Summary of the paradigm. A. Example trial procedure: The saccade target and foveal probe were embedded in full-screen noise images flickering at a frequency of 20 Hz (image duration of 50 ms). After 200 ms, the saccade target (an orientation-filtered patch; filtered to either –45° or +45°; 3 dva in diameter) appeared 10 dva to the left or the right of the screen center, cueing the eye movement. On 50% of trials, a probe (a second orientation-filtered patch; filtered to either –45° or +45°) appeared in the screen center at an early (top panel; highlighted element with dark blue outline), medium (light blue outline) or late (green outline) stage of saccade preparation. The foveal probe was presented for 50 ms and could be oriented either congruently or incongruently to the target. In contrast to our previous investigation, the saccade target was presented at one of four opacities (from 25% to 90%; in different blocks). B. An increase in target opacity translates to an increase in signal-to-noise ratio (SNR; left panel). Within a single trial, the increase in SNR at the target location manifests from the fourth noise image on (i.e., after the target appears; right panel; error bands correspond to the standard deviation across all images). C. Probe and target timing. Probe timing (left panel): histogram of time intervals between probe offset and saccade onset. Bar heights and error bars indicate the mean and standard error of the mean (SEM; n=9) across observers, respectively. On included trials, the probe appeared after target onset and therefore during saccade preparation (‘sac prep’). Trials in which the probe disappeared more than 250 ms before saccade onset (light grey), during the saccade (yellow) or after saccade offset (orange) were excluded. The yellow background rectangle illustrates the median saccade duration. Target timing (right panel): histogram of time intervals between target offset and saccade offset. Bar heights and error bars indicate the mean and standard error of the mean (SEM; n=9) across observers, respectively. Unlike in the previous study, we removed the target upon saccade initiation on all trials.

Influence of target opacity on Hits and FAs across all time points. A. Influence of target opacity on congruent and incongruent HRs (purple and gray data points in the left panel) as well as their difference (orange data points, middle panel). Lines and error bands correspond to the fitted linear regression lines ±2 standard errors of the mean (SEM). The slopes of the fitted regression line per observer (small circles) and their mean and SEM (big circle and error bar) are plotted in the right panel. Asterisks denote statistically significant comparisons (p <.05; determined via bootstrapping; n = 9 observers). B. Influence of target opacity on congruent and incongruent FARs (left panel) as well as their difference (middle and right panel). All conventions are as in A. C. Mean difference in filter energies around the target and non-target orientation for the lower two target opacities (left column) and the higher two target opacities (right panel). Lines connect the values of individual observers (small circles) in both conditions. Large circles and error bars denote the mean and SEM, respectively. D. Pearson correlation between the normalized slope in HRs (A, right panel) and the normalized slope in FARs (B, right panel). Circles indicate individual observers.

Time course of enhancement in HRs for different target opacity levels. A. Probability density distributions of saccade latencies for increasing target opacity. Distributions with thin and thick lines represent individual-observer and mean probability densities, respectively. Vertical lines and shaded regions represent median latencies and SEMs, respectively. B-C. Target-(B) and saccade-locked (C) time course of enhancement. In C, the proportion of different target-locked bins in each saccade-locked bin was equalized across opacities to account for the systematic decrease in latencies with increasing opacity plotted in A. In B and C, x-axis values indicate the center of 50 ms bins. Note that in B, the last bin contains probe onset times between 200 and 300 ms to allow for sufficient trial numbers. Across panels, error bars indicate SEMs. Asterisks denote significant differences between congruent and incongruent HRs (p≤.05; determined via bootstrapping with 10,000 repetitions; n = 9 observers).

HRs and FARs separately for short-latency (A) and long-latency (B) saccades. All conventions are as in Figure 2.

Variation of RMS contrast (first column), Michelson contrast (second column) and SNR (third column) within the saccade target region. A. Probability density distributions per measure and target opacity (yellow to dark red shadings). B. Mean and standard deviation of contrast and SNR separately for each noise image presented during the saccade preparation period. The target was presented from the 4th noise image on.

Calculation of the reverse correlation index plotted in Figure 2C, illustrated for the 59% target opacity condition. In step 1, we identified the average properties (SF*orientation) of the foveal noise window on congruent (purple outlines and font) and incongruent (gray outlines and font) FA trials. In step 2, we determined the difference between them (congruent–incongruent). In step 3, we subtracted filter energies around the non-target orientation (-45°) from filter energies around the target orientation (45°).

The influence of target opacity on saccade metrics. A. Probability density distributions of saccade latencies for different, increasing target opacities (from top to bottom; see Figure 3A). Distributions with thin and thick lines represent individual-observer and mean probability densities, respectively. Vertical lines and shaded regions represent median latencies and standard errors. B. Bivariate Gaussian kernel densities of saccade landing coordinates separately for leftwards and rightwards saccades. The distance between the fixation and target locations was reduced for illustration purposes (see legend). C. Main sequences defined as the relation between saccade amplitudes and peak velocities. Dots symbolize individual trials (n ∼ 29,000). Fitted lines represent the average of logistic function fits to individual-observer data (Conder, 2023). The mean parameters of each fit are provided above the respective panel (‘tHalf’: symmetric inflection point; ‘qInf’: horizontal asymptote; α: decay constant). D. Summary plots for saccade latency, amplitude, landing error and peak velocity. Dots represent median (latency) and mean (amplitude, error, velocity) values across observers, and error bars represent the respective standard errors. Black lines and shaded error bands represent the mean of linear fits to individual-observer data and their standard errors, respectively. Asterisks highlight slopes that are significantly different from zero (determined via bootstrapping, n = 9 observers, p <.05).