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Stereo-thresholds: Simultaneity, target proximity and eye movements
0042-6989/91$3.00+ 0.00 Copyright 0 1991Pergmon Press plc
Vision Res. Vol. 31, No. 12, PP. 2093-2100,1991 Printed in Great Britain. All rights reserved
STEREO-THRESHOLDS: SIMULTANEITY, TARGET PROXIMITY AND EYE MOVEMENTS J. T. ENBIGHT Neurobiology
Unit, A-002, Scripps Institution of Oceanography,
La Jolla, CA 92093, U.S.A.
(Received 19 December 1990; in revised form 19 March 1991) Abstract-Stereo-thresholds are much higher when adjacent targets are presented without temporal overlap than when they are shown simultaneously. Sequentially presented adjacent targets also evoke small involuntary eye movements toward the newly presented target. Neither of these phenomena is evident with widely separated targets; for sequential presentation of targets lo” apart, stereo-thresholds are only slightly higher (a factor of about 1.5) than for simultaneous presentation; and stable fixation can be maintained. If the differing influence of simultaneity on stereoacuity for adjacent and for widely separated targets arises because adjacent alternating targets evoke eye movements, that effect is apparently not mediated exclusively by displacement of retinal images due to the measured eye movements. It could, however, be due to a general long-term instability of fixation associated with repetitive small involuntary eye movements. Stereopsis
Stereoacuity
Disparity
Eye movements
INTRODUCTION
In what is now a classical study, Westheimer (1979) characterized several of the factors that influence stereoacuity; and one of the central conclusions that he drew is that “good stereoacuity has as a prerequisite the simultaneous unencumbered view of at least a pair of targets” (Westheimer, 1979, p. 35 1, emphasis in original). Stereo-thresholds of experienced observers can be as low as 3-10 set arc for a pair of simultaneously presented targets; but if the two targets are presented without temporal overlap, thresholds are many-fold higher. Nevertheless, as Foley (1976) has shown, once targets have no temporal overlap, a dark interval of up to 100 msec can be interposed between their presentations with negligible additional effect on stereo-threshold; and with even further increase in duration of the inter-stimulus interval, threshold then increases only very gradually (Fig. 1). The dramatic and remarkable difference is between simultaneous presentationeven very brief temporal overlap will do-and sequential presentation. Experiments on stereoacuity, like those which led to the results shown in Fig. 1, usually involve adjacent targets, both seen in the fovea, where stereoacuity is best. Stereo-thresholds are considerably higher when one of the targets is
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imaged well outside the fovea (Ogle, 1950), and it turns out that the optimal viewing strategy for depth discrimination with such widely separated targets is not steady fixation-as for fovea1 stereopsis-but instead involves looking back and forth between the targets (Wright, 1951; Enright, 1990, 1991). A variety of evidence indicates that those discriminations are probably based upon sequential comparisons of foveally seen disparities (Enright, 1991). If sequential stimuli can be readily evaluated in that context, why is it that sequential presentation of targets so drastically degrades stereoacuity in other situations involving steady fixation (Fig. l)? The evidence presented here indicates that the discontinuity in threshold shown in Fig. 1 is a peculiar property of adjacent sequentially presented targets; and that such targets are associated with small systematic involuntary eye movements that may well contribute to degraded stereoacuity. METHODS
Stereopsis
For measures of stereoacuity, two small dimly illuminated targets were presented in a darkened room; one was a cross at 5 m distance, with arms about 30 min arc long by 1 min arc wide,
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L--+---l 500
250
ENRIGHT
I 0
TARGET OVERLAPMSEC
0
250
500
750
I 1000
TARGET SEPARATION: MSEC
Fig. 1. Stereo-thresholds as a function of temporal overlap or of temporal separation between a pair of targets. Data in left portion of graph from Westheimer (1979, Fig. 2); open symbols indicate stimuli 500 msec in duration; closed symbols were either IOOmsec in duration (GW) or 50msec in duration (SM). Data in right portion of graph from Foley (1976; Fig. 1). all with stimuli 100 msec in duration. Targets in both studies were adjacent to each other, separated horizontally by 10 min arc in Westheimer (1979) and separated vertically by 7 min arc in Foley (1976). Subjects in both graphs identified by initials adjacent to lines connecting same-subject data. Note the drastic increase in threshold, in left portion of graph, when temporal overlap was reduced lo zero.
and the other was a disk 30 min arc in dia, produced in the form of virtual images by the stimulus generator described in Enright (1989). That instrument consists of an opaque tube with a large lens (12.7 cm dia) across one end; a small circular light source inside the tube; and a partially transparent mirror, mounted at a 45” angle to the axis of the lens and tube, from which the virtual images of the luminous disk (produced by the light source) are reflected to each eye of the observer and through which the background (in this case. the illuminated cross) can be seen. The observer can alter perceived distance to the disk by making small displacements of the light source within the stimulus generator, thereby changing the effective disparity between the left-eye and right-eye virtual images. For these experiments, the intensity of the light source in the original instrument was reduced to produce target luminance of about 1 cd/m2, and apparent brightness of the cross was matched to that of the disk. The subject’s task was to adjust the perceived distance of the disk to match that of the cross. The cross was located either just to the right of the disk (“adjacent”: separation of 20-30 min arc) or at 10” farther to the right. In the primary
experiments, two schedules of target presentation were utilized: “simultaneous” viewing, in which the disk was continuously visible and the cross was lit for 500 msec, extinguished for 1000 msec and then relit for 500 msec, in steady repetition; and “alternating” exposure. in which the disk was lit for 1000 msec, then extinguished for 500 msec during which time the cross was lit, followed by re-illumination of the disk (Fig. 2). In the subsequent control experiments, which used only adjacent targets, the disk was illuminated for 1000 msec in cycles of 2.5 set duration; and the cross was lit either for the last 100 msec during which the disk was visible (simultaneous viewing), or with onset coincident with offset of the disk (alternating exposure). Stimulus timing was controlled by a Grass Stimulator, Model 88, which activated microswitches. For all target arrangements, the subject was instructed to fixate steadily on the disk (or its location, during those intervals when it was not lit) while making the adjustments of apparent distance. Each subject made two sets of 6 adjustments to apparent equidistance for a given target spacing, both with simultaneous-viewing and with alternating-exposure protocols, in a single test session. Each adjustment was typically completed within less than 30 set, but no time limit SIMULTANEOUS TARGETS
I_
R
TARGET
ALTERNATING TARGETS
VIDEO MEASURES
L
R
TARGET
Fig. 2. Temporal schedule for target exposure and for vtdeo fields utilized in main experimental protocol. Lines above I. and R indicate times that the left-hand and rtght-hand targets, respectively, were visible; (A), (B) and (C) indicate blocks or 3 video fields, separated by 50 msec. in which eye position was measured, and then averaged, within each stimulus cycle.
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was imposed. Displacement of the light in the stimulus generator was converted to resultant disparity (1 mm = 2 min arc); and the SDS of these sets of 6 values are taken as measures of stereo-threshold. Reliability of the estimates of threshold (SE) was determined from the duplicate sets of measurements of a single test session. The 3 subjects are male emmetropes with no known oculomotor anomalies. Subjects 1 and 2, aged 14 and 29, have had extensive prior experience with measures of stereoacuity using this instrument; Subject 3 (whose settings were most variable) is 29 years old and had little prior practice. All subjects were uninformed about the purpose of the testing. Eye movement Eye orientation was monitored using the video-recording system described in Enright (1984) supplemented by a frame-counter, which numbers each video field. Precision of a single measurement, based on reproducibility of replicated “blind” readings, is on the order of 4-6 min arc (SD). The targets were two light-emitting diodes (LEDs) presented at 3 m distance, either laterally adjacent (separated by 20 min arc) or 10” apart horizontally. The room lights were extinguished during measurement. Video recording required that narrow light beams from two lamps be aimed at the eyes; the lamps and video cameras were well below the line of sight to the LED-targets, which were then visible only when lit, in an otherwise darkened field. Timing of target illumination was in 150&msec cycles, corresponded exactly to that used for evaluations of stereo-threshold in the primary experiments (Fig. 2). Eye orientation was evaluated for 10 sequential cycles of target presentation, for both target spacings and for both illumination protocols. For each cycle, the horizontal position of each eye was evaluated in 9 video fields, centered around 3 times: 150 msec before the right-hand target was illuminated; 500 msec thereafter (150 msec before the right-hand target was extinguished); and 500 msec later (when the right-hand target had been off again for 350 msec). Around each of those times, sets of 3 video fields, separated by 50 msec, were measured (t - 50 msec; t; and t + 50 msec), and those 3 values were averaged (Fig. 2). Absolute values of change in eye position were derived from two differences per stimulus cycle (I A - B I and I B - C 1,in Fig. 2). Any systematic changes in eye orientation were estimated by
subtracting the average position value obtained while the right-hand target was lit from the of the position values obtained average 500 msec earlier and 500 msec later, i.e. B -(A+C)/2, in Fig. 2. The experimental arrangement of the eye movement measurements was designed to duplicate in its essential features the procedures used in measurements of stereo-threshold. In both sets of experiments, the same subjects participated, and in both cases, small self-luminous targets were presented in a darkened surround, with the same lateral spacing and timing of presentation; target distances were also similar (5 and 3 m). In both cases, the subject was instructed to fixate as steadily as possible on the left-hand target (or its location, when it was not lit); and head stability of the subjects was maintained by bite boards. Nevertheless, completely identical situations were not achieved; the room was completely darkened except for the targets, during threshold measurements, to exclude the possibility that peripheral objects might affect distance judgments, but video monitoring of eye position requires illumination of the eyes. Furthermore, the mirror of the stimulus generator used for stereopsis testing would have fully obstructed the video cameras’ views of the eyes. Hence, during measurements of eye movements, although the illuminated targets were seen in a darkened surround, as in the stereo testing, the lower portion of the visual field included the video cameras and the lamps, located about 15” below the line of sight. The possibility that this difference in conditions might have had an important effect on eye movements will be subsequently considered (Discussion). RESULTS
Stereo-thresholds The estimates of threshold, with SEs, are summarized in Fig. 3, where it is evident that for adjacent targets, alternating exposure resulted in a many-fold increase in threshold, as previously documented by Westheimer (1979; see data in Fig. 1); that thresholds for simultaneously seen targets were considerably higher when the targets were widely separated (as previously reported by Ogle, 1950, among others); and that for widely separated targets, sequential presentation only slightly increased threshold, relative to the same-subject values measured during simultaneous presentation ratio (mean across subjects = 1.5; range
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J. T. ENRIGHT TARGETS
TARGETS
ADJACENT
10’ APART
c
I
500
OVERLAP: MSEC
0
OVERLAP: MSEC
Fig. 3. Stereo-thresholds of 3 subjects, measured for adjacent targets, and for targets lo” apart, either with temporal overlap or without overlap (sequential presentation). (See Fig. 2 for stimulus timing.) Note the drastic increase in threshold when adjacent targets were presented without temporal overlap; and the very much smaller influence of temporal overlap with widely separated targets. Vertical bars attached to data points represent & SE, based on duplicate estimates of threshold. Same-subject values connected by diagonal lines, with subject number adjacent to line.
1.3e1.65). While thresholds are typically compared in terms of a ratio (hence, the logarithmic ordinate in Fig. 3), one can also inquire about the absolute magnitude of the change in threshold due to non-simultaneity of targets; even in this comparison, all 3 subjects showed lesser increase in threshold for the widely-separated targets than for adjacent targets, although this contrast was not statistically significant.
One aspect of the eye movement data is presented in Fig. 4; for each eye of the 3 subjects, the mean absolute value of change in eye orientation between measurements sets (separated by 500 msec) was calculated, for both target spacings and for both simultaneous and sequential presentations. Twenty-one of the 24 values in Fig. 4 are between 3 and 8 min arc: sufficiently similar to each other to suggest that fixation was relatively steady and that most of those calculated changes in eye position were due to random measurement error. The other 3 values are roughly twice as large, and those outliers all involved measurements of the right eye during sequential presentation of adjacent targets. These data, then. represent an objective correlate of the subjective impression that fixation was difficult to maintain, when adjacent targets were presented in alternation. The data in Fig. 4 do not, however, distinguish between the possibility that eye movements arose in directions that were random in timing and direction, relative to target visibility, and the alternative, that they were systematically related to target presentation. In parts (A) and (B) of Table 1, the data are summarized in terms of version and vergence components that dependend upon target exposure. During alternating presentation of adjacent targets, small involuntary versional movements arose, which were consistently
Eye movements When, during estimates of stereo-threshold, the two targets were adjacent and presented in alternation, the subjective impression was that steady fixation was very difficult to maintain: once the fixation target had been extinguished, the newly visible adjacent target seemed inescapably to attract the eyes. The measurements of eye orientation were undertaken to determine whether this subjective impression has objective counterpart, or was illusory. As in the stereo-threshold measurements, the subjects were instructed to fixate steadily on the location of the left-hand target (which was either continuously illuminated, or lit for 1000 out of each 1500 msec); and the LED targets were either 20 min arc apart, or 10” apart.
MEAN ABSOLUTE VALUE OF CHANQES IN ORIENTATION: MINUTES OF ARC
Fig. 4. Average absolute values of change in eye orientation for targets separated by either 20 min arc or 10 deg, and presented either synchronously or in alternation. (See Fig. 2 for timing of target presentation relative to times of measurement.) Average for each eye of each of 3 subjects calculated separately over 10 cycles of stimulus presentation (20 changes in position per value). Unshaded area: left-eye values, regardless of target configuration; solid shading: right-eye values for adjacent targets, presented in alternation; cross-hatched: right-eye values for adjacent simultaneous targets, and for all targets at lo-deg spacing, either adjacent or simultaneous. Note that the three “outliers” represent only the right-eye measurements, from all 3 subjects, obtained for adjacent targets, presented irl alternation
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Stereo-thresholds Table 1. (A) Systematic changes in version (min arc*) Targets 10” apart
Adjacent targets 500 msec overlap
No overlap
500 msec overlap
No overlap
NS NS NS
8.0 f 2.05 6.6 f 2.19 5.9 f 2.53
NS NS NS
NS NS NS
Subject 1 Subject 2 Subject 3
Table 1. (B) Systematic changes in vergence (mitt arct) Targets 10” apart
Adjacent targets 500 msec overlap
No overlap
500 msec overlap
No overlap
NS NS NS
3.3 * 1.66 10.0 + 1.68 9.0 + 2.25
NS NS NS
NS NS 4.6 f 1.26
Subject 1 Subject 2 Subject 3
Table 1. (C) Constituents Target Adjacent, Adjacent, Adjacent, 10” apart,
sequential sequential sequential sequential
of significant vergence changes1 (min arc)
Subject
Right eye
Left eye
Total
1 2 3 3
9.7 11.7 10.5 3.1
-6.4 -1.7 -1.4 1.0
3.3 10.0 9.0 4.6
NS: Not significant (all probability values > 0.10). *Positive values for versional change represent movement toward right-hand target during 500 msec interval during which it was illuminated: mean f SE, N = 10. TPositive values for vergencc change represent divergence during 500 msec interval during which right-hand target was illuminated mean + SE, N = 10. IBreakdown of data tabulated in part (B).
directed toward that target which was illuminated, a result that comports with subjective impressions; surprisingly, however, all 3 subjects also showed consistent vergence changes, when adjacent targets were presented in alternation. As indicated in part (C) of
Table 1, the vergence changes arose because the right eye moved farther rightward, during the 500 msec that the target on the right was visible, than did the left eye; and for Subjects 2 and 3, that asymmetry was quite extreme.
Table 2. Effects of target duration and simultaneity on stereo-threshold 500 msec Target exposure* Subject 1 2 G& SMS
Synchronous viewing
Sequential viewing
10.4 15.5 25.2 11.3 4.5 Average f SE
38.0 141 288 47.1 40.5
Ratio 3.7 9.1 11.4 4.2 9.0 7.48 f 1.51
(set arc)
100 msec Target exposuret Synchronous viewing 29.3 54.3 85.4 14.9 6.4
Sequential viewing 58.9 162 312 52.1 21.9
Ratio 2.0 3.0 3.7 3.5 3.4 3.11 f0.30
r-test of ratios (variances not assumed equal): rs = 2.84, P = 0.021. (similar t-test of log-transformed ratios: fg = 3.16, P = 0.014). *For synchronous viewing by Subjects 1,2 and 3, one target was continuously lit and the other switched on for 500 msec in cycles of 1500 msec duration; and for sequential viewing, one target was lit for 1000 msec and the other was lit thereafter for 500 msec (1500 msec cycles). For Subjects GW and SM (data from Westheimer, 1979, Fig. 2), each target was lit for 500 msec, either simultaneously or sequentially. tFor synchronous viewing by Subjects 1, 2 and 3, one target was lit for 1000 mm-c, in cycles of 2.5 set duration, and the other was lit during the final 100 msec of the illumination of the first target; for sequential viewing, one target was again lit for 1000 msec, in cycles of 2.5 set duration, and the other was lit for 100 msec immediately after the first had been extinguished. For Subjects GW and SM, (data from Westheimer, 1979, Fig. 2), each target was lit for 100 msec (or 50 msec, for SM), either simultaneously or sequentially. $Since thresholds for Subjects l-3 were calculated as SD from replicated adjustments to apparent equidistance, inter-subject comparisons would require that the threshold values tabulated for GW and SM, which were estimated from probit analysis (75% correct criterion), be increased by about 50%.
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J. T. ENRIGHT
with very brief target exposure
If the degradation of stereoacuity that arose when adjacent targets were presented sequentially (Fig. 3) were to be due to unpredictable displacement of retinal images associated with eye movements like those measured here (Table l), then this effect should be absent when adjacent sequential targets are presented very briefly, so that any eye movement triggered by the target exposure would occur only after both targets have been extinguished. Experiments with brief target exposure that were reported by Westheimer (1979) seem to contradict this expectation; and control experiments conducted with the 3 subjects here gave a similar result. In these tests, one of the targets was visible for 1000 msec and the other was lit for 100 msec, either just before the first target was extinguished, or immediately after it had been extinguished. The thresholds measured in these experiments are compared with those from longer-duration target exposure in Table 2, together with data obtained from similar target presentations by Westheimer (1979). Threshold for simultaneously seen targets was somewhat higher with briefly presented targets than with 500msec exposure (column 5 vs column 2); but even with brief target visibility, sequential presentation seriously degraded stereoacuity (column 6 vs column 5). Note, however. that the contrast between simultaneous presentation and sequential presentation was considerably less extreme with brief target exposure (ratios: column 7 vs column 4); to this extent, then, the results partially confirm--but only partially-the prediction that the experiments were designed to test. DISCUSSION
The data summarized in Fig. 3 demonstrate that while good stereoacuity~for adjacent targets requires a simultaneous view of both targets, the deterioration in acuity with non-simultaneous presentation is much less extreme when the targets are widely separated: stereoacuity outside the fovea (which is already relatively poor) is only slightly further degraded by sequential target presentation. (See McKee, Welch, Taylor & Bowne, 1990, Fig. 7, for qualitatively similar results.) The broader implication of this distinction is that simultaneous stimuli from a target pair are not as critical for cortical processing of disparity information as one might presume on the basis only of foveally presented targets.
The data summarized in Fig. 4 and Table I demonstrate that when adjacent targets in an empty surround are exposed sequentially, it is difficult if not impossible to maintain steady fixation. It is conceivable that with appropriate training, such eye movements could be suppressed, but certainly for these subjects, binocular fixation was considerably less stable during alternating presentation of adjacent targets than when one of the targets was continuously visible. With widely separated targets, however, only one of the subjects showed significantly less stable fixation during sequential presentation (a small vergence movement) that during simultaneous presentation. Because the eye movements that were associated with target alternation included a versional component that “followed” target visibility [Table l(A)], despite instructions not to move the eyes, the suspicion arises that this sort of target configuration may trigger the onset of an involuntary “pursuit” reflex. The systematic vergence component of the eye movements. however, was unexpected; it is not explainable by considerations of phoria, and only an ad hoc interpretation can be proposed: perhaps there is a small systematic departure from congruence between the binocular mapping of disparity in the cortex that underlies stereopsis, and the binocular mapping in the colliculus that underlies eye movements. The measurements of eye movement were undertaken because of the strong subjective impression, during stereo-testing, that when adjacent targets were presented in alternation, fixation was very difficult to maintain: the eyes seemed to be strongly and involuntarily drawn to a new target, if it suddenly appeared at the time that the nearby fixation point vanished. The data in Fig. 4 and Table 1 demonstrate that this subjective impression-which was also evident during the eye movement tests-has objective correlates: the subjects’ eyes did indeed tend to make small movements toward newly illuminated targets, despite instructions to maintain fixation as stably as possible. Nevertheless, because the eye movement tests involved visible objects (cameras and lighting sources) in the extreme lower portion of the visual field, and the stereo tests were conducted in an otherwise totally darkened room, considerable uncertainty would be involved in presuming that entirely comparable eye movements would have arisen during measurements of stereo threshold. 1f the
Stereo-thresholds presence of continuously visible objects in the periphery of the visual field during eye movement monitoring were indeed to affect the likelihood of involuntary eye movements, the direction of such an effect might well be toward greater stability of fixation (rather than greater instability), when compared with target alternations in complete darkness. The vergence changes documented in Table l(B) provide a possible basis for deciding whether comparison of the two sorts of experiment is justified. Note that when the righthand adjacent target was illuminated by itself (500 msec out of every 1500 msec), there was a strong tendency for it to be seen with divergence, relative to the eye orientation for the lefthand target. If comparable vergence changes were to occur during attempts to adjust two adjacent targets to equidistance, when they are illuminated in alternation, one should expect biased distance perception, relative to simultaneous presentation: differences in mean setting, independent of any effect on threshold (which is measured by variability of the settings about their mean). An examination of the data which led to the stereo-threshold values summarized in Fig. 3 indicates that this expectation is at least partially fulfilled: Subjects 2 and 3 showed the largest vergence changes in Table 1 (adjacent targets, alternately exposed), and those two subjects also showed statistically significant biases in judgments of apparent equidistance for adjacent targets, when values for simultaneously visible targets are compared with those for alternately exposed targets. In both bases, adjustment to apparent equidistance involved greater convergence for the left-hand target when both were seen simultaneously than when targets were presented in alternation: mean differences were 5.0 min arc ( &-0.67 min arc, SE) and 11,l min arc (L- 1.77 min arc, SE) for Subjects 2 and 3, respectively. None of the 4 other comparisons between simultaneous and alternatingly lit targets involved statistically significant biases in mean distance settings. Hence, this correlation provides modest indirect support for generalizing the data from the eye movement experiments to other situations like that in which stereo-thresholds were evaluated. At the least, it seems evident that if an effect of this sort had not been evident, there would be strong reason to suspect that the measurements of eye orientation and of performance at stereopsis were in some way fundamentally not comparable.
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The association of involuntary eye movements with that situation in which stereoacuity is seriously degraded raises the possibility that there may be a causal connection. Does unpredictable displacement of retinal images, occasioned by those eye movements, explain the drastic decrease in stereoacuity when adjacent targets are not simultaneously visible? The brief target exposure control tests summarized in Table 2 were undertaken to examine this possibility, and those results show: (1) that when eye movements directly triggered by target exposure could not result in image displacement, sequential presentation of adjacent targets nevertheless seriously degrades stereoacuity (by a factor of 3.1, on average); but (2) that this effect is smaller than with longer-duration views of the targets (a factor of 3.1 vs a factor of 7.5). The latter result can be interpreted as reflecting the absence, with briefly exposed targets, of variability in the placement of retinal images occasioned by the sort of eye movements documented in Table 1. These experiments suggest, then, that image displacement due to the measured eye movements may well explain part-but only part-of the drastic increase in stereothreshold, when adjacent targets are illuminated sequentially. It is conceivable, however, that even when target-triggered involuntary eye movements occur after the targets have been extinguished, they might nevertheless degrade stereoacuity; they might, for example, contribute to a general long-term instability of fixation. Measurement of torsional orientation in the aftermath of larger saccades (4”-8” in excursion) has shown that a single saccade can consistently influence torsional eye orientation to an extent that persists for several seconds (Enright, 1986); that sort of effect lends support to the speculation that repetitive smaller eye movements, as measured here, might produce long-term instability of fixation. Another possibility, however, is that the residual 3-fold difference in stereo-threshold, as documented in Table 2, when adjacent targets are briefly and sequentially presented, has nothing to do with eye movements. Hence, while it remains tempting to propose that with widely separated targets, non-simultaneity of presentation has a minimal effect on stereo-threshold (Fig. 3) because fixation can be more stably maintained (Table I), that hypothesis is by no means firmly established.
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Acknowledgements-This
research was supported by grant BNS 89-05401 from the National Science Foundation. Comments on the manuscript by Dr G. Westheimer and an anonymous reviewer are gratefully acknowledged.
REFERENCES Emight, J. T. (1984). Changes in vergence mediated by saccades. Journal of Physiology, 350, 9-3 1. Enright, J. T. (1986). The aftermath of horizontal saccades: Saccadic retraction and cyclotorsion. Vision Research, 26, 1807-1814.
Enright, J. T. (1989). Manipulating stereopsis and vergence in an outdoor setting: Moon, sky and horizon. Vision Research,
29, 1815-1824.
Enright, J. T. (1990). When stereopsis is not good enough.
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Enright, J. T. (1991). Exploring the third dimension with eye movements: Better than stereopsis. Vision Research, 31, 1549-1562. Foley, J. M. (1976). Successive stereo and vernier position discrimination as a function of dark interval duration” Vision Research, 16, 1269-1273. McKee, S. P., Welch, L., Taylor, D. G. & Bowne, S. F. (1990). Finding the common bond: Stereoacuity and other hyperacuities. Vision Research, 30, 879891. Ogle, K. N. (1950). Researches in binocular vision. Philadelphia: Saunders. Westheimer, G. (1979). Cooperative neural processes involved in stereoscopic acuity. Experimental Brain Research, 36, 585-597.
Wright, W. D. (1951). The role of convergence in stereoscopic vision. Proceedings of the Physical Society, Section B, 64, 289-297.
Vision Res. Vol. 31, No. 12, PP. 2093-2100,1991 Printed in Great Britain. All rights reserved
STEREO-THRESHOLDS: SIMULTANEITY, TARGET PROXIMITY AND EYE MOVEMENTS J. T. ENBIGHT Neurobiology
Unit, A-002, Scripps Institution of Oceanography,
La Jolla, CA 92093, U.S.A.
(Received 19 December 1990; in revised form 19 March 1991) Abstract-Stereo-thresholds are much higher when adjacent targets are presented without temporal overlap than when they are shown simultaneously. Sequentially presented adjacent targets also evoke small involuntary eye movements toward the newly presented target. Neither of these phenomena is evident with widely separated targets; for sequential presentation of targets lo” apart, stereo-thresholds are only slightly higher (a factor of about 1.5) than for simultaneous presentation; and stable fixation can be maintained. If the differing influence of simultaneity on stereoacuity for adjacent and for widely separated targets arises because adjacent alternating targets evoke eye movements, that effect is apparently not mediated exclusively by displacement of retinal images due to the measured eye movements. It could, however, be due to a general long-term instability of fixation associated with repetitive small involuntary eye movements. Stereopsis
Stereoacuity
Disparity
Eye movements
INTRODUCTION
In what is now a classical study, Westheimer (1979) characterized several of the factors that influence stereoacuity; and one of the central conclusions that he drew is that “good stereoacuity has as a prerequisite the simultaneous unencumbered view of at least a pair of targets” (Westheimer, 1979, p. 35 1, emphasis in original). Stereo-thresholds of experienced observers can be as low as 3-10 set arc for a pair of simultaneously presented targets; but if the two targets are presented without temporal overlap, thresholds are many-fold higher. Nevertheless, as Foley (1976) has shown, once targets have no temporal overlap, a dark interval of up to 100 msec can be interposed between their presentations with negligible additional effect on stereo-threshold; and with even further increase in duration of the inter-stimulus interval, threshold then increases only very gradually (Fig. 1). The dramatic and remarkable difference is between simultaneous presentationeven very brief temporal overlap will do-and sequential presentation. Experiments on stereoacuity, like those which led to the results shown in Fig. 1, usually involve adjacent targets, both seen in the fovea, where stereoacuity is best. Stereo-thresholds are considerably higher when one of the targets is
Version
Vergence
imaged well outside the fovea (Ogle, 1950), and it turns out that the optimal viewing strategy for depth discrimination with such widely separated targets is not steady fixation-as for fovea1 stereopsis-but instead involves looking back and forth between the targets (Wright, 1951; Enright, 1990, 1991). A variety of evidence indicates that those discriminations are probably based upon sequential comparisons of foveally seen disparities (Enright, 1991). If sequential stimuli can be readily evaluated in that context, why is it that sequential presentation of targets so drastically degrades stereoacuity in other situations involving steady fixation (Fig. l)? The evidence presented here indicates that the discontinuity in threshold shown in Fig. 1 is a peculiar property of adjacent sequentially presented targets; and that such targets are associated with small systematic involuntary eye movements that may well contribute to degraded stereoacuity. METHODS
Stereopsis
For measures of stereoacuity, two small dimly illuminated targets were presented in a darkened room; one was a cross at 5 m distance, with arms about 30 min arc long by 1 min arc wide,
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L--+---l 500
250
ENRIGHT
I 0
TARGET OVERLAPMSEC
0
250
500
750
I 1000
TARGET SEPARATION: MSEC
Fig. 1. Stereo-thresholds as a function of temporal overlap or of temporal separation between a pair of targets. Data in left portion of graph from Westheimer (1979, Fig. 2); open symbols indicate stimuli 500 msec in duration; closed symbols were either IOOmsec in duration (GW) or 50msec in duration (SM). Data in right portion of graph from Foley (1976; Fig. 1). all with stimuli 100 msec in duration. Targets in both studies were adjacent to each other, separated horizontally by 10 min arc in Westheimer (1979) and separated vertically by 7 min arc in Foley (1976). Subjects in both graphs identified by initials adjacent to lines connecting same-subject data. Note the drastic increase in threshold, in left portion of graph, when temporal overlap was reduced lo zero.
and the other was a disk 30 min arc in dia, produced in the form of virtual images by the stimulus generator described in Enright (1989). That instrument consists of an opaque tube with a large lens (12.7 cm dia) across one end; a small circular light source inside the tube; and a partially transparent mirror, mounted at a 45” angle to the axis of the lens and tube, from which the virtual images of the luminous disk (produced by the light source) are reflected to each eye of the observer and through which the background (in this case. the illuminated cross) can be seen. The observer can alter perceived distance to the disk by making small displacements of the light source within the stimulus generator, thereby changing the effective disparity between the left-eye and right-eye virtual images. For these experiments, the intensity of the light source in the original instrument was reduced to produce target luminance of about 1 cd/m2, and apparent brightness of the cross was matched to that of the disk. The subject’s task was to adjust the perceived distance of the disk to match that of the cross. The cross was located either just to the right of the disk (“adjacent”: separation of 20-30 min arc) or at 10” farther to the right. In the primary
experiments, two schedules of target presentation were utilized: “simultaneous” viewing, in which the disk was continuously visible and the cross was lit for 500 msec, extinguished for 1000 msec and then relit for 500 msec, in steady repetition; and “alternating” exposure. in which the disk was lit for 1000 msec, then extinguished for 500 msec during which time the cross was lit, followed by re-illumination of the disk (Fig. 2). In the subsequent control experiments, which used only adjacent targets, the disk was illuminated for 1000 msec in cycles of 2.5 set duration; and the cross was lit either for the last 100 msec during which the disk was visible (simultaneous viewing), or with onset coincident with offset of the disk (alternating exposure). Stimulus timing was controlled by a Grass Stimulator, Model 88, which activated microswitches. For all target arrangements, the subject was instructed to fixate steadily on the disk (or its location, during those intervals when it was not lit) while making the adjustments of apparent distance. Each subject made two sets of 6 adjustments to apparent equidistance for a given target spacing, both with simultaneous-viewing and with alternating-exposure protocols, in a single test session. Each adjustment was typically completed within less than 30 set, but no time limit SIMULTANEOUS TARGETS
I_
R
TARGET
ALTERNATING TARGETS
VIDEO MEASURES
L
R
TARGET
Fig. 2. Temporal schedule for target exposure and for vtdeo fields utilized in main experimental protocol. Lines above I. and R indicate times that the left-hand and rtght-hand targets, respectively, were visible; (A), (B) and (C) indicate blocks or 3 video fields, separated by 50 msec. in which eye position was measured, and then averaged, within each stimulus cycle.
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was imposed. Displacement of the light in the stimulus generator was converted to resultant disparity (1 mm = 2 min arc); and the SDS of these sets of 6 values are taken as measures of stereo-threshold. Reliability of the estimates of threshold (SE) was determined from the duplicate sets of measurements of a single test session. The 3 subjects are male emmetropes with no known oculomotor anomalies. Subjects 1 and 2, aged 14 and 29, have had extensive prior experience with measures of stereoacuity using this instrument; Subject 3 (whose settings were most variable) is 29 years old and had little prior practice. All subjects were uninformed about the purpose of the testing. Eye movement Eye orientation was monitored using the video-recording system described in Enright (1984) supplemented by a frame-counter, which numbers each video field. Precision of a single measurement, based on reproducibility of replicated “blind” readings, is on the order of 4-6 min arc (SD). The targets were two light-emitting diodes (LEDs) presented at 3 m distance, either laterally adjacent (separated by 20 min arc) or 10” apart horizontally. The room lights were extinguished during measurement. Video recording required that narrow light beams from two lamps be aimed at the eyes; the lamps and video cameras were well below the line of sight to the LED-targets, which were then visible only when lit, in an otherwise darkened field. Timing of target illumination was in 150&msec cycles, corresponded exactly to that used for evaluations of stereo-threshold in the primary experiments (Fig. 2). Eye orientation was evaluated for 10 sequential cycles of target presentation, for both target spacings and for both illumination protocols. For each cycle, the horizontal position of each eye was evaluated in 9 video fields, centered around 3 times: 150 msec before the right-hand target was illuminated; 500 msec thereafter (150 msec before the right-hand target was extinguished); and 500 msec later (when the right-hand target had been off again for 350 msec). Around each of those times, sets of 3 video fields, separated by 50 msec, were measured (t - 50 msec; t; and t + 50 msec), and those 3 values were averaged (Fig. 2). Absolute values of change in eye position were derived from two differences per stimulus cycle (I A - B I and I B - C 1,in Fig. 2). Any systematic changes in eye orientation were estimated by
subtracting the average position value obtained while the right-hand target was lit from the of the position values obtained average 500 msec earlier and 500 msec later, i.e. B -(A+C)/2, in Fig. 2. The experimental arrangement of the eye movement measurements was designed to duplicate in its essential features the procedures used in measurements of stereo-threshold. In both sets of experiments, the same subjects participated, and in both cases, small self-luminous targets were presented in a darkened surround, with the same lateral spacing and timing of presentation; target distances were also similar (5 and 3 m). In both cases, the subject was instructed to fixate as steadily as possible on the left-hand target (or its location, when it was not lit); and head stability of the subjects was maintained by bite boards. Nevertheless, completely identical situations were not achieved; the room was completely darkened except for the targets, during threshold measurements, to exclude the possibility that peripheral objects might affect distance judgments, but video monitoring of eye position requires illumination of the eyes. Furthermore, the mirror of the stimulus generator used for stereopsis testing would have fully obstructed the video cameras’ views of the eyes. Hence, during measurements of eye movements, although the illuminated targets were seen in a darkened surround, as in the stereo testing, the lower portion of the visual field included the video cameras and the lamps, located about 15” below the line of sight. The possibility that this difference in conditions might have had an important effect on eye movements will be subsequently considered (Discussion). RESULTS
Stereo-thresholds The estimates of threshold, with SEs, are summarized in Fig. 3, where it is evident that for adjacent targets, alternating exposure resulted in a many-fold increase in threshold, as previously documented by Westheimer (1979; see data in Fig. 1); that thresholds for simultaneously seen targets were considerably higher when the targets were widely separated (as previously reported by Ogle, 1950, among others); and that for widely separated targets, sequential presentation only slightly increased threshold, relative to the same-subject values measured during simultaneous presentation ratio (mean across subjects = 1.5; range
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TARGETS
ADJACENT
10’ APART
c
I
500
OVERLAP: MSEC
0
OVERLAP: MSEC
Fig. 3. Stereo-thresholds of 3 subjects, measured for adjacent targets, and for targets lo” apart, either with temporal overlap or without overlap (sequential presentation). (See Fig. 2 for stimulus timing.) Note the drastic increase in threshold when adjacent targets were presented without temporal overlap; and the very much smaller influence of temporal overlap with widely separated targets. Vertical bars attached to data points represent & SE, based on duplicate estimates of threshold. Same-subject values connected by diagonal lines, with subject number adjacent to line.
1.3e1.65). While thresholds are typically compared in terms of a ratio (hence, the logarithmic ordinate in Fig. 3), one can also inquire about the absolute magnitude of the change in threshold due to non-simultaneity of targets; even in this comparison, all 3 subjects showed lesser increase in threshold for the widely-separated targets than for adjacent targets, although this contrast was not statistically significant.
One aspect of the eye movement data is presented in Fig. 4; for each eye of the 3 subjects, the mean absolute value of change in eye orientation between measurements sets (separated by 500 msec) was calculated, for both target spacings and for both simultaneous and sequential presentations. Twenty-one of the 24 values in Fig. 4 are between 3 and 8 min arc: sufficiently similar to each other to suggest that fixation was relatively steady and that most of those calculated changes in eye position were due to random measurement error. The other 3 values are roughly twice as large, and those outliers all involved measurements of the right eye during sequential presentation of adjacent targets. These data, then. represent an objective correlate of the subjective impression that fixation was difficult to maintain, when adjacent targets were presented in alternation. The data in Fig. 4 do not, however, distinguish between the possibility that eye movements arose in directions that were random in timing and direction, relative to target visibility, and the alternative, that they were systematically related to target presentation. In parts (A) and (B) of Table 1, the data are summarized in terms of version and vergence components that dependend upon target exposure. During alternating presentation of adjacent targets, small involuntary versional movements arose, which were consistently
Eye movements When, during estimates of stereo-threshold, the two targets were adjacent and presented in alternation, the subjective impression was that steady fixation was very difficult to maintain: once the fixation target had been extinguished, the newly visible adjacent target seemed inescapably to attract the eyes. The measurements of eye orientation were undertaken to determine whether this subjective impression has objective counterpart, or was illusory. As in the stereo-threshold measurements, the subjects were instructed to fixate steadily on the location of the left-hand target (which was either continuously illuminated, or lit for 1000 out of each 1500 msec); and the LED targets were either 20 min arc apart, or 10” apart.
MEAN ABSOLUTE VALUE OF CHANQES IN ORIENTATION: MINUTES OF ARC
Fig. 4. Average absolute values of change in eye orientation for targets separated by either 20 min arc or 10 deg, and presented either synchronously or in alternation. (See Fig. 2 for timing of target presentation relative to times of measurement.) Average for each eye of each of 3 subjects calculated separately over 10 cycles of stimulus presentation (20 changes in position per value). Unshaded area: left-eye values, regardless of target configuration; solid shading: right-eye values for adjacent targets, presented in alternation; cross-hatched: right-eye values for adjacent simultaneous targets, and for all targets at lo-deg spacing, either adjacent or simultaneous. Note that the three “outliers” represent only the right-eye measurements, from all 3 subjects, obtained for adjacent targets, presented irl alternation
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Adjacent targets 500 msec overlap
No overlap
500 msec overlap
No overlap
NS NS NS
8.0 f 2.05 6.6 f 2.19 5.9 f 2.53
NS NS NS
NS NS NS
Subject 1 Subject 2 Subject 3
Table 1. (B) Systematic changes in vergence (mitt arct) Targets 10” apart
Adjacent targets 500 msec overlap
No overlap
500 msec overlap
No overlap
NS NS NS
3.3 * 1.66 10.0 + 1.68 9.0 + 2.25
NS NS NS
NS NS 4.6 f 1.26
Subject 1 Subject 2 Subject 3
Table 1. (C) Constituents Target Adjacent, Adjacent, Adjacent, 10” apart,
sequential sequential sequential sequential
of significant vergence changes1 (min arc)
Subject
Right eye
Left eye
Total
1 2 3 3
9.7 11.7 10.5 3.1
-6.4 -1.7 -1.4 1.0
3.3 10.0 9.0 4.6
NS: Not significant (all probability values > 0.10). *Positive values for versional change represent movement toward right-hand target during 500 msec interval during which it was illuminated: mean f SE, N = 10. TPositive values for vergencc change represent divergence during 500 msec interval during which right-hand target was illuminated mean + SE, N = 10. IBreakdown of data tabulated in part (B).
directed toward that target which was illuminated, a result that comports with subjective impressions; surprisingly, however, all 3 subjects also showed consistent vergence changes, when adjacent targets were presented in alternation. As indicated in part (C) of
Table 1, the vergence changes arose because the right eye moved farther rightward, during the 500 msec that the target on the right was visible, than did the left eye; and for Subjects 2 and 3, that asymmetry was quite extreme.
Table 2. Effects of target duration and simultaneity on stereo-threshold 500 msec Target exposure* Subject 1 2 G& SMS
Synchronous viewing
Sequential viewing
10.4 15.5 25.2 11.3 4.5 Average f SE
38.0 141 288 47.1 40.5
Ratio 3.7 9.1 11.4 4.2 9.0 7.48 f 1.51
(set arc)
100 msec Target exposuret Synchronous viewing 29.3 54.3 85.4 14.9 6.4
Sequential viewing 58.9 162 312 52.1 21.9
Ratio 2.0 3.0 3.7 3.5 3.4 3.11 f0.30
r-test of ratios (variances not assumed equal): rs = 2.84, P = 0.021. (similar t-test of log-transformed ratios: fg = 3.16, P = 0.014). *For synchronous viewing by Subjects 1,2 and 3, one target was continuously lit and the other switched on for 500 msec in cycles of 1500 msec duration; and for sequential viewing, one target was lit for 1000 msec and the other was lit thereafter for 500 msec (1500 msec cycles). For Subjects GW and SM (data from Westheimer, 1979, Fig. 2), each target was lit for 500 msec, either simultaneously or sequentially. tFor synchronous viewing by Subjects 1, 2 and 3, one target was lit for 1000 mm-c, in cycles of 2.5 set duration, and the other was lit during the final 100 msec of the illumination of the first target; for sequential viewing, one target was again lit for 1000 msec, in cycles of 2.5 set duration, and the other was lit for 100 msec immediately after the first had been extinguished. For Subjects GW and SM, (data from Westheimer, 1979, Fig. 2), each target was lit for 100 msec (or 50 msec, for SM), either simultaneously or sequentially. $Since thresholds for Subjects l-3 were calculated as SD from replicated adjustments to apparent equidistance, inter-subject comparisons would require that the threshold values tabulated for GW and SM, which were estimated from probit analysis (75% correct criterion), be increased by about 50%.
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with very brief target exposure
If the degradation of stereoacuity that arose when adjacent targets were presented sequentially (Fig. 3) were to be due to unpredictable displacement of retinal images associated with eye movements like those measured here (Table l), then this effect should be absent when adjacent sequential targets are presented very briefly, so that any eye movement triggered by the target exposure would occur only after both targets have been extinguished. Experiments with brief target exposure that were reported by Westheimer (1979) seem to contradict this expectation; and control experiments conducted with the 3 subjects here gave a similar result. In these tests, one of the targets was visible for 1000 msec and the other was lit for 100 msec, either just before the first target was extinguished, or immediately after it had been extinguished. The thresholds measured in these experiments are compared with those from longer-duration target exposure in Table 2, together with data obtained from similar target presentations by Westheimer (1979). Threshold for simultaneously seen targets was somewhat higher with briefly presented targets than with 500msec exposure (column 5 vs column 2); but even with brief target visibility, sequential presentation seriously degraded stereoacuity (column 6 vs column 5). Note, however. that the contrast between simultaneous presentation and sequential presentation was considerably less extreme with brief target exposure (ratios: column 7 vs column 4); to this extent, then, the results partially confirm--but only partially-the prediction that the experiments were designed to test. DISCUSSION
The data summarized in Fig. 3 demonstrate that while good stereoacuity~for adjacent targets requires a simultaneous view of both targets, the deterioration in acuity with non-simultaneous presentation is much less extreme when the targets are widely separated: stereoacuity outside the fovea (which is already relatively poor) is only slightly further degraded by sequential target presentation. (See McKee, Welch, Taylor & Bowne, 1990, Fig. 7, for qualitatively similar results.) The broader implication of this distinction is that simultaneous stimuli from a target pair are not as critical for cortical processing of disparity information as one might presume on the basis only of foveally presented targets.
The data summarized in Fig. 4 and Table I demonstrate that when adjacent targets in an empty surround are exposed sequentially, it is difficult if not impossible to maintain steady fixation. It is conceivable that with appropriate training, such eye movements could be suppressed, but certainly for these subjects, binocular fixation was considerably less stable during alternating presentation of adjacent targets than when one of the targets was continuously visible. With widely separated targets, however, only one of the subjects showed significantly less stable fixation during sequential presentation (a small vergence movement) that during simultaneous presentation. Because the eye movements that were associated with target alternation included a versional component that “followed” target visibility [Table l(A)], despite instructions not to move the eyes, the suspicion arises that this sort of target configuration may trigger the onset of an involuntary “pursuit” reflex. The systematic vergence component of the eye movements. however, was unexpected; it is not explainable by considerations of phoria, and only an ad hoc interpretation can be proposed: perhaps there is a small systematic departure from congruence between the binocular mapping of disparity in the cortex that underlies stereopsis, and the binocular mapping in the colliculus that underlies eye movements. The measurements of eye movement were undertaken because of the strong subjective impression, during stereo-testing, that when adjacent targets were presented in alternation, fixation was very difficult to maintain: the eyes seemed to be strongly and involuntarily drawn to a new target, if it suddenly appeared at the time that the nearby fixation point vanished. The data in Fig. 4 and Table 1 demonstrate that this subjective impression-which was also evident during the eye movement tests-has objective correlates: the subjects’ eyes did indeed tend to make small movements toward newly illuminated targets, despite instructions to maintain fixation as stably as possible. Nevertheless, because the eye movement tests involved visible objects (cameras and lighting sources) in the extreme lower portion of the visual field, and the stereo tests were conducted in an otherwise totally darkened room, considerable uncertainty would be involved in presuming that entirely comparable eye movements would have arisen during measurements of stereo threshold. 1f the
Stereo-thresholds presence of continuously visible objects in the periphery of the visual field during eye movement monitoring were indeed to affect the likelihood of involuntary eye movements, the direction of such an effect might well be toward greater stability of fixation (rather than greater instability), when compared with target alternations in complete darkness. The vergence changes documented in Table l(B) provide a possible basis for deciding whether comparison of the two sorts of experiment is justified. Note that when the righthand adjacent target was illuminated by itself (500 msec out of every 1500 msec), there was a strong tendency for it to be seen with divergence, relative to the eye orientation for the lefthand target. If comparable vergence changes were to occur during attempts to adjust two adjacent targets to equidistance, when they are illuminated in alternation, one should expect biased distance perception, relative to simultaneous presentation: differences in mean setting, independent of any effect on threshold (which is measured by variability of the settings about their mean). An examination of the data which led to the stereo-threshold values summarized in Fig. 3 indicates that this expectation is at least partially fulfilled: Subjects 2 and 3 showed the largest vergence changes in Table 1 (adjacent targets, alternately exposed), and those two subjects also showed statistically significant biases in judgments of apparent equidistance for adjacent targets, when values for simultaneously visible targets are compared with those for alternately exposed targets. In both bases, adjustment to apparent equidistance involved greater convergence for the left-hand target when both were seen simultaneously than when targets were presented in alternation: mean differences were 5.0 min arc ( &-0.67 min arc, SE) and 11,l min arc (L- 1.77 min arc, SE) for Subjects 2 and 3, respectively. None of the 4 other comparisons between simultaneous and alternatingly lit targets involved statistically significant biases in mean distance settings. Hence, this correlation provides modest indirect support for generalizing the data from the eye movement experiments to other situations like that in which stereo-thresholds were evaluated. At the least, it seems evident that if an effect of this sort had not been evident, there would be strong reason to suspect that the measurements of eye orientation and of performance at stereopsis were in some way fundamentally not comparable.
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The association of involuntary eye movements with that situation in which stereoacuity is seriously degraded raises the possibility that there may be a causal connection. Does unpredictable displacement of retinal images, occasioned by those eye movements, explain the drastic decrease in stereoacuity when adjacent targets are not simultaneously visible? The brief target exposure control tests summarized in Table 2 were undertaken to examine this possibility, and those results show: (1) that when eye movements directly triggered by target exposure could not result in image displacement, sequential presentation of adjacent targets nevertheless seriously degrades stereoacuity (by a factor of 3.1, on average); but (2) that this effect is smaller than with longer-duration views of the targets (a factor of 3.1 vs a factor of 7.5). The latter result can be interpreted as reflecting the absence, with briefly exposed targets, of variability in the placement of retinal images occasioned by the sort of eye movements documented in Table 1. These experiments suggest, then, that image displacement due to the measured eye movements may well explain part-but only part-of the drastic increase in stereothreshold, when adjacent targets are illuminated sequentially. It is conceivable, however, that even when target-triggered involuntary eye movements occur after the targets have been extinguished, they might nevertheless degrade stereoacuity; they might, for example, contribute to a general long-term instability of fixation. Measurement of torsional orientation in the aftermath of larger saccades (4”-8” in excursion) has shown that a single saccade can consistently influence torsional eye orientation to an extent that persists for several seconds (Enright, 1986); that sort of effect lends support to the speculation that repetitive smaller eye movements, as measured here, might produce long-term instability of fixation. Another possibility, however, is that the residual 3-fold difference in stereo-threshold, as documented in Table 2, when adjacent targets are briefly and sequentially presented, has nothing to do with eye movements. Hence, while it remains tempting to propose that with widely separated targets, non-simultaneity of presentation has a minimal effect on stereo-threshold (Fig. 3) because fixation can be more stably maintained (Table I), that hypothesis is by no means firmly established.
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ENRIGHT
Acknowledgements-This
research was supported by grant BNS 89-05401 from the National Science Foundation. Comments on the manuscript by Dr G. Westheimer and an anonymous reviewer are gratefully acknowledged.
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Enright, J. T. (1989). Manipulating stereopsis and vergence in an outdoor setting: Moon, sky and horizon. Vision Research,
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