Abstract

Lasers have been used in vision for measuring the neural contrast sensitivity function (CSF) by forming interference fringes on the retina. We distinguish among three kinds of illumination with lasers: incoherent (without noise), Maxwellian or coherent (with coherent noise), and diffuse coherent (with speckle). The three have different characteristics and different CSF’s. A coherent imaging system is designed to measure the CSF with fully coherent illumination. This is the CSF of the whole visual system, although it is measured with gratings imaged on the retina. It therefore differs from the neural CSF’s measured by other authors with partially coherent illumination. However, the neural CSF’s are also obtained in this study with and without noise. The effects of coherent noise and speckle on both the visual system and neural sensitivities are studied and compared. Coherent noise differs from speckle in the following ways: (1) It behaves as a high-pass filter, reducing sensitivity in the low-spatial-frequency range, whereas speckle is a low-pass filter; (2) quantitatively, coherent noise reduces neural sensitivity by a factor km with a maximum value between 4 and 6, whereas speckle reduces neural sensitivity by a factor ks with a maximum value of 25 (1.4 log units) for a 3-mm pupil and up to 35 (1.55 log units) for a 1-mm pupil; (3) the masking effect of the coherent noise is affected by changes in luminance but not by changes in pupil diameter; however, the pupil size is the main parameter affecting the masking effect of the speckle.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Le Grand, “La formation des images rétiniennes. Sur un mode de vision éliminant les défautes optiques de l’oeil,” C. R. Acad. Sci.200, 490 (1935). Referenced in Y. Le Grand, Optique Physiologique (Masson et CIE, Paris, 1972), Vol. III, p. 113.
  2. G. M. Byram, “The physical and photochemical basis of visual resolving power. Part II. Visual acuity and the photochemistry of the retina,” J. Opt. Soc. Am. 34, 718–738 (1944).
    [CrossRef]
  3. B. O’Brien, Untitled communication about the resolving power of the eye. “National Bureau Standard Symposium on Optical Image Evaluation” Washington 1951. J. Opt. Soc. Am. 42, 74 (1952).
  4. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. 181, 576–593 (1965).
  5. D. R. Williams, “Visibility of interference fringes near the resolution limit,” J. Opt. Soc. Am. A 2, 1087–1093 (1985).
    [CrossRef] [PubMed]
  6. N. J. Coletta, V. Sharma, “Effects of luminance and spatial noise on interferometric contrast sensitivity,” J. Opt. Soc. Am. A 12, 2244–2251 (1995).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. X, pp. 491–508.
  8. J. M. Artigas, A. Felipe, M. J. Buades, “Contrast sensitivity of the visual system in speckle imagery,” J. Opt. Soc. Am. A 11, 2345–2349 (1994).
    [CrossRef]
  9. M. Aguilar, A. Felipe, J. M. Artigas, “Coherence of light and visual acuity: the influence of the pupil,” Atti Fond. Giorgio Ronchi 41, 81–97 (1986).
  10. J. M. Artigas, A. Felipe, “Effect of luminance on photopic visual acuity in the presence of laser speckle,” J. Opt. Soc. Am. A 5, 1767–1771 (1988).
    [CrossRef] [PubMed]
  11. S. Lowenthal, D. Joyeux, “Speckle removal by a slowly moving diffuser associated with a motionless diffuser,” J. Opt. Soc. Am. 61, 847–851 (1971).
    [CrossRef]
  12. G. Westheimer, “The Maxwellian view,” Vision Res. 6, 669–682 (1966).
    [CrossRef] [PubMed]
  13. R. W. Nygaard, T. E. Frunkes, “Calibration of the retinal illuminance provided by Maxwellian views,” Vision Res. 22, 433–434 (1982).
    [CrossRef] [PubMed]
  14. W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta. 24, 1211–1216 (1977).
    [CrossRef]
  15. F. L. VanNess, M. A. Bouman, “Spatial modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 401–406 (1967).
    [CrossRef]
  16. 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]
  17. J. J. McCann, J. A. Hall, “Visibility of low-spatial-frequency sine-wave targets. Dependence on size of average-luminance surround,” J. Opt. Soc. Am. 67, 1408 (1977).
  18. J. J. McCann, R. L. Savoy, J. A. Hall, “Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters,” Vision Res. 18, 891–894 (1978).
    [CrossRef]
  19. D. G. Green, J. A. Swets, “Experimental techniques,” in Signal Detection Theory and Psychophysics (Krieger, New York, 1974), App. III, pp. 392–416.
  20. M. Dressler, B. Rassow, “Neural contrast sensitivity measurements with a laser interference system for clinical and scientific screening application,” Invest. Ophthalmol. Visual Sci. 21, 737–744 (1981).
  21. D. R. Williams, “Aliasing in human vision,” Vision Res. 25, 195–205 (1985).
    [CrossRef]
  22. J. J. DePalma, E. M. Lowry, “Sine-wave response of the visual system. II. Sine-wave and square-wave contrast sensitivity,” J. Opt. Soc. Am. 52, 328–335 (1962).
    [CrossRef]
  23. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
  24. E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
    [CrossRef] [PubMed]
  25. A. Fiorentini, L. Maffei, “Spatial contrast sensitivity of myopic subjects,” Vision Res. 16, 437–438 (1976).
    [CrossRef] [PubMed]
  26. M. A. Losada, “Influencia de la calidad óptica del ojo en la percepción espacial de contrastes umbrales,” Ph.D. dissertation (Universidad Complutense, Madrid, 1990).
  27. A. S. Patel, “Spatial resolution by the human visual system. The effect of mean retinal illuminance,” J. Opt. Soc. Am. 56, 689–694 (1966).
    [CrossRef] [PubMed]
  28. J. G. Robson, “Spatial and temporal contrast-sensitivity functions of the visual system,” J. Opt. Soc. Am. 56, 1141–1142 (1966).
    [CrossRef]
  29. 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]
  30. M. J. Wright, “Contrast sensitivity and adaptation as a function of grating length,” Vision Res. 22, 139–149 (1982).
    [CrossRef] [PubMed]
  31. O. Estévez, C. R. Cavonius, “Low-frequency attenuation in the detection of gratings: sorting out the artifacts,” Vision Res. 16, 497–500 (1976).
    [CrossRef]
  32. L. E. Arend, “Response of the human eye to spatially sinusoidal gratings at various exposure durations,” Vision Res. 16, 1311–1315 (1976).
    [CrossRef] [PubMed]
  33. A. Felipe, M. J. Buades, J. M. Artigas, P. Capilla, “The behaviour of the neural CSF in the low spatial frequencies range,” Perception 23 (Suppl.), 79 (1994).
  34. Let us remember that it is unnecessary to divide the Maxwellian CSF by the MTF, since in a coherent imaging system the MTF takes only two values, either zero or unity, depending on whether the points of the spectrum do or do not pass through the pupil.
  35. 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]
  36. S. Lowenthal, H. H. Arsenault, “Image formation for coherent diffuse objects: statistical properties,” J. Opt. Soc. Am. 60, 1478–1483 (1970).
    [CrossRef]
  37. A. van Meeteren, “Calculations on the optical modulation transfer function of the human eye for white light,” Opt. Acta 21, 395–412 (1974).
    [CrossRef]

1995 (1)

1994 (3)

1988 (1)

1987 (1)

1986 (1)

M. Aguilar, A. Felipe, J. M. Artigas, “Coherence of light and visual acuity: the influence of the pupil,” Atti Fond. Giorgio Ronchi 41, 81–97 (1986).

1985 (2)

1982 (2)

M. J. Wright, “Contrast sensitivity and adaptation as a function of grating length,” Vision Res. 22, 139–149 (1982).
[CrossRef] [PubMed]

R. W. Nygaard, T. E. Frunkes, “Calibration of the retinal illuminance provided by Maxwellian views,” Vision Res. 22, 433–434 (1982).
[CrossRef] [PubMed]

1981 (1)

M. Dressler, B. Rassow, “Neural contrast sensitivity measurements with a laser interference system for clinical and scientific screening application,” Invest. Ophthalmol. Visual Sci. 21, 737–744 (1981).

1978 (2)

J. J. McCann, R. L. Savoy, J. A. Hall, “Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters,” Vision Res. 18, 891–894 (1978).
[CrossRef]

E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef] [PubMed]

1977 (2)

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta. 24, 1211–1216 (1977).
[CrossRef]

J. J. McCann, J. A. Hall, “Visibility of low-spatial-frequency sine-wave targets. Dependence on size of average-luminance surround,” J. Opt. Soc. Am. 67, 1408 (1977).

1976 (3)

A. Fiorentini, L. Maffei, “Spatial contrast sensitivity of myopic subjects,” Vision Res. 16, 437–438 (1976).
[CrossRef] [PubMed]

O. Estévez, C. R. Cavonius, “Low-frequency attenuation in the detection of gratings: sorting out the artifacts,” Vision Res. 16, 497–500 (1976).
[CrossRef]

L. E. Arend, “Response of the human eye to spatially sinusoidal gratings at various exposure durations,” Vision Res. 16, 1311–1315 (1976).
[CrossRef] [PubMed]

1975 (1)

1974 (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]

1971 (1)

1970 (1)

1968 (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).

1967 (1)

1966 (3)

1965 (1)

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

1962 (1)

1952 (1)

B. O’Brien, Untitled communication about the resolving power of the eye. “National Bureau Standard Symposium on Optical Image Evaluation” Washington 1951. J. Opt. Soc. Am. 42, 74 (1952).

1944 (1)

Aguilar, M.

M. Aguilar, A. Felipe, J. M. Artigas, “Coherence of light and visual acuity: the influence of the pupil,” Atti Fond. Giorgio Ronchi 41, 81–97 (1986).

Arend, L. E.

L. E. Arend, “Response of the human eye to spatially sinusoidal gratings at various exposure durations,” Vision Res. 16, 1311–1315 (1976).
[CrossRef] [PubMed]

Arsenault, H. H.

Artal, P.

Artigas, J. M.

J. M. Artigas, A. Felipe, M. J. Buades, “Contrast sensitivity of the visual system in speckle imagery,” J. Opt. Soc. Am. A 11, 2345–2349 (1994).
[CrossRef]

A. Felipe, M. J. Buades, J. M. Artigas, P. Capilla, “The behaviour of the neural CSF in the low spatial frequencies range,” Perception 23 (Suppl.), 79 (1994).

J. M. Artigas, A. Felipe, “Effect of luminance on photopic visual acuity in the presence of laser speckle,” J. Opt. Soc. Am. A 5, 1767–1771 (1988).
[CrossRef] [PubMed]

M. Aguilar, A. Felipe, J. M. Artigas, “Coherence of light and visual acuity: the influence of the pupil,” Atti Fond. Giorgio Ronchi 41, 81–97 (1986).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. X, pp. 491–508.

Bouman, M. A.

Buades, M. J.

J. M. Artigas, A. Felipe, M. J. Buades, “Contrast sensitivity of the visual system in speckle imagery,” J. Opt. Soc. Am. A 11, 2345–2349 (1994).
[CrossRef]

A. Felipe, M. J. Buades, J. M. Artigas, P. Capilla, “The behaviour of the neural CSF in the low spatial frequencies range,” Perception 23 (Suppl.), 79 (1994).

Byram, G. M.

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, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).

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

Capilla, P.

A. Felipe, M. J. Buades, J. M. Artigas, P. Capilla, “The behaviour of the neural CSF in the low spatial frequencies range,” Perception 23 (Suppl.), 79 (1994).

Cavonius, C. R.

O. Estévez, C. R. Cavonius, “Low-frequency attenuation in the detection of gratings: sorting out the artifacts,” Vision Res. 16, 497–500 (1976).
[CrossRef]

Charman, W. N.

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta. 24, 1211–1216 (1977).
[CrossRef]

Coletta, N. J.

DePalma, J. J.

Dressler, M.

M. Dressler, B. Rassow, “Neural contrast sensitivity measurements with a laser interference system for clinical and scientific screening application,” Invest. Ophthalmol. Visual Sci. 21, 737–744 (1981).

Estévez, O.

O. Estévez, C. R. Cavonius, “Low-frequency attenuation in the detection of gratings: sorting out the artifacts,” Vision Res. 16, 497–500 (1976).
[CrossRef]

Felipe, A.

J. M. Artigas, A. Felipe, M. J. Buades, “Contrast sensitivity of the visual system in speckle imagery,” J. Opt. Soc. Am. A 11, 2345–2349 (1994).
[CrossRef]

A. Felipe, M. J. Buades, J. M. Artigas, P. Capilla, “The behaviour of the neural CSF in the low spatial frequencies range,” Perception 23 (Suppl.), 79 (1994).

J. M. Artigas, A. Felipe, “Effect of luminance on photopic visual acuity in the presence of laser speckle,” J. Opt. Soc. Am. A 5, 1767–1771 (1988).
[CrossRef] [PubMed]

M. Aguilar, A. Felipe, J. M. Artigas, “Coherence of light and visual acuity: the influence of the pupil,” Atti Fond. Giorgio Ronchi 41, 81–97 (1986).

Fiorentini, A.

A. Fiorentini, L. Maffei, “Spatial contrast sensitivity of myopic subjects,” Vision Res. 16, 437–438 (1976).
[CrossRef] [PubMed]

Frunkes, T. E.

R. W. Nygaard, T. E. Frunkes, “Calibration of the retinal illuminance provided by Maxwellian views,” Vision Res. 22, 433–434 (1982).
[CrossRef] [PubMed]

Green, D. G.

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

D. G. Green, J. A. Swets, “Experimental techniques,” in Signal Detection Theory and Psychophysics (Krieger, New York, 1974), App. III, pp. 392–416.

Hall, J. A.

J. J. McCann, R. L. Savoy, J. A. Hall, “Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters,” Vision Res. 18, 891–894 (1978).
[CrossRef]

J. J. McCann, J. A. Hall, “Visibility of low-spatial-frequency sine-wave targets. Dependence on size of average-luminance surround,” J. Opt. Soc. Am. 67, 1408 (1977).

Hess, R. F.

E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef] [PubMed]

Howell, E. R.

E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef] [PubMed]

Joyeux, D.

Le Grand, Y.

Y. Le Grand, “La formation des images rétiniennes. Sur un mode de vision éliminant les défautes optiques de l’oeil,” C. R. Acad. Sci.200, 490 (1935). Referenced in Y. Le Grand, Optique Physiologique (Masson et CIE, Paris, 1972), Vol. III, p. 113.

Legge, G. E.

Losada, M. A.

M. A. Losada, “Influencia de la calidad óptica del ojo en la percepción espacial de contrastes umbrales,” Ph.D. dissertation (Universidad Complutense, Madrid, 1990).

Lowenthal, S.

Lowry, E. M.

Maffei, L.

A. Fiorentini, L. Maffei, “Spatial contrast sensitivity of myopic subjects,” Vision Res. 16, 437–438 (1976).
[CrossRef] [PubMed]

McCann, J. J.

J. J. McCann, R. L. Savoy, J. A. Hall, “Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters,” Vision Res. 18, 891–894 (1978).
[CrossRef]

J. J. McCann, J. A. Hall, “Visibility of low-spatial-frequency sine-wave targets. Dependence on size of average-luminance surround,” J. Opt. Soc. Am. 67, 1408 (1977).

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]

Mullen, K. T.

Navarro, R.

Nygaard, R. W.

R. W. Nygaard, T. E. Frunkes, “Calibration of the retinal illuminance provided by Maxwellian views,” Vision Res. 22, 433–434 (1982).
[CrossRef] [PubMed]

O’Brien, B.

B. O’Brien, Untitled communication about the resolving power of the eye. “National Bureau Standard Symposium on Optical Image Evaluation” Washington 1951. J. Opt. Soc. Am. 42, 74 (1952).

Patel, A. S.

Rassow, B.

M. Dressler, B. Rassow, “Neural contrast sensitivity measurements with a laser interference system for clinical and scientific screening application,” Invest. Ophthalmol. Visual Sci. 21, 737–744 (1981).

Robson, J. G.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).

J. G. Robson, “Spatial and temporal contrast-sensitivity functions of the visual system,” J. Opt. Soc. Am. 56, 1141–1142 (1966).
[CrossRef]

Savoy, R. L.

J. J. McCann, R. L. Savoy, J. A. Hall, “Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters,” Vision Res. 18, 891–894 (1978).
[CrossRef]

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]

Sharma, V.

Swets, J. A.

D. G. Green, J. A. Swets, “Experimental techniques,” in Signal Detection Theory and Psychophysics (Krieger, New York, 1974), App. III, pp. 392–416.

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]

VanNess, F. L.

Westheimer, G.

G. Westheimer, “The Maxwellian view,” Vision Res. 6, 669–682 (1966).
[CrossRef] [PubMed]

Whitefoot, H.

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta. 24, 1211–1216 (1977).
[CrossRef]

Williams, D. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. X, pp. 491–508.

Woo, G. C.

Wright, M. J.

M. J. Wright, “Contrast sensitivity and adaptation as a function of grating length,” Vision Res. 22, 139–149 (1982).
[CrossRef] [PubMed]

Atti Fond. Giorgio Ronchi (1)

M. Aguilar, A. Felipe, J. M. Artigas, “Coherence of light and visual acuity: the influence of the pupil,” Atti Fond. Giorgio Ronchi 41, 81–97 (1986).

Invest. Ophthalmol. Visual Sci. (1)

M. Dressler, B. Rassow, “Neural contrast sensitivity measurements with a laser interference system for clinical and scientific screening application,” Invest. Ophthalmol. Visual Sci. 21, 737–744 (1981).

J. Opt. Soc. Am. (9)

J. J. McCann, J. A. Hall, “Visibility of low-spatial-frequency sine-wave targets. Dependence on size of average-luminance surround,” J. Opt. Soc. Am. 67, 1408 (1977).

G. M. Byram, “The physical and photochemical basis of visual resolving power. Part II. Visual acuity and the photochemistry of the retina,” J. Opt. Soc. Am. 34, 718–738 (1944).
[CrossRef]

A. S. Patel, “Spatial resolution by the human visual system. The effect of mean retinal illuminance,” J. Opt. Soc. Am. 56, 689–694 (1966).
[CrossRef] [PubMed]

S. Lowenthal, H. H. Arsenault, “Image formation for coherent diffuse objects: statistical properties,” J. Opt. Soc. Am. 60, 1478–1483 (1970).
[CrossRef]

S. Lowenthal, D. Joyeux, “Speckle removal by a slowly moving diffuser associated with a motionless diffuser,” J. Opt. Soc. Am. 61, 847–851 (1971).
[CrossRef]

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]

F. L. VanNess, M. A. Bouman, “Spatial modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 401–406 (1967).
[CrossRef]

J. J. DePalma, E. M. Lowry, “Sine-wave response of the visual system. II. Sine-wave and square-wave contrast sensitivity,” J. Opt. Soc. Am. 52, 328–335 (1962).
[CrossRef]

J. G. Robson, “Spatial and temporal contrast-sensitivity functions of the visual system,” J. Opt. Soc. Am. 56, 1141–1142 (1966).
[CrossRef]

J. Opt. Soc. Am. A (6)

J. Physiol. (2)

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

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).

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]

Opt. Acta. (1)

W. N. Charman, H. Whitefoot, “Pupil diameter and the depth-of-field of the human eye as measured by laser speckle,” Opt. Acta. 24, 1211–1216 (1977).
[CrossRef]

Perception (1)

A. Felipe, M. J. Buades, J. M. Artigas, P. Capilla, “The behaviour of the neural CSF in the low spatial frequencies range,” Perception 23 (Suppl.), 79 (1994).

Vision Res. (9)

M. J. Wright, “Contrast sensitivity and adaptation as a function of grating length,” Vision Res. 22, 139–149 (1982).
[CrossRef] [PubMed]

O. Estévez, C. R. Cavonius, “Low-frequency attenuation in the detection of gratings: sorting out the artifacts,” Vision Res. 16, 497–500 (1976).
[CrossRef]

L. E. Arend, “Response of the human eye to spatially sinusoidal gratings at various exposure durations,” Vision Res. 16, 1311–1315 (1976).
[CrossRef] [PubMed]

D. R. Williams, “Aliasing in human vision,” Vision Res. 25, 195–205 (1985).
[CrossRef]

E. R. Howell, R. F. Hess, “The functional area for summation to threshold for sinusoidal gratings,” Vision Res. 18, 369–374 (1978).
[CrossRef] [PubMed]

A. Fiorentini, L. Maffei, “Spatial contrast sensitivity of myopic subjects,” Vision Res. 16, 437–438 (1976).
[CrossRef] [PubMed]

G. Westheimer, “The Maxwellian view,” Vision Res. 6, 669–682 (1966).
[CrossRef] [PubMed]

R. W. Nygaard, T. E. Frunkes, “Calibration of the retinal illuminance provided by Maxwellian views,” Vision Res. 22, 433–434 (1982).
[CrossRef] [PubMed]

J. J. McCann, R. L. Savoy, J. A. Hall, “Visibility of low-frequency sine-wave targets: dependence on number of cycles and surround parameters,” Vision Res. 18, 891–894 (1978).
[CrossRef]

Washington 1951. J. Opt. Soc. Am. (1)

B. O’Brien, Untitled communication about the resolving power of the eye. “National Bureau Standard Symposium on Optical Image Evaluation” Washington 1951. J. Opt. Soc. Am. 42, 74 (1952).

Other (5)

M. A. Losada, “Influencia de la calidad óptica del ojo en la percepción espacial de contrastes umbrales,” Ph.D. dissertation (Universidad Complutense, Madrid, 1990).

D. G. Green, J. A. Swets, “Experimental techniques,” in Signal Detection Theory and Psychophysics (Krieger, New York, 1974), App. III, pp. 392–416.

Y. Le Grand, “La formation des images rétiniennes. Sur un mode de vision éliminant les défautes optiques de l’oeil,” C. R. Acad. Sci.200, 490 (1935). Referenced in Y. Le Grand, Optique Physiologique (Masson et CIE, Paris, 1972), Vol. III, p. 113.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), Chap. X, pp. 491–508.

Let us remember that it is unnecessary to divide the Maxwellian CSF by the MTF, since in a coherent imaging system the MTF takes only two values, either zero or unity, depending on whether the points of the spectrum do or do not pass through the pupil.

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 (18)

Fig. 1
Fig. 1

Apparatus used in the experiments. (a) Coherent imaging system. SF, spatial filter; P0, polarizer; D1 and D2, diaphragms. In the absence of the object, the lens L forms the image of the source point on the pupil plane Pu. When the object O is situated behind L, it is illuminated with directed light, and the lens then provides its Fourier spectrum on the pupil plane. An electronic shutter R controls the exposure time. (b) Two diffusers, S, are situated in front of the object. One is rotated by the motor M. Thus the object is now illuminated by incoherent diffused light, and it is observed through an artificial pupil Pu. The diaphragm D2 limits the object size to 1° of subtended angle. Obs, observer.

Fig. 2
Fig. 2

Illustration of the working of the coherent imaging system in Fig. 1(a). The lens L conveys the Fourier transform of the object O to the pupil plane Pu. The optics of the eye mediates between the pupil plane and the retinal image. Mathematically, a Fourier transform provides the object spectrum on the pupil plane, and the inverse Fourier transform of the spectrum provides the image on the retina.

Fig. 3
Fig. 3

Appearance of the gratings with the three kinds of illumination: (a) incoherent, (b) Maxwellian coherent, and (c) coherent diffuse.

Fig. 4
Fig. 4

Scheme showing the procedure for measuring the retinal illumination in Maxwellian vision (from Ref. 13).

Fig. 5
Fig. 5

(a) Coherent CSF determined with the apparatus shown in Fig. 1(a), with Maxwellian vision, 3-mm pupil diameter and 500 td retinal illumination. The mean difference between observers is 0.07 log unit. (b) Incoherent CSF determined in the same conditions of luminance and pupil as in (a) but with the apparatus shown in Fig. 1(b). The difference between observers is lower than 0.08 log unit. Here and in subsequent figures cpd stands for cycles/deg.

Fig. 6
Fig. 6

Maxwellian coherent CSF for three different retinal illuminations for observer AF, with 3-mm pupil diameter. The influence of the luminance on this CSF is apparent.

Fig. 7
Fig. 7

Comparison of the Maxwellian coherent CSF and the incoherent CSF at different levels of retinal illumination for observer AF. Only the curves at 1 td are in the proper vertical location. The curves at 100 and 500 td are shifted 1 log unit from each other.

Fig. 8
Fig. 8

Coherent CSF of observer AF with two different pupil diameters and 100 td retinal illumination.

Fig. 9
Fig. 9

CSF’s of different authors showing a concavity in the low-frequency range. The plotted points are as in the authors’ original papers, but the fitted curves have been modified in the actual figure. (a) The influence of the grating profile (square or sinusoidal) on the CSF’s shape is apparent. (b) All the curves were obtained with sinusoidal gratings, and the concavity is also obtained. Experimental conditions: (a) Campbell and Robson23: 2–10° field, 2.5-mm pupil diameter, 500 and 0.05 cd/m2 (2500 and 0.25 td), Lm (mean luminance) surround; (b) Losada26: 2.5° field, natural pupil, 20 cd/m2 (220td), dark surround; Patel27: 2°×4.6° field, 2-mm pupil, 100 td; Lm surround; Robson28: 2.5°×2.5° field, natural pupil, 20 cd/m2 (220 td); Lm surround; Fiorentini and Maffei25: 3° ×2.3° field, natural pupil, 10 cd/m2 (160 td), dark surround; Observer AF: 1° field, 3-mm pupil; 500 td, dark surround; Savoy and McCann29: 0.83° field, natural pupil, 9.3 cd/m2 (150 td), dark surround.

Fig. 10
Fig. 10

Maxwellian coherent CSF of observer AF and the neural CSF of several authors. Experimental conditions: Campbell and Green4: interference fringes, contrast varied by addition of incoherent light, 30° field, 500 td; Dressler and Rassow20: same as Ref. 4 but 5° field, 1000 td. Losada26: neural CSF derived from the CSF of the whole visual system and the eye’s MTF, 2.5° field, natural pupil; 20 cd/m2 (220 td); Williams5: interference fringes, contrast varied by changing the temporal overlap of the light beams, 1.5° field, 500 td; observer AF: grating imaged on the retina by a coherent imaging system, contrast varied with the fully coherent condition kept, 1° field, 100 td, 3-mm pupil diameter.

Fig. 11
Fig. 11

Coherent CSF’s measured with a square grating are compared with the same CSF’s when the contrast threshold value is corrected according to Eq. (B3). The difference between the pairs of curves is 4/π, that is, the difference between sensitivity with square and with sinusoidal gratings. Observer AF, 3-mm pupil diameter. The curves at 100 and 500 td are shifted in the vertical direction as in Fig. 7.

Fig. 12
Fig. 12

Ratio km of the incoherent CSF and the Maxwellian CSF. We have corrected both curves to compensate for the difference between the contrast of square and sinusoidal gratings (see explanation in the text). The curve km versus spatial frequency shows the effect of the coherent noise on the sensitivity of the whole visual system. Observer AF, 3-mm pupil diameter.

Fig. 13
Fig. 13

From the incoherent CSF’s (Fig. 7), and dividing by the MTF given by Eq. (5), one deduces the neural CSF’s without noise shown in this figure.

Fig. 14
Fig. 14

Neural CSF of Fig. 13 is compared with the Maxwellian coherent CSF (corrected as in Appendix B). Observer AF, 3-mm pupil diameter. The curves at 100 and 500 td are shifted in the vertical direction as in Fig. 7.

Fig. 15
Fig. 15

Ratio km of the neural and the Maxwellian sensitivities. The curve km versus spatial frequency shows a maximum at intermediate spatial frequencies. Observer AF, 3-mm pupil diameter.

Fig. 16
Fig. 16

CSF’s with the three kinds of illumination studied illustrate the influence of illumination on contrast sensitivity. Observer AF, 100 td, and 3-mm pupil diameter.

Fig. 17
Fig. 17

Comparison of the effect of speckle and the effect of coherent noise on neural sensitivity. Observer AF, 100 td, and 3-mm pupil diameter.

Fig. 18
Fig. 18

Intensity and amplitude profiles of the square grating.

Equations (17)

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

E=LAr2+d2.
ER=E(r2+d2).
EREd2.
fc(cycles/deg)=13.79d(mm).
km=incoherentsensitivityMaxwelliansensitivity.
km=neuralsensitivityMaxwelliansensitivity,
MTF(f)=0.72 exp(-0.16f)+0.28 exp(-0.05f),
ks=neutralCSF(withoutspeckle)neutralCSF(withspeckle)=CSF(incoherent)CSF(diffusecoherent)=ks.
A(x)=A0+noddAn cos(2πnfx),
A0=a+b-a2,An=2(-)(n-1)/2nπ(a-b).
a=a+(b-a)2[1-F],
b=a+(b-a)2[1+F],
C=b-ab+a.
n13.79d(mm)f(cycles/deg).
Cr=2A0A1A02+12noddAn2.
ηn=exp[-71×10-6f2(cycles/deg)].
Cr=2A0F1η1A1A02+12nodd(FnηnAn)2.

Metrics