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The Wells–Hering's laws of perceived egocentric visual direction (EVD) assume that information about eye position includes equal contributions from both eyes. An implication of this assumption is that only versional eye movements should lead to a change in perceived EVD. Previously, we showed that a differential weighting of eye-position information occurs in some individuals during asymmetric vergence. To extend this finding, we determined here whether a differential weighting of eye-position information occurs also during symmetric vergence eye movements. Open-loop pointing responses to a bright target were obtained in five subjects to estimate the contribution of each eye's position information to perceived EVD during symmetric vergence demands that ranged from 6 prism diopters base in to 18 prism diopters base out. In all five subjects, the slopes of the lines fit to the pointing responses were in the direction that was predicted from an unequal weighting of eye-position information. We conclude that symmetric vergence movements can result in a change in perceived visual direction, contrary to an assumption of the Wells–Hering's laws.

We examined Wheatstone's (1838 Philosophical Transactions of the Royal Society of London128 371–394) claim that images falling on retinally corresponding points can be seen in two different directions, in violation of Hering's law of identical visual direction. Our analyses showed that random-dot stereograms contain stimulus elements that are conceptually equivalent to the line stimuli in the stereogram from which Wheatstone made his claim. Our experiment demonstrated that two lines embedded in a random-dot stereogram appeared in two different directions when they stimulated retinally corresponding points, if the disparity gradient value of the lines was infinity relative to adjacent elements. To ensure that the two lines stimulated corresponding points, observers made vergence eye movements while maintaining the perception of the two lines in two different directions.

We have observed quantitative depth perception with a dichoptic stimulus which possessed no contrast-defined binocular corresponding features (phantom stereogram). The depth perception can be the result of appreciation of a partial-occlusion situation depicted by the stimulus, or the result of activities of low-level disparity detectors which are capable of combining dissimilar local features in the stimulus. Although both mechanisms predict similar depth perception, they predict different vergence eye-movement outputs, especially in the vertical dimension. To identify the underlying mechanisms of the phantom stereopsis, we recorded vergence tracking eye movements to four types of dichoptic stimuli: (a) conventional stereogram with horizontal disparity (HD); (b) horizontal phantom stereogram (HP); (c) conventional stereogram with vertical disparity (VD); and (d) vertical phantom stereogram (VP). We found that HD, HP, and VD stimuli could elicit robust vergence tracking eye movements but VP stimulus could not. While the success of HP stimulus in eliciting vergence tracking may be explained by proximal vergence, the failure of VP stimulus in eliciting vergence tracking clearly indicates that phantom stereogram could not elicit coherent responses among low-level disparity detectors. Partial occlusion, therefore, has to play an important role in the depth perception from the phantom stereogram.

Vergence responses were recorded from practised observers viewing narrow-band spatial-frequency-filtered planar random-dot stereograms. It was found that low spatial frequencies of 1·75–3·5 cycles deg−1 could trigger appropriate vergence responses to larger disparities than could the relatively high spatial frequency of 7·0 cycles deg−1. Nevertheless, appropriate vergence shifts were observed reliably for spatial-frequency/disparity combinations well outside the range predicted by Marr and Poggio's (1979) model of stereo vision. It was also found that for large-disparity/high-spatial-frequency combinations which the subjects could not fuse, the vergence system went into oscillation with the eyes diverging and converging at a frequency of about 1·5 Hz and with an amplitude of about 10–20 min arc. Finally, it was demonstrated that when a prominent monocular cue was superimposed upon a large-disparity/high-spatial-frequency stereogram then a speedy vergence response occurred which resulted in successful fusion. This latter finding supports the hypothesis advanced earlier that monocular cues can facilitate stereopsis by triggering appropriate vergence shifts.

It has usually been thought that the coupling between accommodation and convergence of the eyes is fixed and not modifiable by experience. Experiments are reported which show that the ratio of accommodative vergence to the accommodation stimulus, the stimulus AC/A ratio (one measure of the coupling), is elevated by brief periods (∼30 min) of experience of viewing the world through periscopic spectacles which increase the effective interocular separation. Experience of viewing through ‘cyclopean’ spectacles, which superimpose the line of sight of the two eyes, reduced the stimulus AC/A ratio in one subject and increased it in another, while it remained hardly affected in a third.