago, Ill., 1957).

Raninen, A.

J. Rovamo, A. Raninen, S. Lukkarinen, K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767–3774 (1996).
[CrossRef] [PubMed]

Rovamo, J.

J. Rovamo, A. Raninen, S. Lukkarinen, K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767–3774 (1996).
[CrossRef] [PubMed]

J. Rovamo, H. Kukkonen, “The effect of noise check size and shape on grating detectability,” Vision Res. 36, 271–279 (1996).
[CrossRef] [PubMed]

J. Rovamo, J. Mustonen, R. Näsänen, “Neural modulation transfer function of the human visual system at various eccentricities,” Vision Res. 35, 767–774 (1995).
[CrossRef] [PubMed]

J. Rovamo, J. Mustonen, R. Näsänen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

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

J. Rovamo, O. Luntinen, R. Näsänen, “Modelling the dependence of contrast sensitivity on grating area and spatial frequency,” Vision Res. 33, 2773–2788 (1993).
[CrossRef] [PubMed]

J. Rovamo, H. Kukkonen, K. Tiippana, R. Näsänen, “Effects of luminance and exposure time on contrast sensitivity in spatial noise,” Vision Res. 33, 1123–1129 (1993).
[CrossRef] [PubMed]

R. Näsänen, H. Kukkonen, J. Rovamo, “Spatial intergration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef]

J. Rovamo, R. Franssila, R. Näsänen, “Contrast sensitivity as a function of spatial frequency, viewing distance and eccentricity with and without spatial noise,” Vision Res. 32, 1123–1129 (1992).
[CrossRef]

Rovamo, J. M.

M. I. Kankaanpää, J. M. Rovamo, J. Hallikainen, “Neural modulation transfer function for equiluminous chromatic gratings,” Perception Suppl. 25, 78 (1996).

J. K. Mustonen, J. M. Rovamo, R. Näsänen, “The effects of grating area and spatial frequency on contrast sensitivity as a function of light level,” Vision Res. 33, 2065–2072 (1993).
[CrossRef] [PubMed]

Savoy, R. L.

Simonet, P.

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef] [PubMed]

Slansky, S.

F. Berny, S. Slansky, “Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. H. Dickson, ed. (Oriel, Birmingham, UK, 1969).

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 6, 766–795 (1962).

Spekreijse, H.

T. J. T. P. van den Berg, J. K. Ijspeert, H. Spekreijse, “Discrepancies in high frequency optical modulation transfer of the human eye, reply to Drasdo, Thompson and Charman (1994),” Vision Res. 34, 1251–1253 (1994).
[CrossRef]

J. K. Ijspeert, T. J. P. P. van den Berg, H. Spekreijse, “An improved mathematical description of the foveal visual point spread function with parameters for age, pupil size and pigmentation,” Vision Res. 33, 15–20 (1993).
[CrossRef] [PubMed]

Tanner, W. P.

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and n as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Tiippana, K.

J. Rovamo, H. Kukkonen, K. Tiippana, R. Näsänen, “Effects of luminance and exposure time on contrast sensitivity in spatial noise,” Vision Res. 33, 1123–1129 (1993).
[CrossRef] [PubMed]

Tucker, J.

J. Tucker, W. N. Charman, P. A. Ward, “Modulation dependence on the accommodation response to sinusoidal gratings,” Vision Res. 26, 1693–1707 (1986).
[CrossRef]

van den Berg, T. J. P. P.

J. K. Ijspeert, T. J. P. P. van den Berg, H. Spekreijse, “An improved mathematical description of the foveal visual point spread function with parameters for age, pupil size and pigmentation,” Vision Res. 33, 15–20 (1993).
[CrossRef] [PubMed]

van den Berg, T. J. T. P.

T. J. T. P. van den Berg, J. K. Ijspeert, H. Spekreijse, “Discrepancies in high frequency optical modulation transfer of the human eye, reply to Drasdo, Thompson and Charman (1994),” Vision Res. 34, 1251–1253 (1994).
[CrossRef]

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]

van Nes, F. L.

Walsh, G.

Ward, P. A.

J. Tucker, W. N. Charman, P. A. Ward, “Modulation dependence on the accommodation response to sinusoidal gratings,” Vision Res. 26, 1693–1707 (1986).
[CrossRef]

Waterworth, M. D.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Westheimer, G.

G. Westheimer, “Modulation thresholds for sinusoidal light distributions on the retina,” J. Physiol. (London) 152, 67–74 (1960).

Wetherill, G. B.

G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psychol. 18, 1–10 (1965).
[CrossRef] [PubMed]

Wildsoet, C. F.

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Williams, D. R.

Zhang, L.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biophys. J. (1)

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 6, 766–795 (1962).

Br. J. Math. Stat. Psychol. (1)

G. B. Wetherill, H. Levitt, “Sequential estimation of points on a psychometric function,” Br. J. Math. Stat. Psychol. 18, 1–10 (1965).
[CrossRef] [PubMed]

Br. J. Physiol. Opt. (1)

J. A. M. Jennings, W. N. Charman, “An analytical approximation for the modulation transfer function of the eye,” Br. J. Physiol. Opt. 29, 64–72 (1974).
[PubMed]

J. Acoust. Soc. Am. (1)

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and n as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (7)

J. Physiol. (London) (3)

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

G. Westheimer, “Modulation thresholds for sinusoidal light distributions on the retina,” J. Physiol. (London) 152, 67–74 (1960).

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

Ophthalmic Physiol. Opt. (1)

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

Opt. Acta (1)

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

Perception Suppl. (1)

M. I. Kankaanpää, J. M. Rovamo, J. Hallikainen, “Neural modulation transfer function for equiluminous chromatic gratings,” Perception Suppl. 25, 78 (1996).

Photograph. Sci. Eng. (1)

J. J. McCann, “Visibility of gradients and low spatial frequency sinusoids: evidence for a distance constancy mechanism,” Photograph. Sci. Eng. 22, 64–68 (1978).

Proc. IRE (1)

J. W. Coltman, A. E. Anderson, “Noise limitations to resolving power in electronic imaging,” Proc. IRE 48, 858–865 (1960).
[CrossRef]

Vision Res. (20)

J. Rovamo, R. Franssila, R. Näsänen, “Contrast sensitivity as a function of spatial frequency, viewing distance and eccentricity with and without spatial noise,” Vision Res. 32, 1123–1129 (1992).
[CrossRef]

R. Näsänen, H. Kukkonen, J. Rovamo, “Spatial intergration of band-pass filtered patterns in noise,” Vision Res. 33, 903–911 (1993).
[CrossRef]

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

M. C. W. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef] [PubMed]

J. A. M. Jennings, W. N. Charman, “Off-axis image quality on the human eye,” Vision Res. 21, 445–455 (1981).
[CrossRef]

J. K. Ijspeert, T. J. P. P. van den Berg, H. Spekreijse, “An improved mathematical description of the foveal visual point spread function with parameters for age, pupil size and pigmentation,” Vision Res. 33, 15–20 (1993).
[CrossRef] [PubMed]

J. K. Mustonen, J. M. Rovamo, R. Näsänen, “The effects of grating area and spatial frequency on contrast sensitivity as a function of light level,” Vision Res. 33, 2065–2072 (1993).
[CrossRef] [PubMed]

J. Rovamo, J. Mustonen, R. Näsänen, “Neural modulation transfer function of the human visual system at various eccentricities,” Vision Res. 35, 767–774 (1995).
[CrossRef] [PubMed]

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

J. Rovamo, O. Luntinen, R. Näsänen, “Modelling the dependence of contrast sensitivity on grating area and spatial frequency,” Vision Res. 33, 2773–2788 (1993).
[CrossRef] [PubMed]

J. Rovamo, J. Mustonen, R. Näsänen, “Modelling contrast sensitivity as a function of retinal illuminance and grating area,” Vision Res. 34, 1301–1314 (1994).
[CrossRef] [PubMed]

N. S. Graham, D. C. Hood, “Quantal noise and decision rules in dynamic models of light adaptation,” Vision Res. 32, 779–787 (1992).
[CrossRef] [PubMed]

J. Rovamo, H. Kukkonen, K. Tiippana, R. Näsänen, “Effects of luminance and exposure time on contrast sensitivity in spatial noise,” Vision Res. 33, 1123–1129 (1993).
[CrossRef] [PubMed]

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1350 (1991).
[CrossRef] [PubMed]

J. Rovamo, H. Kukkonen, “The effect of noise check size and shape on grating detectability,” Vision Res. 36, 271–279 (1996).
[CrossRef] [PubMed]

T. J. T. P. van den Berg, J. K. Ijspeert, H. Spekreijse, “Discrepancies in high frequency optical modulation transfer of the human eye, reply to Drasdo, Thompson and Charman (1994),” Vision Res. 34, 1251–1253 (1994).
[CrossRef]

J. A. M. Jennings, W. N. Charman, “Analytic approximation of the off-axis modulation transfer function of the eye,” Vision Res. 37, 697–704 (1997).
[CrossRef] [PubMed]

J. Rovamo, A. Raninen, S. Lukkarinen, K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767–3774 (1996).
[CrossRef] [PubMed]

J. Tucker, W. N. Charman, P. A. Ward, “Modulation dependence on the accommodation response to sinusoidal gratings,” Vision Res. 26, 1693–1707 (1986).
[CrossRef]

D. A. Atchison, M. J. Collins, C. F. Wildsoet, J. Christensen, M. D. Waterworth, “Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the Howland aberroscope technique,” Vision Res. 35, 313–323 (1995).
[CrossRef] [PubMed]

Other (3)

R. L. De Valois, K. K. De Valois, Spatial Vision (Oxford U. Press, New York, 1990).

S. Polyak, The Vertebrate Visual System (Chicago U. Press, Chicago, Ill., 1957).

F. Berny, S. Slansky, “Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. H. Dickson, ed. (Oriel, Birmingham, UK, 1969).

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Figures (3)

Fig. 1
Fig. 1

Spatial rms contrast sensitivity functions, measured at various pupil sizes of 1–8 mm, are indicated by open symbols. In these experiments retinal flux, grating shape, and the number of cycles were kept constant across the spatial frequencies in each frame. Solid symbols for 2- and 4-mm pupils refer to the optical MTF’s calculated from the data of Fig. 2 by Eqs. (6) and (7) and superimposed on the contrast sensitivity data by means of a scaling factor calculated as explained in Section 2. Subjects are as indicated. In each frame the solid curve is calculated by Eqs. (8) and (9) fitted to the combined data of all the subjects. Percentage indicates the goodness of fit. The dashed curves show the optical MTF’s of the perfect diffraction-limited system for the circular pupil sizes studied.

Fig. 2
Fig. 2

Spatial rms contrast sensitivity functions with and without spatial noise for pupil sizes of 2 and 4 mm. The line segments connect the geometrical averages of the sensitivities from two subjects in each condition. Subjects are as indicated.

Fig. 3
Fig. 3

Values of fc and n plotted as a function of pupil size. They were obtained when Eqs. (8) and (9) were fitted to the data of Fig. 1 separately at each pupil diameter of 1–8 mm as well as to the previously published data from various sources.3-6 The solid line and curve decreasing with pupil size are least-squares fits to the data. The dashed lines refer to the diffraction-limited system.

Equations (11)

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

E=c2(x, y)p2,
crms=(E/A),
Ne=cn2Ap,
(Nc+Ne)/En=Nc/E0,
Nc=O-2(f)P-2(f)Nis.
kO(f)=(f2Nc)-0.5,
Nc=Ne/[(S0/Sn)2-1],
O(f)=exp[-(f/fc)n],
S=SmaxO(f),
ln S=ln Smax-(f/fc)n,
Te(f)=(2/π)[arccos(f/f0)-(f/f0)1-(f/f0)2],

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