Abstract

An afterimage method has been used to investigate the relative magnitudes of the nonmotor and motor components of the fusional response to vertical disparity in a complex visual stimulus of diameter 57° consisting of 50 horizontal lines and a square of side 2.5° in the middle. The largest vertical disparity that evokes a stable fusional response was found to be in the range 3–6°, of which the nonmotor component amounted only to 8–15′, i.e., 2–10% of the total. At these fusional amplitudes, binocular single vision was already disrupted in the foveola. When the 50 horizontal lines were omitted from the stimulus so that only the central square of side 2.5° remained, the fusional amplitudes decreased by only 25% while the absolute level of the nonmotor components remained the same. The nonmotor components found here are much smaller than those (amounting to about 2°, or 25–40% of the total response) reported recently in the literature.

© 1982 Optical Society of America

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References

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  1. A. E. Kertesz, “Effect of stimulus size on fusion and vergence,” J. Opt. Soc. Am. 71, 289–293 (1981).
    [Crossref] [PubMed]
  2. V. J. Ellerbrock, “Experimental investigation of vertical fusional movements,” Am. J. Optom. 26, 327–337 (1949).
    [Crossref]
  3. K. N. Ogle and A. de H. Prangen, “Observations on vertical divergences and hyperphorias,” Arch. Ophthalmol. 49, 313–334 (1953).
    [Crossref]
  4. F. W. Hebbard, “Comparison of subjective and objective measurements of fixation disparity,” J. Opt. Soc. Am. 52, 706–712 (1962).
    [Crossref]
  5. R. A. Crone and Y. Everhard-Halm, “Optically induced eye torsion,” Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 195, 231–239 (1975).
    [PubMed]
  6. A. L. Duwaer, G. van den Brink, G. van Antwerpen, and C. J. Keemink, “Comparison of subjective and objective measurement of ocular alignment in the vertical direction,” Vision Res. (to be published).
  7. L. A. Riggs and E. W. Niehl, “Eye movements recorded during convergence and divergence,” J. Opt. Soc. Am. 50, 913–920 (1960).
    [Crossref]
  8. K. N. Ogle, F. Mussey, and A. de H. Prangen, “Fixation disparity and the fusional processes in binocular single vision,” Am. J. Ophthalmol. 32, 1069–1087 (1949).
    [PubMed]
  9. A. L. Duwaer and G. van den Brink, “Foveal diplopia thresholds and fixation disparities,” Percept. Psychophys. 30, 321–329 (1982).
    [Crossref]
  10. D. Fender and B. Julesz, “Extension of Panum’s fusional area in binocular stabilized vision,” J. Opt. Soc. Am. 57, 819–830 (1967).
    [Crossref] [PubMed]
  11. Fender and Julesz10 reported an extension of foveal diplopia thresholds (for horizontal disparity) by an order of magnitude up to 1.1° for binocularly stabilized bars and up to 2° for binocularly stabilized random-dot patterns (with a hidden square of side 1.37° and a relative horizontal disparity of 8′). This result would suggest a major change in retinal correspondence. In an attempt to demonstrate changes in retinal correspondence directly by using afterimages, Flom and Eskridge12 found that retinal correspondence remained stable to within the visual resolving power. Diner13 replicated the experiments of Fender and Julesz for binocularly stabilized bars and failed to obtain foveal diplopia thresholds beyond the classical limit of 0.4°. Crone and Hardjowijoto14 determined fusional limits for nonstabilized random-dot patterns (with a hidden square of side 13° and a relative horizontal disparity of 90′) and found values exceeding 2°. These limits were, however, based on the disappearance of global stereoscopic depth in the hidden square and not on disruption of singleness of local stimulus features in the fovea. It is well known that stereoscopic depth can be perceived in the presence of image doubling and during monocular image suppression, especially when the stimulus is scanned with the eyes, as was done by the subjects in the study of Crone and Hardjowijoto.15–18 Their fusional limits therefore can not be interpreted as foveal diplopia thresholds. As a result, Kertesz’s findings seem to be the first confirmation of the results obtained by Fender and Julesz.
  12. M. C. Flom and J. B. Eskridge, “Change in retinal correspondence with viewing distance,” J. Am. Optom. Assoc. 39, 1094–1097 (1968).
    [PubMed]
  13. D. Diner, “Hysteresis in human binocular fusion: a second look,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1978).
  14. R. A. Crone and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47, 163–199 (1979).
    [Crossref] [PubMed]
  15. K. N. Ogle, “Precision and validity of stereoscopic depth perception from double images,” J. Opt. Soc. Am. 43, 906–913 (1953).
    [Crossref]
  16. G. Westheimer and I. J. Tanzman, “Qualitative depth localization with diplopic images,” J. Opt. Soc. Am. 46, 116–117 (1956).
    [Crossref] [PubMed]
  17. R. W. Reading, “The threshold of distance discrimination for objects located outside Panum’s area,” Am. J. Optom. 47, 99–105 (1970).
    [Crossref]
  18. J. Linschoten, “Strukturanalyse der binokularen tiefenwahrnehmung,” Ph.D. Thesis (University of Utrecht, Utrecht, The Netherlands, 1956).
  19. A. J. Duwaer, “Assessment of retinal image displacements during head movements using an afterimage method,” Vision Res. (to be published).
  20. R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, 1973).
  21. A. L. Duwaer and G. van den Brink, “What is the diplopia threshold?” Percept. Psychophys. 29, 295–309 (1981).
    [Crossref] [PubMed]

1982 (1)

A. L. Duwaer and G. van den Brink, “Foveal diplopia thresholds and fixation disparities,” Percept. Psychophys. 30, 321–329 (1982).
[Crossref]

1981 (2)

A. E. Kertesz, “Effect of stimulus size on fusion and vergence,” J. Opt. Soc. Am. 71, 289–293 (1981).
[Crossref] [PubMed]

A. L. Duwaer and G. van den Brink, “What is the diplopia threshold?” Percept. Psychophys. 29, 295–309 (1981).
[Crossref] [PubMed]

1979 (1)

R. A. Crone and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47, 163–199 (1979).
[Crossref] [PubMed]

1975 (1)

R. A. Crone and Y. Everhard-Halm, “Optically induced eye torsion,” Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 195, 231–239 (1975).
[PubMed]

1970 (1)

R. W. Reading, “The threshold of distance discrimination for objects located outside Panum’s area,” Am. J. Optom. 47, 99–105 (1970).
[Crossref]

1968 (1)

M. C. Flom and J. B. Eskridge, “Change in retinal correspondence with viewing distance,” J. Am. Optom. Assoc. 39, 1094–1097 (1968).
[PubMed]

1967 (1)

1962 (1)

1960 (1)

1956 (1)

1953 (2)

K. N. Ogle, “Precision and validity of stereoscopic depth perception from double images,” J. Opt. Soc. Am. 43, 906–913 (1953).
[Crossref]

K. N. Ogle and A. de H. Prangen, “Observations on vertical divergences and hyperphorias,” Arch. Ophthalmol. 49, 313–334 (1953).
[Crossref]

1949 (2)

V. J. Ellerbrock, “Experimental investigation of vertical fusional movements,” Am. J. Optom. 26, 327–337 (1949).
[Crossref]

K. N. Ogle, F. Mussey, and A. de H. Prangen, “Fixation disparity and the fusional processes in binocular single vision,” Am. J. Ophthalmol. 32, 1069–1087 (1949).
[PubMed]

Crone, R. A.

R. A. Crone and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47, 163–199 (1979).
[Crossref] [PubMed]

R. A. Crone and Y. Everhard-Halm, “Optically induced eye torsion,” Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 195, 231–239 (1975).
[PubMed]

Diner, D.

D. Diner, “Hysteresis in human binocular fusion: a second look,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1978).

Ditchburn, R. W.

R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, 1973).

Duwaer, A. J.

A. J. Duwaer, “Assessment of retinal image displacements during head movements using an afterimage method,” Vision Res. (to be published).

Duwaer, A. L.

A. L. Duwaer and G. van den Brink, “Foveal diplopia thresholds and fixation disparities,” Percept. Psychophys. 30, 321–329 (1982).
[Crossref]

A. L. Duwaer and G. van den Brink, “What is the diplopia threshold?” Percept. Psychophys. 29, 295–309 (1981).
[Crossref] [PubMed]

A. L. Duwaer, G. van den Brink, G. van Antwerpen, and C. J. Keemink, “Comparison of subjective and objective measurement of ocular alignment in the vertical direction,” Vision Res. (to be published).

Ellerbrock, V. J.

V. J. Ellerbrock, “Experimental investigation of vertical fusional movements,” Am. J. Optom. 26, 327–337 (1949).
[Crossref]

Eskridge, J. B.

M. C. Flom and J. B. Eskridge, “Change in retinal correspondence with viewing distance,” J. Am. Optom. Assoc. 39, 1094–1097 (1968).
[PubMed]

Everhard-Halm, Y.

R. A. Crone and Y. Everhard-Halm, “Optically induced eye torsion,” Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 195, 231–239 (1975).
[PubMed]

Fender, D.

Flom, M. C.

M. C. Flom and J. B. Eskridge, “Change in retinal correspondence with viewing distance,” J. Am. Optom. Assoc. 39, 1094–1097 (1968).
[PubMed]

Hardjowijoto, S.

R. A. Crone and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47, 163–199 (1979).
[Crossref] [PubMed]

Hebbard, F. W.

Julesz, B.

Keemink, C. J.

A. L. Duwaer, G. van den Brink, G. van Antwerpen, and C. J. Keemink, “Comparison of subjective and objective measurement of ocular alignment in the vertical direction,” Vision Res. (to be published).

Kertesz, A. E.

Linschoten, J.

J. Linschoten, “Strukturanalyse der binokularen tiefenwahrnehmung,” Ph.D. Thesis (University of Utrecht, Utrecht, The Netherlands, 1956).

Mussey, F.

K. N. Ogle, F. Mussey, and A. de H. Prangen, “Fixation disparity and the fusional processes in binocular single vision,” Am. J. Ophthalmol. 32, 1069–1087 (1949).
[PubMed]

Niehl, E. W.

Ogle, K. N.

K. N. Ogle, “Precision and validity of stereoscopic depth perception from double images,” J. Opt. Soc. Am. 43, 906–913 (1953).
[Crossref]

K. N. Ogle and A. de H. Prangen, “Observations on vertical divergences and hyperphorias,” Arch. Ophthalmol. 49, 313–334 (1953).
[Crossref]

K. N. Ogle, F. Mussey, and A. de H. Prangen, “Fixation disparity and the fusional processes in binocular single vision,” Am. J. Ophthalmol. 32, 1069–1087 (1949).
[PubMed]

Prangen, A. de H.

K. N. Ogle and A. de H. Prangen, “Observations on vertical divergences and hyperphorias,” Arch. Ophthalmol. 49, 313–334 (1953).
[Crossref]

K. N. Ogle, F. Mussey, and A. de H. Prangen, “Fixation disparity and the fusional processes in binocular single vision,” Am. J. Ophthalmol. 32, 1069–1087 (1949).
[PubMed]

Reading, R. W.

R. W. Reading, “The threshold of distance discrimination for objects located outside Panum’s area,” Am. J. Optom. 47, 99–105 (1970).
[Crossref]

Riggs, L. A.

Tanzman, I. J.

van Antwerpen, G.

A. L. Duwaer, G. van den Brink, G. van Antwerpen, and C. J. Keemink, “Comparison of subjective and objective measurement of ocular alignment in the vertical direction,” Vision Res. (to be published).

van den Brink, G.

A. L. Duwaer and G. van den Brink, “Foveal diplopia thresholds and fixation disparities,” Percept. Psychophys. 30, 321–329 (1982).
[Crossref]

A. L. Duwaer and G. van den Brink, “What is the diplopia threshold?” Percept. Psychophys. 29, 295–309 (1981).
[Crossref] [PubMed]

A. L. Duwaer, G. van den Brink, G. van Antwerpen, and C. J. Keemink, “Comparison of subjective and objective measurement of ocular alignment in the vertical direction,” Vision Res. (to be published).

Westheimer, G.

Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. (1)

R. A. Crone and Y. Everhard-Halm, “Optically induced eye torsion,” Albrecht von Graefes Arch. Klin. Exp. Ophthalmol. 195, 231–239 (1975).
[PubMed]

Am. J. Ophthalmol. (1)

K. N. Ogle, F. Mussey, and A. de H. Prangen, “Fixation disparity and the fusional processes in binocular single vision,” Am. J. Ophthalmol. 32, 1069–1087 (1949).
[PubMed]

Am. J. Optom. (2)

V. J. Ellerbrock, “Experimental investigation of vertical fusional movements,” Am. J. Optom. 26, 327–337 (1949).
[Crossref]

R. W. Reading, “The threshold of distance discrimination for objects located outside Panum’s area,” Am. J. Optom. 47, 99–105 (1970).
[Crossref]

Arch. Ophthalmol. (1)

K. N. Ogle and A. de H. Prangen, “Observations on vertical divergences and hyperphorias,” Arch. Ophthalmol. 49, 313–334 (1953).
[Crossref]

Doc. Ophthalmol. (1)

R. A. Crone and S. Hardjowijoto, “What is normal binocular vision?” Doc. Ophthalmol. 47, 163–199 (1979).
[Crossref] [PubMed]

J. Am. Optom. Assoc. (1)

M. C. Flom and J. B. Eskridge, “Change in retinal correspondence with viewing distance,” J. Am. Optom. Assoc. 39, 1094–1097 (1968).
[PubMed]

J. Opt. Soc. Am. (6)

Percept. Psychophys. (2)

A. L. Duwaer and G. van den Brink, “What is the diplopia threshold?” Percept. Psychophys. 29, 295–309 (1981).
[Crossref] [PubMed]

A. L. Duwaer and G. van den Brink, “Foveal diplopia thresholds and fixation disparities,” Percept. Psychophys. 30, 321–329 (1982).
[Crossref]

Other (6)

D. Diner, “Hysteresis in human binocular fusion: a second look,” Ph.D. Thesis (California Institute of Technology, Pasadena, Calif., 1978).

A. L. Duwaer, G. van den Brink, G. van Antwerpen, and C. J. Keemink, “Comparison of subjective and objective measurement of ocular alignment in the vertical direction,” Vision Res. (to be published).

Fender and Julesz10 reported an extension of foveal diplopia thresholds (for horizontal disparity) by an order of magnitude up to 1.1° for binocularly stabilized bars and up to 2° for binocularly stabilized random-dot patterns (with a hidden square of side 1.37° and a relative horizontal disparity of 8′). This result would suggest a major change in retinal correspondence. In an attempt to demonstrate changes in retinal correspondence directly by using afterimages, Flom and Eskridge12 found that retinal correspondence remained stable to within the visual resolving power. Diner13 replicated the experiments of Fender and Julesz for binocularly stabilized bars and failed to obtain foveal diplopia thresholds beyond the classical limit of 0.4°. Crone and Hardjowijoto14 determined fusional limits for nonstabilized random-dot patterns (with a hidden square of side 13° and a relative horizontal disparity of 90′) and found values exceeding 2°. These limits were, however, based on the disappearance of global stereoscopic depth in the hidden square and not on disruption of singleness of local stimulus features in the fovea. It is well known that stereoscopic depth can be perceived in the presence of image doubling and during monocular image suppression, especially when the stimulus is scanned with the eyes, as was done by the subjects in the study of Crone and Hardjowijoto.15–18 Their fusional limits therefore can not be interpreted as foveal diplopia thresholds. As a result, Kertesz’s findings seem to be the first confirmation of the results obtained by Fender and Julesz.

J. Linschoten, “Strukturanalyse der binokularen tiefenwahrnehmung,” Ph.D. Thesis (University of Utrecht, Utrecht, The Netherlands, 1956).

A. J. Duwaer, “Assessment of retinal image displacements during head movements using an afterimage method,” Vision Res. (to be published).

R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, 1973).

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Figures (6)

Fig. 1
Fig. 1

Schematic representation of the stimuli used in this study. The outer diameter of stimulus (a) was 57°. The square in the middle of stimulus (a) and the square in (b) were of sides 2.5° and had white disks of diameter 10′ at their centers. Stimulus in (a) is identical with that used by Kertesz.1

Fig. 2
Fig. 2

Schematic representation of the directions of the visual axis of the left and right eye (indicated by f1 and fr, respectively) and the positions of the fixation disk for (a) stimulus with vertical disparity and (b) stimulus without vertical disparity. The solid dots in (c) represent the afterimages of the fixation disk imprinted under conditions (a) (small dots) and (b) (large dots). The coordinates y1 and yr are estimated by the subject. The discrepancy (y1yr) is a measure of the fixation disparity introduced by the test disparity in the stimulus.

Fig. 3
Fig. 3

Estimated vertical disparity as a function of the physical relative vertical disparity, in scale units (one physical scale unit is 15′). The dotted line was fitted to the experimental data points by linear regression under the condition that it pass directly through the origin. (a) Results for subject ALD, (b) results for subject JvZ.

Fig. 4
Fig. 4

Fixation disparity (in minutes of arc) as a function of the vertical disparity (in degrees of arc) in the stimulus of Fig. 1(a) for (a) subject ALD and (b) subject JvZ. The length of the vertical bars through the experimental points is equal to twice the standard deviation (n = 10). The broken vertical bars represent the fusional amplitudes. Positive vertical disparities are disparities for which the stimulus presented to the right eye has a higher position than the stimulus presented to the left eye.

Fig. 5
Fig. 5

Fixation disparity (in minutes of arc) as a function of the vertical disparity (in degrees of arc) in the stimulus of Fig. 1(b). For further details see Fig. 4 caption.

Fig. 6
Fig. 6

Fixation disparity (in minutes of arc) as a function of the vertical disparity (in degrees of arc) in the stimulus of Fig. 1(a) but with the fixation disk deleted from the center of the square. For further details see Fig. 4 caption.

Tables (1)

Tables Icon

Table 1 Comparison of Fixation Disparities Obtained when the Subject’s Head is Supported by a Chin Rest and those Obtained when the Subject’s Head is Stabilized with a Bite Bar