Abstract

Binocular summation was studied with two different hyperacuity tests, a bisection test and a vernier-type test. The summation factor differed between the two tests and depended on the test configuration. In the bisection test, binocular summation increased with decreasing line separation, and for the largest separation binocular inhibition was found. In the vernier test summation was essentially more constant for different separations. It is argued that, for a bisection test with a small intertarget distance, the hyperacuity thresholds involve a component of intensity discrimination that is due to overlapping retinal line-spread functions. An additional, unexplained finding was that in a vertically oriented three-dot alignment test the monocularly perceived alignment always occurred while the center dot was displaced toward the nasal side.

© 1989 Optical Society of America

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References

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  1. L. Frisén, B. Lindblom, “Binocular summation in humans: evidence for a hierarchic model,”J. Physiol. 402, 773–782 (1988).
    [PubMed]
  2. G. Westheimer, “Visual acuity and hyperacuity,” Invest. Ophthalmol. 14, 570–572 (1975).
    [PubMed]
  3. R. N. Berry, “Quantitative relations among vernier, real depth and stereoscopic depth acuities,”J. Exp. Psychol. 38, 708–721 (1948).
    [CrossRef] [PubMed]
  4. D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
    [CrossRef] [PubMed]
  5. F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,”J. Physiol. 186, 558–578 (1966).
    [PubMed]
  6. D. M. Levi, G. Westheimer, “Spatial-interval discrimination in the human fovea: what delimits the interval?” J. Opt. Soc. Am. A 4, 1304–1313 (1987).
    [CrossRef] [PubMed]
  7. G. E. Legge, “Binocular contrast summation. II. Quadratic summation,” Vision Res. 24, 385–394 (1984).
    [CrossRef]
  8. A. I. Cogan, “Human binocular interaction: towards a neural model,” Vision Res. 12, 2125–2139 (1987).
    [CrossRef]
  9. K. N. Ogle, Researches in Binocular Vision (Saunders, Philadelphia, Pa., 1950).
  10. G. K. von Noorden, Binocular Vision and Ocular Motility, 3rd ed. (Mosby, St. Louis, Mo., 1985).

1988 (1)

L. Frisén, B. Lindblom, “Binocular summation in humans: evidence for a hierarchic model,”J. Physiol. 402, 773–782 (1988).
[PubMed]

1987 (2)

1985 (1)

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

1984 (1)

G. E. Legge, “Binocular contrast summation. II. Quadratic summation,” Vision Res. 24, 385–394 (1984).
[CrossRef]

1975 (1)

G. Westheimer, “Visual acuity and hyperacuity,” Invest. Ophthalmol. 14, 570–572 (1975).
[PubMed]

1966 (1)

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

1948 (1)

R. N. Berry, “Quantitative relations among vernier, real depth and stereoscopic depth acuities,”J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

Aitsebaomo, A. P.

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

Berry, R. N.

R. N. Berry, “Quantitative relations among vernier, real depth and stereoscopic depth acuities,”J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

Campbell, F. W.

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

Cogan, A. I.

A. I. Cogan, “Human binocular interaction: towards a neural model,” Vision Res. 12, 2125–2139 (1987).
[CrossRef]

Frisén, L.

L. Frisén, B. Lindblom, “Binocular summation in humans: evidence for a hierarchic model,”J. Physiol. 402, 773–782 (1988).
[PubMed]

Gubisch, R. W.

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

Klein, S. A.

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

Legge, G. E.

G. E. Legge, “Binocular contrast summation. II. Quadratic summation,” Vision Res. 24, 385–394 (1984).
[CrossRef]

Levi, D. M.

D. M. Levi, G. Westheimer, “Spatial-interval discrimination in the human fovea: what delimits the interval?” J. Opt. Soc. Am. A 4, 1304–1313 (1987).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

Lindblom, B.

L. Frisén, B. Lindblom, “Binocular summation in humans: evidence for a hierarchic model,”J. Physiol. 402, 773–782 (1988).
[PubMed]

Ogle, K. N.

K. N. Ogle, Researches in Binocular Vision (Saunders, Philadelphia, Pa., 1950).

von Noorden, G. K.

G. K. von Noorden, Binocular Vision and Ocular Motility, 3rd ed. (Mosby, St. Louis, Mo., 1985).

Westheimer, G.

Invest. Ophthalmol. (1)

G. Westheimer, “Visual acuity and hyperacuity,” Invest. Ophthalmol. 14, 570–572 (1975).
[PubMed]

J. Exp. Psychol. (1)

R. N. Berry, “Quantitative relations among vernier, real depth and stereoscopic depth acuities,”J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. Physiol. (2)

L. Frisén, B. Lindblom, “Binocular summation in humans: evidence for a hierarchic model,”J. Physiol. 402, 773–782 (1988).
[PubMed]

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

Vision Res. (3)

G. E. Legge, “Binocular contrast summation. II. Quadratic summation,” Vision Res. 24, 385–394 (1984).
[CrossRef]

A. I. Cogan, “Human binocular interaction: towards a neural model,” Vision Res. 12, 2125–2139 (1987).
[CrossRef]

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

Other (2)

K. N. Ogle, Researches in Binocular Vision (Saunders, Philadelphia, Pa., 1950).

G. K. von Noorden, Binocular Vision and Ocular Motility, 3rd ed. (Mosby, St. Louis, Mo., 1985).

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Figures (3)

Fig. 1
Fig. 1

Graphic representation of the light distribution in the cross section of the retinal images of three bright lines with (a) large separation and (b) small separation. The three-line configuration with just-detectably unequal separations has been convoluted with the line-spread function of the eye.5 Note that in (a) the troughs between the peaks are approximately equal in depth, whereas with a small line separation, as in (b), the troughs are different.

Fig. 2
Fig. 2

Binocular summation in decibels in the bisection test (experiment 1) for different line separations. Binocular sensitivity was compared with (a) the best monocular sensitivity and (b) the expected value according to the quadratic summation theory. Insets show the test configuration and observer identification.

Fig. 3
Fig. 3

Binocular summation in decibels as measured with the three-dot test (experiment 2) for different line separations. Binocular sensitivity was compared with (a) the best monocular sensitivity and (b) the expected value according to the quadratic summation theory. Insets show the test configuration. For observer identification, see Fig. 2(a).

Tables (2)

Tables Icon

Table 1 Thresholds and Mean Values for the Bisection Test (Experiment 1) for Different Line Separations

Tables Icon

Table 2 Thresholds and Mean Values for the Three-Dot Test (Experiment 2) for Different Dot Separations

Equations (1)

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S B = ( S R + S L ) 1 / 2 ,

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