Following this assumption, many experimental studies of changes in fixation have used targets intended to produce either conjugate saccades or pure vergence movements. For example, to investigate conjugate saccades, Collewijn and colleagues developed a paradigm where participants were asked to look back and forth between light emitting diodes (LEDs) at the pace of a metronome (e.g., Collewijn, Erkelens, & Steinman,
1988a,
1995; Collewijn et al.,
1997). To avoid any stimulation of vergence, in some of their experiments stimuli were presented on iso-vergence circles (i.e., circles passing through the rotational centers of the two eyes and through the targets). In contrast, studies investigating pure vergence movements would present targets in the mid-sagittal plane at varying viewing distances (e.g., Rashbass & Westheimer,
1961). The amplitude of the vergence movement tends to be dysmetric, i.e., moving gaze from a near to a far target leads to excessive convergence (over-convergence), and moving gaze from a far to a near target to insufficient convergence (under-convergence; Cornell, MacDougall, Predebon, & Curthoys,
2003). Convergence is usually faster than divergence (Hung, Zhu, & Ciuffreda,
1997; see Straumann,
2007, for a recent review on disconjugate eye movements). If version and vergence movements were completely independent, saccades would be superimposed upon a slower ongoing vergence movement (see Figure 6 in Yarbus,
1957, for illustration). Research employing simple scanning tasks has shown, however, that normal human eye movements often violate Hering's Law (e.g., Collewijn et al.,
1995,
1997; Zee, Fitzgibbon, & Optican,
1992). Much of the total vergence change takes place during the saccade. During a saccade, the eyes initially diverge, but convergence occurs in the latter part of the saccade, continuing into the fixation period following the saccade (e.g., Collewijn et al.,
1988a,
1997). This pattern originates from an asymmetry between saccades made by the abducting (temporally moving) and adducting (nasally moving) eye. In a typical horizontal saccade, the abducting eye has a larger amplitude, a higher peak velocity, and a shorter duration (Collewijn et al.,
1988a). The transient divergence during saccades was confirmed by an investigation of the binocular fixation point, which showed an outward-looping, curved trajectory (Collewijn et al.,
1997). The loops were disproportionately larger for far than for near targets, due to the nonlinear relation between vergence and viewing distance (but see Yang & Kapoula,
2003, suggesting that effects of target distance cannot be due to geometry alone). Furthermore, the relative contributions of the two eyes to post-saccadic (or intra-fixational) vergence appear to be asymmetric (Collewijn et al.,
1988a; Enright,
1998; but see Collewijn et al.,
1997, reporting symmetry). Gaze shifts in a natural setting typically require composite eye movements, i.e., movements between targets that differ simultaneously in both direction and distance from the observer. A number of studies investigated combined version and vergence; a key finding is that version accelerates vergence while vergence slows down version (Collewijn et al.,
1995). Finally, little is known about vertical fixation disparities. Collewijn et al. (
1997) note that their recordings of the vertical components of horizontal binocular eye movements indicated only small vertical disparity. In addition, vertical conjugacy for vertical saccades is good though not perfect (Collewijn, Erkelens, & Steinman,
1988b).