Slow saccades are saccadic eye movements whose peak velocities are slower than normal ones. Slow eye movements are unstable (i.e., fluctuating or drifting) fixational eye movements. Because very slowed slow saccades are no longer distinguishable from slow eye movements, we first detect them together by modifying one of the most popular conventional saccade detection algorithms (
Engbert et al., 2015a). All conjugate eye movements (normal saccades, slow saccades, and slow eye movements) that emerge without external stimuli can be separated from fixation by adjusting the threshold of the algorithm for detecting normal saccades. The conventional algorithm uses two thresholds to detect normal saccades: one for saccadic velocity and the other for saccadic duration. One major caveat of this algorithm is that high-frequency noise in the eye data may be misdetected as saccades (see Test Session in the
Evaluation of detection algorithms of OAIs section). It would not have been an issue in the study of
Engbert, Trukenbrod, Barthelmé, and Wichmann (2015b), because they evaluated only normal saccades with an amplitude ≥ 0.5°. By contrast, the current study deals with smaller saccades and other eye movements (amplitude ≥ 0.07°). We modified this algorithm to detect normal saccades together with slow saccades and slow eye movements without misdetecting noise by using a double-step velocity thresholding procedure, as well as a duration threshold and an amplitude threshold (
Figure 2A). In the first step of the double-step velocity thresholding, a velocity threshold was set to three times the
SD of eye velocity data instead of five times in the conventional algorithm to detect normal saccades, slow saccades, and slow eye movements with relatively high peak velocities (
Figure 2A①). In the second step, another velocity threshold was set to 1
SD of the eye velocity data after excluding those detected by the first step (
Figure 2A②). Furthermore, we reset these thresholds every 10 seconds to set them adaptively in accordance with changes in eye velocity characteristics corresponding to participants’ alertness (
Wakui & Hirata, 2013). In this way, small normal saccades, slow saccades, and slow eye movements that all have comparable peak velocities may be reliably detected altogether. Start times of these eye movements were assigned just before their eye velocities exceeded 2°/s before exceeding the threshold (3 or 1
SD of eye velocity for each participant) (
Figure 2A③). Their end times were assigned to the timing when eye velocities fell below 2°/s for the first time after exceeding the threshold if they did not overshoot, or after gaze corrections that followed over-shoots (
Bahill, Clark, & Stark, 1975a;
Kapoula, Robinson, & Hain, 1986) (
Figure 2A③). The end time of one of these eye movements and a start time of another sometimes overlapped. If these two were in the same direction, they were regarded as one continuum eye movement (
Figure 2A④). To prevent misdetections strictly, in our modified algorithm, we adopted a longer duration threshold of ≥ 0.04 second instead of 0.006 second used in the conventional algorithm (
Figure 2A⑤), as well as an amplitude threshold of ≥ 0.07° (
Figure 2A⑥).