Abstract

The effects of Seidel aberrations (primary defocus, spherical aberration, astigmatism, and coma) were simulated on four images using a digital image-processing system. The tolerances of the human visual system to different levels and combinations of the aberration types were determined by a forced-choice discrimination technique. The resulting threshold levels, expressed in units of wavelength, specify the changes in wave-front aberration that can be detected with some defined probability and represent just-noticeable differences (JND’s) in image quality. The results are related to the corresponding Strehl intensity ratios and to the equivalent modulation transfer functions. The ultimate aim of the work is to link wave-front distortion to human visual discrimination, in order that meaningful methods of assessing visual image quality may be devised. The present investigation lays the foundations for further work, which, inter alia, will determine the effects of some higher-order aberrations.

© 1984 Optical Society of America

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References

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  1. M. K. Giles, “Aberration tolerances for visual optical systems,” J. Opt. Soc. Am. 67, 634–643 (1977).
    [CrossRef] [PubMed]
  2. P. Mouroulis, “On the correction of astigmatism and field curvature in telescopic systems,” Opt. Acta 29, 1133–1159 (1982).
    [CrossRef]
  3. G. J. Burton, N. D. Haig, “Criteria for testing of afocal visual instruments,” Proc. Soc. Photo-Opt. Instrum. Eng. 274, 191–201 (1981).
  4. J. Eggert, K. J. Rosenbruch, “Vergleich der visuell und der photoelektrisch gemessenen Abbildungsguete von Fernrohren,” Optik 48, 439–450 (1977).
  5. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. London 181, 576–593 (1965).
    [PubMed]
  6. W. K. Pratt, Digital Image Processing (Wiley, New York, 1978), Chap. 4.
  7. P. Davis, P. Rabinowitz, Numerical Integration (Blaisdell, Waltham, Mass., 1967), Chap. 2.
  8. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York1966).
  9. D. J. Finney, Probit Analysis (Cambridge U. Press, Cambridge, England, 1971).
  10. H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, England, 1950), Chap. 4.
  11. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974), Chap. 11.
  12. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).
  13. E. R. Kretzmer, “Statistics of television signals,” Bell Syst. Tech. J. 31, 751–763 (1952).
  14. J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image descriptors for displays,” RCA Labs, Princeton, N.J., Contract N00014-74-C-0184 (Feb.1977).
  15. G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967), pp. 562–563.
  16. H. Leibowitz, “The effect of pupil size on visual acuity for photometrically equated test fields at various levels of luminance,” J. Opt. Soc. Am. 42, 416–420 (1952).
    [CrossRef] [PubMed]
  17. J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [CrossRef] [PubMed]
  18. C. R. Carlson, A. Pica, “Invariance in sine wave contrast discrimination,” Suppl. Invest. Ophthalmol. Vis. Sci. (April1979), p. 61.
  19. G. J. Burton, “Contrast discrimination by the human visual system,” Biol. Cybernet. 40, 27–38 (1981).
    [CrossRef]
  20. G. E. Legge, J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
    [CrossRef] [PubMed]
  21. H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
    [CrossRef] [PubMed]
  22. A. B. Watson, “Summation of grating patches indicates many types of detector at one retinal location,” Vision Res. 22, 17–25 (1982).
    [CrossRef] [PubMed]
  23. D. Burr, “Sensitivity to spatial phase,” Vision Res. 20, 391–396 (1980).
    [CrossRef] [PubMed]
  24. G. J. Burton, I. R. Moorhead, “Visual form perception and the spatial phase transfer function,” J. Opt. Soc. Am. 71, 1056–1063 (1981).
    [CrossRef] [PubMed]
  25. T. Caelli, P. Bevan, “Visual sensitivity to two-dimensional spatial phase,” J. Opt. Soc. Am. 72, 1375–1381 (1982).
    [CrossRef] [PubMed]
  26. F. W. Campbell, J. Nachmias, J. Jukes, “Spatial-frequency discrimination in human vision,” J. Opt. Soc. Am. 60, 555–559 (1970).
    [CrossRef] [PubMed]
  27. J. Hirsch, R. Hylton, “Limits of spatial-frequency discrimination as evidence of neural interpolation,” J. Opt. Soc. Am. 72, 1367–1374 (1982).
    [CrossRef] [PubMed]
  28. W. N. Charman, A. Olin, “Image quality criteria for aerial camera systems,” Phot. Sci. Eng. 9, 385–397 (1965).
  29. H. L. Snyder, “Image quality and observer performance,” in Perception of Displayed Information, L. M. Biberman, ed. (Plenum, New York, 1973), Chap. 3.
    [CrossRef]
  30. S. W. Kuffler, “Discharge patterns and functional organization of mammalian retina,” J. Neurophysiol. 16, 37–68 (1953).
    [PubMed]
  31. D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. London 195, 215–243 (1968).
    [PubMed]
  32. D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s striate cortex,” J. Physiol. London 160, 106–154 (1962).
  33. C. Blakemore, J. Nachmias, “The orientation specificity of two visual after-effects,” J. Physiol. London 213, 157–174 (1971).
    [PubMed]
  34. G. J. Burton, K. H. Ruddock, “Visual adaptation to patterns containing two-dimensional spatial structure,” Vision Res. 18, 93–99 (1978).
    [CrossRef] [PubMed]
  35. C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. London 203, 237–260 (1969).
    [PubMed]
  36. W. N. Charman, H. Whitefoot, “Astigmatism, accommodation, and visual instrumentation,” Appl. Opt. 17, 3903–3910 (1978).
    [CrossRef] [PubMed]
  37. I. A. Newton, “Astigmatism and user performance,” unpublished APRE Memo. 43/75, UK Ministry of Defence (July1975).

1982 (4)

P. Mouroulis, “On the correction of astigmatism and field curvature in telescopic systems,” Opt. Acta 29, 1133–1159 (1982).
[CrossRef]

A. B. Watson, “Summation of grating patches indicates many types of detector at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef] [PubMed]

T. Caelli, P. Bevan, “Visual sensitivity to two-dimensional spatial phase,” J. Opt. Soc. Am. 72, 1375–1381 (1982).
[CrossRef] [PubMed]

J. Hirsch, R. Hylton, “Limits of spatial-frequency discrimination as evidence of neural interpolation,” J. Opt. Soc. Am. 72, 1367–1374 (1982).
[CrossRef] [PubMed]

1981 (3)

G. J. Burton, I. R. Moorhead, “Visual form perception and the spatial phase transfer function,” J. Opt. Soc. Am. 71, 1056–1063 (1981).
[CrossRef] [PubMed]

G. J. Burton, “Contrast discrimination by the human visual system,” Biol. Cybernet. 40, 27–38 (1981).
[CrossRef]

G. J. Burton, N. D. Haig, “Criteria for testing of afocal visual instruments,” Proc. Soc. Photo-Opt. Instrum. Eng. 274, 191–201 (1981).

1980 (2)

1979 (2)

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[CrossRef] [PubMed]

C. R. Carlson, A. Pica, “Invariance in sine wave contrast discrimination,” Suppl. Invest. Ophthalmol. Vis. Sci. (April1979), p. 61.

1978 (2)

G. J. Burton, K. H. Ruddock, “Visual adaptation to patterns containing two-dimensional spatial structure,” Vision Res. 18, 93–99 (1978).
[CrossRef] [PubMed]

W. N. Charman, H. Whitefoot, “Astigmatism, accommodation, and visual instrumentation,” Appl. Opt. 17, 3903–3910 (1978).
[CrossRef] [PubMed]

1977 (3)

J. Eggert, K. J. Rosenbruch, “Vergleich der visuell und der photoelektrisch gemessenen Abbildungsguete von Fernrohren,” Optik 48, 439–450 (1977).

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image descriptors for displays,” RCA Labs, Princeton, N.J., Contract N00014-74-C-0184 (Feb.1977).

M. K. Giles, “Aberration tolerances for visual optical systems,” J. Opt. Soc. Am. 67, 634–643 (1977).
[CrossRef] [PubMed]

1974 (1)

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

1971 (1)

C. Blakemore, J. Nachmias, “The orientation specificity of two visual after-effects,” J. Physiol. London 213, 157–174 (1971).
[PubMed]

1970 (1)

1969 (1)

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. London 203, 237–260 (1969).
[PubMed]

1968 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. London 195, 215–243 (1968).
[PubMed]

1965 (2)

W. N. Charman, A. Olin, “Image quality criteria for aerial camera systems,” Phot. Sci. Eng. 9, 385–397 (1965).

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

1962 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s striate cortex,” J. Physiol. London 160, 106–154 (1962).

1953 (1)

S. W. Kuffler, “Discharge patterns and functional organization of mammalian retina,” J. Neurophysiol. 16, 37–68 (1953).
[PubMed]

1952 (2)

Bergen, J. R.

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[CrossRef] [PubMed]

Bevan, P.

Blakemore, C.

C. Blakemore, J. Nachmias, “The orientation specificity of two visual after-effects,” J. Physiol. London 213, 157–174 (1971).
[PubMed]

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. London 203, 237–260 (1969).
[PubMed]

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

Burr, D.

D. Burr, “Sensitivity to spatial phase,” Vision Res. 20, 391–396 (1980).
[CrossRef] [PubMed]

Burton, G. J.

G. J. Burton, “Contrast discrimination by the human visual system,” Biol. Cybernet. 40, 27–38 (1981).
[CrossRef]

G. J. Burton, N. D. Haig, “Criteria for testing of afocal visual instruments,” Proc. Soc. Photo-Opt. Instrum. Eng. 274, 191–201 (1981).

G. J. Burton, I. R. Moorhead, “Visual form perception and the spatial phase transfer function,” J. Opt. Soc. Am. 71, 1056–1063 (1981).
[CrossRef] [PubMed]

G. J. Burton, K. H. Ruddock, “Visual adaptation to patterns containing two-dimensional spatial structure,” Vision Res. 18, 93–99 (1978).
[CrossRef] [PubMed]

Caelli, T.

Campbell, F. W.

F. W. Campbell, J. Nachmias, J. Jukes, “Spatial-frequency discrimination in human vision,” J. Opt. Soc. Am. 60, 555–559 (1970).
[CrossRef] [PubMed]

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. London 203, 237–260 (1969).
[PubMed]

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

Carlson, C. R.

C. R. Carlson, A. Pica, “Invariance in sine wave contrast discrimination,” Suppl. Invest. Ophthalmol. Vis. Sci. (April1979), p. 61.

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image descriptors for displays,” RCA Labs, Princeton, N.J., Contract N00014-74-C-0184 (Feb.1977).

Charman, W. N.

W. N. Charman, H. Whitefoot, “Astigmatism, accommodation, and visual instrumentation,” Appl. Opt. 17, 3903–3910 (1978).
[CrossRef] [PubMed]

W. N. Charman, A. Olin, “Image quality criteria for aerial camera systems,” Phot. Sci. Eng. 9, 385–397 (1965).

Cohen, R. W.

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image descriptors for displays,” RCA Labs, Princeton, N.J., Contract N00014-74-C-0184 (Feb.1977).

Davis, P.

P. Davis, P. Rabinowitz, Numerical Integration (Blaisdell, Waltham, Mass., 1967), Chap. 2.

Eggert, J.

J. Eggert, K. J. Rosenbruch, “Vergleich der visuell und der photoelektrisch gemessenen Abbildungsguete von Fernrohren,” Optik 48, 439–450 (1977).

Finney, D. J.

D. J. Finney, Probit Analysis (Cambridge U. Press, Cambridge, England, 1971).

Foley, J. M.

Giles, M. K.

Green, D. G.

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

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York1966).

Haig, N. D.

G. J. Burton, N. D. Haig, “Criteria for testing of afocal visual instruments,” Proc. Soc. Photo-Opt. Instrum. Eng. 274, 191–201 (1981).

Hirsch, J.

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, England, 1950), Chap. 4.

Hubel, D. H.

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. London 195, 215–243 (1968).
[PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s striate cortex,” J. Physiol. London 160, 106–154 (1962).

Hylton, R.

Jukes, J.

Kretzmer, E. R.

E. R. Kretzmer, “Statistics of television signals,” Bell Syst. Tech. J. 31, 751–763 (1952).

Kuffler, S. W.

S. W. Kuffler, “Discharge patterns and functional organization of mammalian retina,” J. Neurophysiol. 16, 37–68 (1953).
[PubMed]

Legge, G. E.

Leibowitz, H.

Mezrich, J. J.

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image descriptors for displays,” RCA Labs, Princeton, N.J., Contract N00014-74-C-0184 (Feb.1977).

Moorhead, I. R.

Mouroulis, P.

P. Mouroulis, “On the correction of astigmatism and field curvature in telescopic systems,” Opt. Acta 29, 1133–1159 (1982).
[CrossRef]

Nachmias, J.

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

C. Blakemore, J. Nachmias, “The orientation specificity of two visual after-effects,” J. Physiol. London 213, 157–174 (1971).
[PubMed]

F. W. Campbell, J. Nachmias, J. Jukes, “Spatial-frequency discrimination in human vision,” J. Opt. Soc. Am. 60, 555–559 (1970).
[CrossRef] [PubMed]

Newton, I. A.

I. A. Newton, “Astigmatism and user performance,” unpublished APRE Memo. 43/75, UK Ministry of Defence (July1975).

Olin, A.

W. N. Charman, A. Olin, “Image quality criteria for aerial camera systems,” Phot. Sci. Eng. 9, 385–397 (1965).

Pica, A.

C. R. Carlson, A. Pica, “Invariance in sine wave contrast discrimination,” Suppl. Invest. Ophthalmol. Vis. Sci. (April1979), p. 61.

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978), Chap. 4.

Rabinowitz, P.

P. Davis, P. Rabinowitz, Numerical Integration (Blaisdell, Waltham, Mass., 1967), Chap. 2.

Rosenbruch, K. J.

J. Eggert, K. J. Rosenbruch, “Vergleich der visuell und der photoelektrisch gemessenen Abbildungsguete von Fernrohren,” Optik 48, 439–450 (1977).

Ruddock, K. H.

G. J. Burton, K. H. Ruddock, “Visual adaptation to patterns containing two-dimensional spatial structure,” Vision Res. 18, 93–99 (1978).
[CrossRef] [PubMed]

Sansbury, R. V.

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

Snyder, H. L.

H. L. Snyder, “Image quality and observer performance,” in Perception of Displayed Information, L. M. Biberman, ed. (Plenum, New York, 1973), Chap. 3.
[CrossRef]

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967), pp. 562–563.

Swets, J. A.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York1966).

Watson, A. B.

A. B. Watson, “Summation of grating patches indicates many types of detector at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef] [PubMed]

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974), Chap. 11.

Whitefoot, H.

Wiesel, T. N.

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. London 195, 215–243 (1968).
[PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s striate cortex,” J. Physiol. London 160, 106–154 (1962).

Wilson, H. R.

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[CrossRef] [PubMed]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967), pp. 562–563.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

E. R. Kretzmer, “Statistics of television signals,” Bell Syst. Tech. J. 31, 751–763 (1952).

Biol. Cybernet. (1)

G. J. Burton, “Contrast discrimination by the human visual system,” Biol. Cybernet. 40, 27–38 (1981).
[CrossRef]

J. Neurophysiol. (1)

S. W. Kuffler, “Discharge patterns and functional organization of mammalian retina,” J. Neurophysiol. 16, 37–68 (1953).
[PubMed]

J. Opt. Soc. Am. (7)

J. Physiol. London (5)

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

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. London 195, 215–243 (1968).
[PubMed]

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s striate cortex,” J. Physiol. London 160, 106–154 (1962).

C. Blakemore, J. Nachmias, “The orientation specificity of two visual after-effects,” J. Physiol. London 213, 157–174 (1971).
[PubMed]

C. Blakemore, F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. London 203, 237–260 (1969).
[PubMed]

Opt. Acta (1)

P. Mouroulis, “On the correction of astigmatism and field curvature in telescopic systems,” Opt. Acta 29, 1133–1159 (1982).
[CrossRef]

Optik (1)

J. Eggert, K. J. Rosenbruch, “Vergleich der visuell und der photoelektrisch gemessenen Abbildungsguete von Fernrohren,” Optik 48, 439–450 (1977).

Phot. Sci. Eng. (1)

W. N. Charman, A. Olin, “Image quality criteria for aerial camera systems,” Phot. Sci. Eng. 9, 385–397 (1965).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

G. J. Burton, N. D. Haig, “Criteria for testing of afocal visual instruments,” Proc. Soc. Photo-Opt. Instrum. Eng. 274, 191–201 (1981).

RCA Labs, Princeton, N.J., Contract N00014-74-C-0184 (1)

J. J. Mezrich, C. R. Carlson, R. W. Cohen, “Image descriptors for displays,” RCA Labs, Princeton, N.J., Contract N00014-74-C-0184 (Feb.1977).

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

C. R. Carlson, A. Pica, “Invariance in sine wave contrast discrimination,” Suppl. Invest. Ophthalmol. Vis. Sci. (April1979), p. 61.

Vision Res. (5)

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
[CrossRef] [PubMed]

A. B. Watson, “Summation of grating patches indicates many types of detector at one retinal location,” Vision Res. 22, 17–25 (1982).
[CrossRef] [PubMed]

D. Burr, “Sensitivity to spatial phase,” Vision Res. 20, 391–396 (1980).
[CrossRef] [PubMed]

G. J. Burton, K. H. Ruddock, “Visual adaptation to patterns containing two-dimensional spatial structure,” Vision Res. 18, 93–99 (1978).
[CrossRef] [PubMed]

Other (10)

I. A. Newton, “Astigmatism and user performance,” unpublished APRE Memo. 43/75, UK Ministry of Defence (July1975).

H. L. Snyder, “Image quality and observer performance,” in Perception of Displayed Information, L. M. Biberman, ed. (Plenum, New York, 1973), Chap. 3.
[CrossRef]

G. Wyszecki, W. S. Stiles, Color Science (Wiley, New York, 1967), pp. 562–563.

W. K. Pratt, Digital Image Processing (Wiley, New York, 1978), Chap. 4.

P. Davis, P. Rabinowitz, Numerical Integration (Blaisdell, Waltham, Mass., 1967), Chap. 2.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York1966).

D. J. Finney, Probit Analysis (Cambridge U. Press, Cambridge, England, 1971).

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, England, 1950), Chap. 4.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974), Chap. 11.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J., 1974).

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Figures (12)

Fig. 1
Fig. 1

MTF’s determined by Campbell and Green5 are shown for different pupil diameters and for the diffraction limit by continuous lines. The dashed line gives the MTF determined by interpolation for a 1-mm pupil. As indicated by the arrow, the experiments were set up to fix the Nyquist limit for the visual display at the MTF cutoff spatial frequency. A scale is shown at the top of the figure giving spatial frequency in units of cycles/deg (appropriate only to a 2-mm pupil and a wavelength of 530 nm).

Fig. 2
Fig. 2

PSF’s are shown on an angular scale of minutes of arc for a 2-mm-diameter pupil and a wavelength of 530 nm. The dotted line (DIFF) describes the diffraction-limited PSF, and the continuous line (INV) shows the corresponding inverse spatial filter. The dashed line, DIFF ⊛ INV, gives the result of convolving the two PSF’s. Each function is normalized to the value of 1000 at the central peak.

Fig. 3
Fig. 3

Calibration functions are shown for the display system. (A) The relative spectral radiance distribution with the wavelengths for the peak and half-peak values. (B) Contrast versus gray-scale calibration (open circles) used for the aberration discrimination experiments. The filled circles show the low-contrast calibration used for the contrast threshold measurements. The gray-scale level, 135, that provides the background luminance is indicated in the figure. The continuous lines are the fitted calibration curves. (C) The system MTF’s (dashed lines), from the framestore to the monitor display, for modulation in the horizontal and vertical directions. The lower scale is in cycles/millimeter on the monitor face, and the upper scale shows the spatial frequency in terms of cycles/degree for the main viewing distance of 3.41 m. The diffraction-limited MTF for a 2-mm-diameter pupil is shown, for comparison, by the continuous line. The dotted line describes the composite MTF resulting from the product of the two MTF curves, marked DIFF and HORIZ.

Fig. 4
Fig. 4

The layout of comparison and aberrated targets within the framestore is shown for the VEHICLE. Method B, the inverse-filter technique, was used. The comparison targets, in the first and third columns, are denoted by the letter C. Numbers 0 to 7 show increasing levels of defocus from 0.0 to 0.7 wavelength in steps of 0.1. Note that in the experiments only one comparison and one aberrated target were visible at the center of the screen on a uniform background field. The figure must be viewed from a range of about 1 m in order to simulate the viewing conditions for the experiments. The maximum (negative) point contrast is 0.78. Note that the letters and numbers shown in the figure were not present during the experiments.

Fig. 5
Fig. 5

The four targets used in the experiments. In the order A to D, they are VEHICLE, COTTAGE, RANPAT, and DISC. In each case, the largest value of point contrast is ±0.78.

Fig. 6
Fig. 6

A comparison is shown of results obtained for defocus using four observers. Percent-correct responses are plotted against the simulated level of wave-front distortion in units of wavelength. The continuous line illustrates the probit curve-fitting procedure described in Section 4. Values at the 60, 75, and 90% points are indicated by dashed lines. The error bars indicate the 90% confidence limits.

Fig. 7
Fig. 7

Discrimination results are shown for defocus, spherical aberration, astigmatism, and coma. All four targets were used, values being indicated by open and filled circles for VEHICLE and COTTAGE and open and filled triangles for RANPAT and DISC. The results are for observer NDH. Interpolated values at the 60, 75, and 90% points are given in Table 1 together with the equivalent values for observer GJB. The dashed line in each panel shows the variation of the Strehl ratio as indicated by the ordinate scale at the right-hand side. Note the different abscissa scale for coma.

Fig. 8
Fig. 8

Through-focus data are shown for spherical aberration (W40) and astigmatism (W22). Results are given for two observers (upper and lower panels) and four targets. Values of the Strehl ratio are indicated by the dashed lines. Target symbols are as for Fig. 7.

Fig. 9
Fig. 9

The effects of different artificial pupil diameters on the results for defocus are shown for the RANPAT target. Values are given for the 60, 75, and 90% discrimination levels. A pupil diameter of 2 mm, indicated by the vertical dashed line, was used for the main part of the investigation.

Fig. 10
Fig. 10

Discrimination levels for defocus are shown for different values of the maximum (negative) point contrast in the VEHICLE target. Data are given for two observers. The target appearance for a maximum point contrast of −0.78 is illustrated in Fig. 4.

Fig. 11
Fig. 11

The histograms illustrate the effects on target discrimination of convolving the original target (ORIG) with the diffraction-limited filter (DIFF) and the inverse filter (INV) in various combinations. The filter functions, PSF’s, are shown in Fig. 2. The ordinate shows the percentage of times that the target in Column A of the inset was selected as being less “aberrated’ than that in Column B. The numbers 1–4 on the abscissa identify the pair of targets used for discrimination, as specified in the inset. Error bars show the 90% confidence limits.

Fig. 12
Fig. 12

MTF’s are shown corresponding to the 75% discrimination levels given in Table 2(A). The type of aberration appropriate to each curve is given in the legend. The bold continuous line denotes the diffraction-limited case. Error bars show typical standard errors derived from those given in Table 2(A). MTF values for astigmatism, W22, and coma, W31, were calculated for the azimuth angle (90°), which provides the lowest possible values.

Tables (2)

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Table 1 Values of Wave-Front Distortion, in Units of Wavelength, for All the Single-Aberration Types, Targets, and Observersa

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Table 2 (A) Mean Values of Wave-Front Aberration, Derived from Table 1, for Each Aberration Typea (B) Strehl Intensity Ratios and Standard Errors for Each Wave-Front Aberration Value Taken from Table 2(A)b

Equations (11)

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Aberrated target = target ABER
Comparison target = target DIFF .
Retinal aberrated target = target ABER DIFF = new target ABER
Retinal comparison target = target DIFF DIFF = new target DIFF ,
Aberrated target = target INV ABER
Comparison target = target INC DIFF .
Retinal aberrated target = target INV ABER DIFF = target ABER
Retinal comparison target = target INV DIFF DIFF = target DIFF .
P ( W ) = 0.5 + 0.5 2 π - ( W - W 0 ) / σ exp ( - Z 2 / 2 ) d Z ,
W ( r , θ ) = W 11 r sin θ + W 20 r 2 + W 40 r 4 + W 22 r 2 sin 2 θ + W 31 r 3 sin θ ,
D = 8 λ W · 10 - 3 / d 2 ,

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