Monocularly programmed human saccades during vergence changes?

Authors


J. T. Enright: Neurobiology Unit 0202, Scripps Institution of Oceanography, La Jolla, CA 92093, USA. Email: jenright@ucsd.edu

Abstract

  • 1When binocular fixation is shifted to a new target located at a different distance and in a different direction from initial fixation, a binocularly unbalanced saccade occurs at or near the onset of the composite eye movement. Those saccades typically produce good post-saccadic foveation of the target by one eye or the other.
  • 2Following such saccades, the better-aligned eye is typically as well aimed at the target as after pure versional saccades, but the partner eye deviates much more, thus requiring asymmetrical post-saccadic vergence movement.
  • 3This phenomenon suggests that during binocular viewing, the retinal eccentricity of a new-target's image from one of the eyes can be used to programme that eye's own saccade, so that it arrives reliably on target; and that the images of that target from both eyes participate in generating the saccadic excursion of the partner eye.
  • 4The ecologically useful result is rapid achievement of a high-resolution monocular view of the new target, although full binocular foveation is achieved much later.

Specifying the location of a target in subjective visual space requires stipulation of both its direction from the observer and its distance. This semantic and conceptual dichotomy between direction and distance seems also to be respected by the human oculomotor system. Conjugate movements, predominantly saccades, adjust gaze for differences in target direction, and disjunctive eye movements (convergence and/or divergence) adjust for differences in target distance. That distinction was formalized by Hering (1868) in his ‘law of equal innervation’. Two separate sources of movement for changes of fixation in the horizontal plane were postulated, each of which produces equal and/or opposite activation of pairs of horizontal recti. Hering's proposal is attractive because of an algebraic truism: any steady-state binocular horizontal re-orientation of the eyes can be achieved simply by summing the two processes he envisioned.

This conceptual scheme presumes complete independence of those two modes of eye movement. Following that assumption, most experimental studies of changes in fixation have used targets intended to produce either conjugate saccades (isovergence targets) or pure vergence movements (targets in the mid-sagittal plane). Changes of fixation in a natural setting, however, ordinarily involve a pair of targets that differ simultaneously in both direction and distance from the observer. Some of the first measurements of composite eye movements for such targets were reported by Yarbus (1957), and his oft-cited schematic diagram (Fig. 1A, purportedly summarizing many examples of such behaviour) vividly illustrates the natural consequence of complete independence of vergence and version movements. Saccades are shown as having been additively superimposed upon a slower ongoing vergence movement.

Figure 1.

Plan-view schematic diagrams

Schematic diagrams illustrating time course of the fixation point (intersection of visual axes, progressing along thick lines) during changes in fixation between a pair of targets (•) separated from each other in both distance and direction: left-side plots: divergence to right; right-side plots: convergence to left. A, purported behaviour, a tracing from Yarbus (1957, 1967). Note that the saccade additively incorporates the small fraction of ongoing vergence change that would be expected during saccade's short duration. B, modified version of part A, to conform with the now well-established finding that with such targets, much of total vergence change takes place during the saccade - 55 % here. (See Collewijn et al. 1997, for data on measured intra-saccadic fixation paths, which involve major outward deviations from shortest paths shown here.)

Extensive recent research (Enright, 1984, 1986, 1994; Erkelens et al. 1989; Maxwell & King, 1992; Zee et al. 1992; Collewijn et al. 1994; Collewijn et al. 1995, 1997) has demonstrated that this diagram is fundamentally wrong in at least one way. As indicated in Fig. 1B, far more of the required vergence change takes place during the saccade than Yarbus indicated. Hence, the saccades of the two eyes are usually strikingly unequal in excursion, rather than just slightly so as Yarbus (Fig. 1A) implied. (Careful examination of the single relevant eye-movement recording provided by Yarbus himself (1957) shows that even those measurements did not conform with his own schematic diagram in this regard (Enright, 1984).)

The research described here examines two further properties of the composite eye movements as illustrated by Yarbus (1957; shown in Fig. 1 this study): does directionally appropriate pre-saccadic vergence change usually take place, as shown there? And is the post-saccadic vergence movement fully symmetrical as indicated there? These two questions were recently considered by Collewijn et al. (1997), who answered both of them in the affirmative. Data presented here, however, raise doubts about the existence of pre-saccadic convergence (diagrams on right-hand side of Fig. 1A and B) and argue strongly against symmetry in post-saccadic vergence movements. This latter result is of broader significance because of its implications about the generation of disconjugate saccades.

METHODS

Fixation was shifted at intervals of about 3 s, self-timed with a metronome. The targets were the pointed, continuously visible tips of steel rods, 2 mm in diameter, which were suspended from above through a target board. Refixation ordinarily required a horizontal versional movement of about 10 deg, symmetrical about the mid-line, and vergence change of about 4 deg, with the nearer target about 20 cm from the eyes of the subject and the farther target at about 26 cm. Both targets were initially placed at the nearer distance, and some thirty saccades of about 10 deg excursion were made in each direction, providing calibration values as well as comparison data for isovergence saccades. These saccades were followed by two blocks of tests, one with the farther target placed on the right and the other with it on the left. Each block required about thirty alternations of converging and diverging changes of fixation. In a supplementary test session with one subject (far targets), the fixation rods were at distances of 40 and 73 cm, requiring a vergence change of about 4 deg, and version of about 8 deg.

Trials in which a blink occurred were discarded. Except in one block of measurements (see Appendix), trials were usually also excluded in which two conspicuous initial saccades occurred in very rapid succession. For each subject and each target configuration, however, twenty-five trials in each direction were measured, so first saccades of a few such two-saccade pairs were included.

A two-camera video system (60 Hz), with single measurement precision of about 6 min arc, was used to monitor eye orientation (Enright, 1984, 1996). That system now uses CCD cameras with shutter speeds of 1/250 or 1/500 s. Each video field (60 Hz) was automatically numbered. During pre-screening of the recordings, the time of first detectable saccadic displacement (onset) was noted; and eye orientation was then measured in four video pictures for each change of fixation: (1) 117 ms before detected saccade onset; (2) the field immediately before onset; (3) the field at end of the saccade, 67 ms after the pre-onset frame in more than 90 % of the cases, 83 ms in the others; and (4) the picture 1500 ms after onset. The differences between pictures 1 and 2 were used to evaluate changes in vergence over the 100 ms interval preceding the saccade; between pictures 2 and 3 to evaluate intra-saccadic vergence changes; and between pictures 3 and 4 to evaluate post-saccadic changes in orientation, thereby also quantifying orientational inaccuracies just after the saccade, relative to steady-state fixation. (Accurate binocular foveation was assumed to be achieved within 1500 ms after the saccade, appreciably longer than is usually required (Carpenter, 1988).) Since interpretation is based upon measurements at discrete, pre-determined times, the poor temporal resolution (60 Hz) of video does not (with one exception, noted subsequently) complicate interpretation. Details about the post-saccadic paths of the eyes were examined qualitatively, but are largely ignored here. Movement recordings with much finer temporal resolution (488 Hz), based on similar target configurations, can be found in Collewijn et al. (1997). Those data demonstrate that during the saccades themselves, fixation paths often deviated strikingly from shortest-path movement, but details of that sort are not needed here.

All three experimental subjects, who gave informed written consent (two males and one female, between 21 and 33 years old), are emmetropic and have no known oculomotor anomalies (normal appearing saccades in all directions, good pursuit in all quadrants). Ocular dominance was determined by the usual binocular pointing test, which was an easy distinction for all three. Subject 1 has often participated in prior oculomotor studies; the other two had previously participated in only two brief recording sessions. The quantitative similarity of the central elements in the results from the three subjects suggests that their performances provide a fair sample of normal oculomotor behaviour. Experimental procedures were approved by the Human-Subjects Committee of the University of California at San Diego.

RESULTS

Intra-saccadic vergence changes

The binocular inequality of the saccades observed here (Fig. 2) corresponds with results reported from several similar recent studies (Enright, 1984, 1986, 1994; Erkelens et al. 1989; Zee et al. 1992; Maxwell & King, 1992; Collewijn et al. 1994, 1997), as well as with the modified Yarbus diagram of Fig. 1B. The excursions of the two eyes were conspicuously and appropriately unbalanced, so that on average, some 40–75 % of the total required vergence changes took place during the saccades. Because of those other recent precedents, this phenomenon was fully expected, despite the indication of Yarbus (1957, 1967) to the contrary (Fig. 1A).

Figure 2.

Plots of ratio of larger saccadic excursion to smaller excursion for all three subjects and both target configurations

Ratios from individual trials shown as •, with adjacent ‘box’ diagrams showing averages (thick horizontal lines), ± standard errors (wide boxes), and ± standard deviations (vertically elongated boxes). Mean observed ratios are all much greater than implied by Yarbus's diagram. Numbers shown on graphs are percentage values which give mean portion of total demanded vergence change that took place during saccades; all observed percentages are much greater than the 3–5 % indicated by Yarbus.

Pre-saccadic vergence changes

The question of whether consistent, directionally appropriate pre-saccadic vergence changes occurred in response to these target configurations is addressed by data in Fig. 3. The three upper graphs demonstrate that in most of those trials that demanded a divergent eye movement, a small amount of appropriate divergence occurred before saccadic onset. The overall mean was about 5 % of the total vergence change required, rather than the 10 % illustrated by Yarbus (1957; 1967), but a modest quantitative deviation from a schematic diagram like that of Fig. 1 should not be of serious concern. When convergence was required, however, none was consistently measured during the 100 ms interval before the saccades for any of the three subjects (lower graphs of Fig. 3); instead, the first detected eye movement was usually a saccade. The individual test results suggest that only random variability was responsible for the observed modest single-trial deviations around mean values of zero.

Figure 3.

Pre-saccadic divergence (upper graphs) and convergence (lower graphs) during 100 ms interval preceding observed saccadic onset

Twenty-five tests, for each target configuration and direction of version, shown as •; adjacent ‘box’ diagrams show means (thick horizontal lines), ± standard errors (wide boxes), and ± standard deviations (vertically elongated boxes). Adjacent probability values (P) based on two-tailed t test of null hypothesis that true average is zero.

In contrast, Collewijn et al. (1997) reported consistent pre-saccadic convergence in their similar experiments, but their targets were considerably farther from the subject than those here, demanding less than half as much baseline convergence. Hence, the bias toward divergence evident in Fig. 3 might indicate a tendency for the eyes, when already strongly converged, to diverge during refixation, perhaps even overcoming incipient convergence. This hypothesis was examined by testing subject 1 with targets requiring amounts of version and vergence change similar to those in the other tests, but with the farther target located at 73 cm (a distance comparable with that of Collewijn et al. 1997) rather than 26 cm, thereby reducing baseline convergence from about 14 to about 5 deg. Data on pre-saccadic vergence changes in those far-target tests are summarized in Fig. 4. There was again no consistent evidence for convergence during the 100 ms interval before the saccade, and pre-saccadic divergence was on average similar to, or (divergence-left tests) even modestly larger (rather than smaller) than that of this subject with the closer targets. Those observations thus provide no support for the suspicion that the main results (Fig. 3) might have been biased because of overall target proximity.

Figure 4.

Pre-saccadic divergence and convergence

Far-target tests (subject 1 between targets at distances of 40 and 73 cm), during 100 ms interval preceding observed saccadic onset, see text. Other details as in Fig. 3.

Eye orientations immediately after the saccades

The question of whether post-saccadic eye movements could have represented more or less symmetrical vergence changes (as shown in the Yarbus diagram, Fig. 1) can be evaluated on the basis of differences between eye orientation at the end of the saccades and that at final steady state. Deviations of roughly similar magnitude in the two eyes, and with appropriate direction (both deviations being either nasalward or temporalward from the new target) would be consistent with (but of course would not prove) approximately symmetrical, slow-velocity post-saccadic vergence movements. In order to quantify ‘roughly similar magnitude’, a generous criterion was chosen for quasi-symmetrical vergence movements: that at the end of the saccade, the eye that deviated more from the target be no more than 50 % farther off target than the nearer eye (both being of appropriate sign).

Overall, less than 10 % of the vergence-version refixation trials involved post-saccadic eye orientations that meet this relatively liberal criterion (Table 1, column 3). Instead, in most cases, one eye or the other was considerably farther from the target than its partner. (In Table 1, R is the ratio of the size of the larger of the two post-saccadic eye movements required to that of the other eye, with positive sign for nasalward movements during convergence and for temporalward movement during divergence.) As a criterion for extremes of asymmetry, a threshold ratio of 4 : 1 was initially chosen; ‘extremely asymmetrical’ post-saccadic eye movements would be necessary if, at the end of the saccade, the eye that was more distant from the target was at least four times farther off target than the nearer eye. (A broad range of asymmetries is considered below.) For each of the three subjects, more than half of the changes in fixation meet this factor-of-four criterion of asymmetry at the ends of the saccades (column 2 of Table 1). The lower part of Table 1 presents similar data on post-saccadic deviation ratios from the trials with isovergence targets. In those results, the fraction of quasi-symmetrical ratios is similar to that of intra-vergence saccades (mean 7 vs. 8 %), but extremes of asymmetry were much less common (mean 17 vs. 55 %).

Table 1. Frequency* of saccadic ratios
A. Convergence and divergence targets
Subject∣R∣> 4.01 < R < 1.5OtherTotal
1561034100
255936100
3 †53542100
Totals16424112300
1 (Far targets)531334100
B. Isovergence targets
Subject∣R∣> 4.01 < R < 1.5OtherTotal
  1. *Number of trials with given values of R; saccades for leftward and rightward target configurations combined. R = ratio of larger amplitude to smaller (see text). †The twenty-five divergence-left trials of subject 3 were handled differently; see Appendix.

11533250
2434350
3653950
Totals2511114150

Qualitative, frame-by-frame examination of the post-saccadic recordings demonstrated that in the asymmetrical-deviation cases of Table 1, smooth, slow-velocity, strongly asymmetrical vergence movement was consistently the primary means of achieving final, steady-state binocular fixation; but small saccades sometimes also intervened. Such saccades occurred in more of the convergence trials than in the divergence trials; they were usually quite small (typically 0.3 to 0.6 deg) in the eye that was better aligned with the target; and their timing, within the 1500 ms post-saccadic window, was quite variable, so that they would be obscured in cross-trial means of data (as in Collewijn et al. 1997). In any case, those occasional small saccades do not contradict the conclusion that post-saccadic movements consisting only of slow-velocity symmetrical vergence, as illustrated by Yarbus (Fig. 1A), were remarkably rare.

The differences between post-saccadic and final eye orientations from all 100 tests with each subject are presented in Fig. 5 as plots of right-eye deviation from the target versus left-eye deviation. Symmetrical vergence after the saccade would involve data points along the 45 deg diagonal, from lower left to upper right of the graphs; such cases (open symbols) were quite rare. Instead, strong post-saccadic asymmetry is evident in the predominance of filled symbols clustered around the horizontal and vertical axes. Geometry dictates that the regions of those graphs that include cases with |R| > 4 represent ±14 deg around the axes. If the data were distributed at random in this co-ordinate system, only about 31 % of the observations would be expected to fall within those regions (i.e. (8 × 14)/360). The actual data deviate markedly from this expectation (56, 55 and 53 %), differences that are highly significant for all three subjects, χ2 values (1 d.f.) being between 21.1 and 27.5, all with probability of < 0.001, indicating very strong bias toward positions near the axes.

Figure 5.

Post-saccadic eye deviations from new target

Deviations between eye orientation immediately after saccades and proper alignment on a new target: right-eye deviations plotted against left-eye deviations, with 100 trials for each subject. Convergence shortfall shown as positive, divergence shortfall as negative. ○, cases involving quasi-symmetrical deviations (1 < R < 1.5), where R is the deviation ratio defined in the text; •, cases involving strongly asymmetrical deviations (|R| > 4); ×, cases not meeting first two criteria (meaning either that −4 < R < −1 - modestly asymmetrical version - or that 1.5 < R < 4 - modestly asymmetrical vergence).

This predominance of ‘extremely asymmetrical’ eye deviations could conceivably be a peculiarity of the four-to-one threshold value, which seems quite arbitrary. That suspicion is vitiated by the curves in Fig. 6, which demonstrate that for any threshold of asymmetry with a ratio between 3:1 and 20:1, the number of observed cases meeting the criterion considerably exceeds expectations based on random-area calculations like those of the preceding paragraph. Considering all eighteen integer threshold ratios in the range from 3:1 to 20:1 plotted in Fig. 6, the minimumχ2 values (1 d.f.) for those deviations for subjects 1, 2 and 3 are 27.1, 5.4 and 17.2 (P < 0.001, P < 0.025 and P < 0.001, respectively). Thus, any threshold for ‘extremely asymmetrical’ in the range between 3:1 and 20:1 would have led to the same conclusion: pronounced asymmetry was remarkably common.

Figure 6.

Observed number of extremely asymmetrical cases, out of 100 trials

Observed number of extremely asymmetrical cases vs. expected number, depending on the ratio, R, used to define ‘asymmetrical’, in range (going from right to left) between |R|= 3 and |R|= 20. S1, S2 and S3 are subject numbers applicable to adjacent curves. Dashed 45 deg line indicates match of observed with ‘expected,’ which assumes random distribution of data within co-ordinate system like that of Fig. 5.

An alternative and interesting way of considering the data on asymmetry of post-saccadic eye orientations is obtained by plotting in target space the locations of the post-saccadic fixation points (intersections of the visual axes). An example of this kind of plot (plan view) is presented in Fig. 7, with the spatial region near the target shown in expanded scale on the right. Such expanded-scale plots for the saccadic-vergence results from all four target configurations and all three subjects are presented in Figs 8 and 9. These plots demonstrate that in cases of ‘extremely asymmetrical’ post-saccadic eye orientations (filled symbols: |R| > 4), the new target was usually quite well foveated immediately after the saccade by one or the other of eyes of the subject. In fact, as is documented below, the better aligned eye was typically as well aimed at the target as occurs with isovergence saccades. The other eye usually deviated considerably more.

Figure 7.

Plan view of locations of post-saccadic fixation points (intersections of visual axes) for the twenty-five convergence-left trials of subject 1

Left and right eyes connected by continuous lines (left) through the new target to show each eye's eventual orientation at new steady state. Dashed arrow schematically indicates mean shortest-distance path of fixation point between origins and ends of saccades, but not actual paths. (See Collewijn et al. 1997.) Ellipse on right: expanded view, showing details in spatial region around target, with ○ showing post-saccadic fixation for cases with quasi-symmetrical deviations of fixation relative to target (1 < R < 1.5); • for cases with strongly asymmetrical deviations (|R| > 4); and × for cases not meeting those two criteria. Symbols and numbers in box: frequency of cases out of twenty-five trials. Note that • (strongly asymmetrical cases) are aggregated near final lines-of-sight from one eye or the other, toward location of new target.

Figure 8.

Expanded scale plan views of locations of post-saccadic fixation relative to target locations for convergence trials

Locations of post-saccadic fixation points (intersections of visual axes), relative to target locations (large open circles), for sets of twenty-five convergence trials in both directions for three subjects. ○, cases involving quasi-symmetrical deviations (1 < R < 1.5); •, cases involving strongly asymmetrical deviations (|R| > 4). Data from trials not meeting either of these two criteria not plotted (frequency equal to difference between 25 and number of illustrated data points in each graph). As in Fig. 7, diagonal lines through target originate at the subject's right and left eyes. Arrows indicate shortest-distance mean path between origins and ends of the saccades, but not actual paths. Other details as in Fig. 7. Note that • (strongly asymmetrical cases) are predominantly aggregated near lines-of-sight from eyes toward location of new target.

Figure 9.

Expanded scale plan views of fixation points relative to target locations for divergence tests

Locations of post-saccadic fixation points (intersections of the visual axes), relative to target locations, for divergence tests in both directions for three subjects: twenty-five trials for each graph. Other details as in Fig. 8.

With certain subjects and target configurations (e.g. converge-right trials of subjects 1 and 3 in Fig. 8), better alignment was almost always achieved by the same eye, but with other subjects and targets, the distribution was more evenly divided. Table 2 presents subdivisions of the ‘extremely asymmetrical’ (|R| > 4) cases according to several criteria. Parts A and B of that Table indicate that such cases were about equally common for both convergence and divergence; and for rightward and leftward saccades. Part C demonstrates that the dominant eye of subject 1 was usually (but not always) the one that achieved better foveation at the end of the saccade, and that subject 3 showed a modest trend of the same sort. Subject 2, however, showed no such tendency.

Table 2. Correlates of well-foveated alignments
A. Convergence versus divergence
SubjectConvergeDiverge P
12729> 0.20
22926> 0.20
33023> 0.20
1 (Far targets)2825> 0.20
B. Rightward versus leftward movement
SubjectRightwardLeftward P
12927> 0.20
22134> 0.10
32924> 0.20
1 (Far targets)2627> 0.20
C. Dominant versus non-dominant eye aligned
SubjectDominant eyeNon-dominant eye P
143 ***13< 0.001
22629> 0.20
33221> 0.10
1 (Far targets)38 ***15< 0.001
D. Smaller- versus larger-movement eye aligned
SubjectSmaller movementLarger movement 
  1. Numbers of trials with ∣R∣ > 4. * Proportion > 0.50 with probability < 0.05; *** proportion > 0.50 with probability < 0.001.

12927> 0.20
21936*> 0.05
343***10> 0.001
1 (Far targets)1637***> 0.001

Another factor that might affect post-saccadic foveation is whether the image of the new target was initially seen closer to, or farther, from the fovea. Location of the image closer to the fovea might, for example, lead that eye to better foveation. Part D of Table 2 indicates that for subject 3, there was indeed a very strong association between an eye seeing the new target at lesser eccentricity, and better post-saccadic foveation by that same eye. In contrast, subject 2 weakly showed the opposite tendency: good foveation by the eye that had seen the image of the new target farther from the fovea. This sort of criterion was apparently irrelevant for subject 1 for the standard targets, but for the far-target arrangement, greater image eccentricity before the saccade was associated with better post-saccadic foveation by that eye. The variability evident in Table 2 indicates that a full characterization of the results must remain relatively unspecific. One eye or the other commonly achieved quite good target foveation at the end of the saccade, regardless of whether convergence or divergence was required or whether rightward or leftward saccades were involved.

Since these saccades, which were embedded in a change in vergence, so often resulted in good post-saccadic foveation by only one of the eyes, comparisons of their accuracy with ordinary conjugate saccades for isovergence targets can best be undertaken by separate consideration of the ‘better-aligned’ and ‘less-well-aligned’ eye in each test. Cumulative frequency plots of angular deviations by the better-aligned eye are presented in the upper graphs of Fig. 10, and similar plots for the less-well aligned eye are presented in the lower graphs. For the better-aligned eye, the saccades associated with vergence change typically provided a post-saccadic image that was as well foveated (and thus of as high a resolution) as the saccades made for isovergence targets. In none of the six comparisons (upper plots in Fig. 10) was there a significant difference between convergence/divergence trials and the isovergence trials (Kolmogorov-Smirnov tests; all probability values > 0.10). The lower plots of Fig. 10 show, however, that the less-well-aligned eye ordinarily was considerably farther off target following vergence-change saccades than after saccades for isovergence targets.

Figure 10.

Cumulative percentile plots of differences between post-saccadic eye orientation and full alignment with new target

Upper three graphs present data for better-aligned eye, lower graphs for less-well-aligned eye. (Note differences in abscissa scales and line representation as top left graph.) Individual curves based on fifty trials, combining data from all leftward and rightward saccades. Better-aligned eye was usually aimed as close to target immediately after vergence-associated saccades as after isovergence tests, but less-well-aligned eye was usually much worse after saccade than in isovergence tests.

DISCUSSION

Pre-saccadic vergence changes

Although the report by Yarbus (1957) is the source of the questions underlying the present study, the paucity of measurement data there precludes quantitative comparison with the new results. A suitable basis for comparison, however, is provided by the recent study of Collewijn et al. (1997), which involved similar issues and experiments. The results here conflict with that report in the apparent absence (Figs 3 and 4) of consistent pre-saccadic convergence. Four of the five subjects whom Collewijn et al. (1997) tested commonly showed pre-saccadic convergence - albeit smaller than pre-saccadic divergence. With target configurations similar to those here, they reported (for 3 of their 5 subjects) that convergence before the saccades averaged about 20 min arc, which was consistent enough across the three subjects to be statistically significant.

That discrepancy between the results from the two studies might conceivably be due to factors that differed somewhat between the experiments: (1) differences in target distance; (2) differences in data analysis; (3) differences in eye-monitoring systems; and (4) differences among subjects.

Differences in target distance. As indicated previously, the proximity of the targets used in this study might have produced a bias toward divergence. That hypothesis was tested and discredited by the far-target tests (Fig. 4).

Differences in data analysis. Collewijn et al. (1997) averaged the measurements from their several replicate trials (3 ± 1) before plotting or further analysis of the data, whereas here each trial was treated separately. This averaging across trials could have led to mean convergence that would not be evident in most single trials only if pre-saccadic convergence of quite large magnitude were to occur on a very occasional basis. As can be seen in Figs 3 and 4, the single-trial results here show no evidence of such occasional anomalously large convergence.

Differences in eye-monitoring systems. Collewijn et al. (1997) monitored eye movements with a search-coil system operated at 488 Hz, compared with a 60 Hz video recording used here. In their plotted example (ibid., Fig. 13), pre-saccadic convergence was observed primarily during the last 20 ms before saccadic onset, saccade onset being defined by a version-velocity threshold of 15 deg s−1. In the present analyses, the last pre-saccade eye-position measurement (17 ms before detectable saccadic displacement), which was used to evaluate the end of any pre-saccadic vergence movement, would be expected to have preceded essentially all pre-saccadic convergence that was timed like that in their Fig. 13. That same illustration (their Fig. 13) also shows that pre-saccadic divergence of the same subject began more than 100 ms before the saccade, which would be easily detected in the 60 Hz measurements here. This suggests, then, that the difference in pre-saccadic results in the two studies might well be due to a remarkable (and unexplained) difference in timing between pre-saccadic convergence and divergence movements, combined with the difference in temporal resolution of the two monitoring systems.

Figure 13.

A, scale drawing of eye and target configuration for 10 deg rightward version with 5 deg divergence, for far target at 75 cm distance. Dashed line, iso-direction line through new target; End saccade, plane in which intersection of the visual axes determines extent of post-saccadic asymmetry. B and C, scale drawings of near-target space, showing examples of differences between path of fixation point during fully symmetrical vergence changes (dashed ‘iso-direction line’) and strongly asymmetrical post-saccadic divergence and convergence (thick lines: |R|= 4.0), for targets at distances like those used by Collewijn et al. (1997). Calculations based on inter-ocular spacing of 65 mm; target distances of 37 and 75 cm; 5 deg of total vergence change, of which 2 deg was post-saccadic; and 10 deg saccadic version symmetrical about mid-line. The angle between iso-direction line and asymmetrical vergence line is 1.5 deg in B and 3.4 deg in C. Other end-of-saccade eye orientations with |R|= 4 (when R is negative, indicating requirement for major post-saccadic version, an uncommon situation in single-trial results and even rarer in cross-trial averaged results) can produce somewhat larger deviations between iso-direction line and asymmetrical vergence lines (maximum angles of 4.1 deg for divergence, 7.9 deg for convergence).

Differences among subjects. The subjects in Collewijn et al. (1997) had extensive prior experience in oculomotor studies, but two of the three who participated here lacked that background. Recent unpublished results from Collewijn's laboratory (Van Leeuwen & Collewijn, personal communication, September 1997) have documented major variability among normal subjects in the extent of pre-saccadic vergence movements, with ‘many’ individuals behaving as reported here, that is showing no convincing pre-saccadic convergence (Fig. 3), although pre-saccadic divergence was usually evident.

In the final analysis then, the apparent discrepancy between the pre-saccadic vergence results reported here and those in Collewijn et al. (1997) does not seem to represent grounds for serious concern. It can plausibly be accounted for by differences in the temporal resolution of the two monitoring systems, combined with major variation among subjects in this behaviour.

The visual significance of post-saccadic eye orientations

If post-saccadic eye movements for targets like those provided here were to consist only of symmetrical, slow-velocity vergence movements, as illustrated by Yarbus (Fig. 1; see, also, Collewijn et al. 1997), then immediately after the saccade, the image of the new target would initially be located off the visual axes of both eyes, by half of the residual required post-saccadic vergence change - sometimes, then, even outside the foveas. Symmetrical vergence movements are much slower than saccades (Carpenter, 1988), so a high-resolution view of the new target by either eye would thereby be considerably postponed. The facilitation of vergence changes by saccades (Figs 1B and 2) obviously accelerates rapid target foveation, compared with the symmetrical slow-velocity vergence movements envisioned by Yarbus (1957). Good post-saccadic monocular fixation, as documented here, provides for even more rapid, efficient shifts of gaze. A foveated, high-resolution view of the new target is obtained - albeit only a monocular view - immediately after the saccade, and that foveated image is usually achieved just as rapidly as with ordinary saccades for isovergence targets (upper graphs of Fig. 10). Good monocular foveation after the saccade is thus a supplementary means of circumventing the potential timing handicap imposed by the slow velocity of ordinary vergence movements. (Monocular perception of detailed target structure should not be taken to imply that vision immediately after a saccade is exclusively monocular; for example, detection of small binocular disparities can occur immediately after a saccade (Enright, 1991).) With the simple targets used here, rapidly obtaining a high-resolution image of the new target would be irrelevant, but in more natural settings that require similar refixation, speedy resolution of details in the image of an initially peripheral target could be an obvious advantage.

Post-saccadic eye orientations: discrepancies with Collewijn et al. (1997)?

The most significant finding of this study, that post-saccadic eye movements are typically strongly asymmetrical, and not symmetrical as shown in the Yarbus diagram, also conflicts with the report by Collewijn et al. (1997). They summarized: ‘…the last part of the trajectory was slow again, and consisted mainly of convergence along the iso-direction line (i.e., binocular-symmetry line) through the new target.’ (ibid., pp. 1060–1061); and further, ‘…the trajectory followed the appropriate iso-direction line in a nearly pure divergent movement…’ (ibid., p. 1066). Post-saccadic fixations measured here (Table 1: n= 400) indicate that such symmetrical behaviour (generously defined as full symmetry ±50 %) could, at a maximum, have arisen in less than 10 % of the trials. This major apparent discrepancy between the two sets of results deserves careful consideration.

Among the several methodological differences between two studies (listed above), the emphasis by Collewijn et al. (1997) on average eye orientations across trials probably contributed importantly to the difference in reported symmetry/asymmetry of post-saccadic eye movements. The consequences of such averaging were examined by averaging the post-saccadic fixations summarized in Table 1 for each twenty-five-item data set. The resulting mean post-saccadic fixation points are presented in Fig. 11, along with similar results from isovergence trials. Those cross-trial average fixation points are sufficiently close to mid-line alignment to give the impression that on average, the required post-saccadic eye movements could well have been essentially symmetrical, as Collewijn et al. (1997) reported, despite predominance of asymmetry in the single-trial data (Table 1 and Figs 8 and 9).

Figure 11.

Plan views of the locations of the mean post-saccadic intersections of the visual axes, relative to target locations

Target shown by large open circle. Other symbols represent means across locations in twenty-five tests, with diagonal or horizontal lines from symbols indicating direction from which eye moved toward target. ▴, divergence tests; *, convergence tests; •, isovergence tests. For divergence-left tests of subject 3 (lower ▴, well right of mid-line), mean location represents position following first saccades of two-saccade pairs; mean intersection following second saccades in those tests was almost exactly below target (0.8 mm to right; see, also, Appendix).

Using Fig. 11 to interpret the report of Collewijn et al. (1997) could be misleading because twenty-five trials were involved here, while they averaged only two to five replicates. Therefore, a kind of ‘bootstrap’ re-analysis (Tukey, 1977) was undertaken, based on repeated random selection and averaging of sets of five tests from the twenty-five available for each subject and target configuration. A summary of some of the results of that multiple resampling-and-averaging analysis is presented in Fig. 12. Compared with single-trial results, five-trial averaging of eye orientations produced more than twice as many cases in which quasi-symmetrical post-saccadic vergence movements apparently might have occurred (Fig. 12A). Averaging across eye movements also resulted (Fig. 12B) in a striking decrease in proportion of trials with extremely asymmetrical post-saccadic eye deviations (|R| > 4). These calculations demonstrate that the strong tendency for good foveation by one eye or the other in the single-trial results (Figs 8 and 9) would have been considerably obscured by averaging across even a few trials.

Figure 12.

Relative frequency of quasi-symmetrical and of very asymmetrical post-saccadic eye deviations

For both single trials and five-item means of individual measurements across trials. Single-trial data are those presented in Table 1 (n= 100 each); five-trial means derived from bootstrap sampling of five eye-position values from twenty-five observed positions for each target configuration and subject, with 200 replications of that process for each data set. (See text.) A, percentage of quasi-symmetrical cases (1 < R < 1.5); B, percentage of strongly asymmetrical cases (|R| > 4). Horizontal lines (at 12.5 and 31 %) represent expectations, based on randomization within co-ordinate system like that of Fig. 5 (see text).

Another factor that would have contributed importantly to the impression of quasi-symmetrical post-saccadic vergence changes is the use by Collewijn et al. (1997) of targets that were considerably more distant than those used here. Increasing target distance did not, in itself, alter the basic outcome as evaluated here (far-target data in Table 1), but with more distant targets, the distinction between symmetrical and markedly asymmetrical-vergence changes becomes relatively inconspicuous in plots of the time course of the binocular fixation point. A schematic demonstration of this difficulty is presented in Fig. 13, with a target arrangement matching the one used by Collewijn et al. (1997), which had vergence and version demands similar to those used here. If one were to decide about the symmetry or asymmetry of post-saccadic movement by examining plots like those of Fig. 13 (instead of calculating the actual asymmetry ratio as done here), it would be an extremely subtle problem to distinguish between symmetrical (iso-direction: R ≈ 1.0) and strongly asymmetrical vergence movements (|R| > 4). The hypothetical results of Fig. 13B, for example, with an asymmetry ratio of 4, look very much like ‘nearly pure divergent movement’ (Collewijn et al. 1997, p. 1066); and the plot of Fig. 13C, also with R = 4, appears compatible with the interpretation that ‘the last part of the trajectory…consisted mainly of convergence along the iso-direction line’ (ibid., pp. 1060–1061).

In view of these two factors (averaged data vs. single-trial results; and the difficulty, for targets at greater distances, in distinguishing between truly symmetrical and strongly asymmetrical movement in target-space plots like those of Fig. 13), there may well be no genuine discrepancy in the extent of post-saccadic asymmetry between the eye movements quantified here and those that actually occurred in the experiments of Collewijn et al. (1997). The discrepancy in reported results may well be more apparent than real.

Monocularly programmed saccades?

Relatively good post-saccadic target foveation by one eye or the other seems to suggest that location of the new target, as seen by one of the eyes, led to the generation of a saccade for that same eye, so as to produce good alignment with the new target, while the other eye was left to achieve its foveation at a considerably later time. Hence, the saccades of the better-aligned eye seem very often to have been programmed predominantly by monocular considerations. Before further consideration of this seemingly self-evident interpretation, however, some alternatives must be examined.

To account for the unbalanced saccades that arise with targets like those used here, an oft-proposed hypothesis is that some sort of ‘interaction’ between vergence and version signals is involved (Erkelens et al. 1989; Zee et al. 1992; Collewijn et al. 1994). That postulate assumes that vergence and version are the outputs of systems that are fully balanced binocularly, as envisioned by Hering (1868); but that when those systems are activated simultaneously, a movement is produced based on multiplicative combination of their signals rather than simple addition. As that proposal does not differentiate between the two eyes, it does not account naturally for the remarkably good post-saccadic target alignment achieved by only one of the eyes. Interaction between vergence and version signals might, of course, occasionally produce such a result by chance; but the observed frequency with which that occurred argues strongly against the phenomenon being only the occasional product of coincidence.

Another conceivable alternative interpretation is that averaging of the image locations seen by the two eyes determines a binocularly fully conjugate component of the saccade, but that the disparity of the images produces a vergence signal that is unequally partitioned (with or without interaction) between the two eyes (Erkelens, personal communication, October, 1997). This notion maintains the classical assumption that saccades are, in principle, fully conjugate and arise from arithmetic averaging of binocular visual input. The difficulty with this suggestion, however, is similar to that with the less specific hypothesis of ‘interaction’. The unequal partitioning of the vergence component must be of a very special sort, so that the versional excess or shortfall (relative to the target) of one of the eyes is usually almost exactly balanced by its share of the vergence signal. This very special kind of ‘sharing’ would, then, represent an additional, ad hoc requirement, which converts the overall proposition, that the vergence signal is suitably partitioned, into a remarkably complex suggestion.

Since alternatives of this sort, which invoke signals from the vergence system being interjected into the generation of saccades, have such difficulty in accounting for the surprisingly good post-saccadic target foveation by one eye or the other, the possibility that those results might be entirely the response of the saccade-generating system to these kind of targets deserves further consideration. It is, of course, quite clear that monocular visual input is sufficient for normal saccades. With a pair of equidistant targets, binocular saccades between them of appropriate excursion can be generated when vision by either one of the eyes is occluded. The interesting question then arises: what happens to those monocular visual signals during binocular viewing, when both eyes could potentially provide visual guidance to the saccade generator?

It is difficult to address this question with equidistant targets, because the visual inputs about target location from the two eyes would be essentially identical. Such doubled potential input simply results in saccades that are usually indistinguishable from those during monocular viewing. That outcome could represent use by the saccade generator of visual input from one eye or the other (its partner's message being ignored), or it could - as is seemingly often assumed without further hesitation - result from simple averaging of both eyes' visual stimuli, a notion that can be specified as:

display math(1)

where SC represents the joint, common saccadic versional excursion, and θL and θR represent the image eccentricities seen by the left and right eyes, respectively.

Target configurations like those used here offer a better prospect of unravelling the saccadic consequences of binocular visual stimuli, because the images of the new target fall at differing retinal eccentricities in the two eyes. The usual responses to such targets include saccades with striking binocular differences in excursion (Fig. 2). The hypothesis that those binocularly unbalanced saccades indicate ‘interaction’ between the neural signals that produce version and those for vergence movements cannot, as indicated above, readily account for the results of interest here. An alternative interpretation of those unbalanced saccades can also be based on a suggestion of Ditchburn (1973) and of Krauskopf et al. (1960), a notion that was originally proposed for unbalanced microsaccades during fixation. This alternative proposal is that such saccades may instead reflect the way in which the saccade-generating system itself responds to binocular differences in image location (Enright, 1984, 1992, 1994, 1996).

In that situation, with the images of the new target falling at somewhat different retinal eccentricities in the two eyes, a ‘disparity’ signal is available, which is, of course, recognized as one of the normal inputs for the slow-velocity vergence-movement system; that fact has undoubtedly encouraged speculation about ‘interaction’ of vergence and version signals. It is not, however, self-evident, how the saccade-generating system itself, independent of the vergence-movement system, would deal with binocularly different retinal images. The schematic diagram of Yarbus (Fig. 1A) implies that the saccades superimposed on the vergence movement were generated by direct averaging of the visual inputs to the two eyes, as in eqn (1).

Results like those shown in Fig. 1B require a somewhat more complex interpretation. They are, however, compatible with the suggestion of a saccade-generating system that can provide outputs of different magnitude to the two eyes, on the basis of weighted averaging of the visual stimuli from each eye (Enright, 1992, 1994, 1996). This interpretation can be specified with two equations:

display math(2)

and

display math(3)

where SL and SR are saccadic excursions of left and right eyes; θL and θR represent horizontal angular separation between targets (retinal eccentricity), as seen by left and right eyes; and αL, αR, βL and βR are eye-specific weighting factors for visual stimuli, with α being self-eye weight and β being contralateral-eye weight. (The α and β values can be combined into single parameters for each eye (Enright, 1994), but the equations thereby become less transparent.)

If the hypothesis of weighted averaging that underlies eqns (2) and (3) is to account for the results of interest here, it must be supplemented by the additional stipulation that very commonly, either βL or βR is zero, meaning that the saccade of one eye or the other dispenses entirely with visual input from the contralateral eye:either

display math(4)

or

display math(5)

and with the size of the saccade of the other partner eye then being determined by weighted averaging like that of either eqn (3) (for use with eqn (4)) or eqn (2) (for use with eqn (5)). In essence, then, the implication would be that one eye or the other predominates saccade generation; its own visual stimuli are used to programme its own saccade, uninfluenced by what its partner sees of the target, while the saccade of the partner's eye is then derived from visual stimuli of both eyes.

This proposed interpretation of unbalanced saccades attributes their excursions entirely to the saccade-generating system, thereby ignoring any possible contribution to saccadic movement made by the vergence system. There is good reason to presume that the vergence-movement system is largely responsible for the usual slow post-saccadic movements (albeit asymmetrically; see, also, Enright, 1996), as well as for any pre-saccadic vergence changes that occur, but its effect on saccadic eye movement is provisionally treated here as negligible.

Equations (2) and (3) can describe many sorts of vergence-associated saccades, but most of those same results can also be qualitatively interpreted with the general hypothesis that signals from version and vergence systems ‘interact.’ (Erkelens et al. 1989; Zee et al. 1992; Collewijn et al. 1994) The experimental results emphasized here, however (predominance of relatively good post-saccadic foveation by one eye or the other), constrain speculation to a much greater extent. Such results seem to provide a prima-facie case for a process that conforms approximately with the degenerate forms of eqns (4) or (5) for behaviour of the better-aligned eye. Alternative hypotheses are seemingly forced to interpret these remarkable results as being nothing more than the result of coincidence - but an exceedingly common and visually very useful coincidence.

APPENDIX

The divergence-left trials of subject 3 were strikingly different from all other eleven data sets: in every single one of those twenty-five trials, the initial saccades were followed immediately by a second saccade in the same direction. The intervals between those saccadic pairs averaged 127 ms (median of 117 ms), and 92 % of the latency values were less than the 175 ms value usually taken as a minimum for visually guided saccades (Carpenter, 1988). These short latencies suggest that saccadic pairs may well have been pre-programmed by initial visual stimuli as a two-saccade ‘packet’, with no guidance by intervening visual stimuli for the second saccades. The second saccades of those pairs primarily served to overcome versional shortfall (average, 1.8 deg, s.d., 0.55 deg) from the first saccades.

When those second, largely versional saccades were treated as ‘post-saccadic movement’ (the usual method of treatment), the ‘extremely asymmetrical’ threshold (|R| > 4) was seldom reached (2 cases, compared with a mean of 14, range from 10–18 in the other 11 data sets). If we tentatively accept the ‘two-saccade-packet’ interpretation, post-saccadic movements in those trials can be evaluated instead by comparing eye positions after the second saccades with the final, steady-state orientations. These anomalous trials from subject 3 are thereby brought into conformity with the other eleven data sets: one trial with 1 < R < 1.5 and eleven ‘extremely asymmetrical’ trials (|R| > 4). For that subset of the data, therefore, these modified estimates (using ends of the second saccades) were used for Table 1 and elsewhere (except for Fig. 11).

None of the other data sets commonly included initial, short-latency two-saccade sequences, so for 375 out of 400 version-vergence trials, as well as all 150 isovergence trials, ‘post-saccadic’ eye orientation was consistently evaluated immediately after the initial large saccades.

Acknowledgements

This research was supported by grant IBN 93-13038 from the National Science Foundation. A preliminary report on these results was presented at the 1997 meeting of the Association for Research on Vision and Ophthalmology (Enright, 1997). Valuable comments on an earlier draft of this manuscript were provided by Professor H. Collewijn.

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