**Participants**
We will collect data from 6 naive participants, recruited through campus mailing lists. Each participant will be asked to complete six sessions of about 1h each. They receive monetary compensation for their participation.
**Aparatus**
Stimuli will be projected onto a standard 16:9 (200 x 113 cm) video-projection screen (Celexon HomeCinema, Tharston, Norwich, UK), mounted on a wall, 270 cm in front of the participant. The projector is a ProPixx (Vpixx Technologies, Saint-Bruno, QC, Canada) running at 1440 Hz vertical refresh and a resolution of 960 x 540 pixels. The experimental code is implemented in MATLAB (Mathworks, Natick, MA, USA), using the Psychophysics and Eyelink toolboxes (Kleiner et al., 2007; Cornelissen et al., 2002) and runs on a Dell Precision T7810 Workstation with a Debian 8 operating system. Eye movements are recorded via an EyeLink 2 head-mounted system (SR Research, Osgoode, ON, Canada) at a sampling rate of 500 Hz. The eye tracker will be calibrated before every block of trials and whenever necessary. Responses are collected with a standard keyboard.
**Procedure**
Participants will complete six sessions of data collection, each consisting of 1440 trials, distributed over a total of 8 blocks, alternating between blocks of trials in a perceptual task (280 trials per block; 4 blocks per session) and blocks of trials in a saccade task (80 trials per block; 4 blocks per session).
*Perceptual task.* Each trial is preceded by a fixation check: a fixation spot (diameter: 0.15 degrees of visual angle, dva) is displayed at the center of the screen, and once fixation is detected in an area of 2.0 dva around the fixation spot for at least 200 ms, the trial starts. The fixation spot stays on the screen throughout the trial. After 50 to 100 ms of fixation, a Gabor stimulus appears either left or right (for horizontal motion) or above or below (for vertical motion) of the screen center (chosen randomly on each trial), ramping up from zero to full contrast in 100 ms. Once at full contrast, the stimulus rapidly moves—in a curved trajectory such that it passes the center above or below the fixation spot (for horizontal motion) or left or right (for vertical motion), with a maximum distance of 30% of the overall movement amplitude—towards the other side of fixation, following a certain velocity profile (see below), before ramping back to zero contrast in 100 ms. Once the stimulus has disappeared, the observer presses one of two buttons to indicate whether the stimulus moved in an upward vs downward curvature (for horizontal motion) or a leftward vs rightward curvature (for vertical motion).
Motion stimuli are Gabor patches (1 cycle per degree, sigma of the envelope: 1/3 deg; with an orientation orthogonal to the movement direction), traveling on a motion path corresponding to an arc of a circle with a radius chosen such that the maximum deviation from a straight line was exactly 30% (reached at the center of the screen, when closest to fixation). The velocity of the Gabor (in its main movement direction) is constant throughout the movement, corresponding either to the peak velocity of a saccade at that amplitude, a slowed-down, or a sped-up version of it (peak velocity multiplied by factors of 1/4, 1/3, 1/2, 1/1.5, 1/1.25, 1, 1.25). The peak velocity is determined using the parameters of the standard main sequence described by Collewijn et al. (1988). The amplitude of the movement will be either 4, 6, 8, 10, or 12 dva (randomly interleaved across trials).
Each combination of movement amplitude (4, 6, 8, 10, 12 dva), movement velocity (1/4, 1/3, 1/2, 1/1.5, 1/1.25, 1, or 1.25 times the saccadic peak velocity of a given amplitude), curvature direction (up vs down or left vs right), and motion direction (leftward vs rightward vs upward vs downward), occurs once per block of 280 trials (total number of perceptual blocks: 24). For all analyses, we intend to collapse across curvature directions, resulting in a total of 48 trials per data point.
*Saccade task.* Each trial is preceded by a fixation check: a fixation spot (diameter: 0.15 degrees of visual angle, dva) is displayed at a location offset from the center of the screen in the horizontal or vertical direction. Once fixation is detected in an area of 2.0 dva around the fixation spot for at least 200 ms, the trial starts. The fixation spot stays on the screen throughout the trial. After 50 to 100 ms of fixation, the fixation point jumps to the opposite side of the screen center, and participants execute a saccade to the new target location. Initial and end points of the fixation target will be displaced from the center of the screen by half the instructed saccade amplitude, such that gaze passes the center of the screen during each saccade. We will detect the execution of saccades online, by registring saccade landing within a ±50% of the target eccentricity within 400 ms of target onset. The instructed saccade amplitude will be between 4 and 12 dva, in steps of 1 dva (randomly interleaved across trials). Each saccade vector will be tested twice in each block of 80 saccade trials (total number of saccade blocks: 24).
**Data analysis**
We will confirm successful fixation and saccacde behavior during each trial off-line, using standard procedures for (micro)saccade detection (Engbert & Mergenthaler, 2006). Saccadic peak velocities will be determined for each saccade as the maximum of the velocity profile of smoothed the eye movement trace along the main direction of movement. An exponential function (Collewijn et al., 1988) will be fit to the dependence of peak velocity on saccade amplitude (main sequence), to obtain robust predictions of velocity for any given movement amplitude.
We will exclude trials with (1) saccades larger than 1 dva during required fixation (in perceptual and saccade trials), (2) saccades outside ±50% of the required saccade amplitude (in saccade trials), (3) missing data (e.g., due to blinks).
All remaining trials will be included in subsequent analyses. For each combination of movement vector and velocity, stimulus visibility will be assessed by computing each observer's ability to correctly identify the curvature of the stimulus (up vs down, left vs right). We will compute both the percentage of correct reports and a bias-free measure of visual sensitivity (*d'*). Psychometric functions will be fit to the data collected for each movement vector to obtain corresponding speed thresholds (velocities at which the movement becomes invisible).
Manual reaction times will be evaluated to rule out any speed-accuracy tradeoffs. Fixational eye movements may be inspected for potential traces of conscious detection of the stimulus (see White & Rolfs, 2016). Given the rapid succession of events in a trial, however, we do not expect a high rate of microsaccades.
**References**
Collewijn, H., Erkelens, C. J., & Steinman, R. M. (1988). Binocular co-ordination of human vertical saccadic eye movements. The Journal of Physiology, 404, 183–197.
Cornelissen, F. W., Peters, E. M., & Palmer, J. (2002). The Eyelink Toolbox: Eye tracking with MATLAB and the Psychophysics Toolbox. Behavior Research Methods, Instruments, & Computers, 34, 613–617.
Engbert, R., & Mergenthaler, K. (2006). Microsaccades are triggered by low retinal image slip. Proceedings of the National Academy of Sciences USA, 103(18), 7192–7197. http://doi.org/10.1073/pnas.0509557103
Kleiner, M., Brainard, D. H., Pelli, D. G., Ingling, A., Murray, R., & Broussard, C. (2007). What’s new in Psychtoolbox-3? Perception 36: 1–16.
White, A. L., & Rolfs, M. (2016). Oculomotor inhibition covaries with conscious detection. Journal of Neurophysiology, 116(3), 1507–1521. http://doi.org/10.1152/jn.00268.2016