Abstract

Visual perception seems continuous, but recent evidence suggests that the underlying perceptual mechanisms are in fact periodic—particularly visual attention. Because visual attention is closely linked to the preparation of saccadic eye movements, the question arises how periodic attentional processes interact with the preparation and execution of voluntary saccades. In two experiments, human observers made voluntary saccades between two placeholders, monitoring each one for the presentation of a threshold-level target. Detection performance was evaluated as a function of latency with respect to saccade landing. The time course of detection performance revealed oscillations at around 4 Hz both before the saccade at the saccade origin and after the saccade at the saccade destination. Furthermore, oscillations before and after the saccade were in phase, meaning that the saccade did not disrupt or reset the ongoing attentional rhythm. Instead, it seems that voluntary saccades are executed as part of an ongoing attentional rhythm, with the eyes in flight during the troughs of the attentional wave. This finding for the first time demonstrates that periodic attentional mechanisms affect not only perception but also overt motor behavior.

INTRODUCTION

We experience a smoothly evolving visual world, in which representations of objects and events in the outside world appear to be continuously and seamlessly updated in our visual awareness. However, recent evidence suggests that the brain's visual system might in fact process the continuous stream of incoming visual information in successive snapshots, like the sequential frames of a video camera (e.g., Chakravarthi & VanRullen, 2012). In a video camera, individual frames are sampled from the continuous input stream by a shutter mechanism. It has been suggested that, in the brain's visual system, that role might be played by visual attention (Busch & VanRullen, 2010; VanRullen, Carlson, & Cavanagh, 2007). In this analogy, attentional sampling takes place rhythmically, with sequential periods of high attentional resources alternating with periods where attention is unavailable, resulting in a sequence of snapshots that are subsequently submitted to further analysis. For instance, Landau and Fries (2012) demonstrated that drawing attention to one of two possible target locations resulted in rhythmic oscillations in detection performance at each of the two locations, indicating that attention was effectively alternating between the two locations. This is true even when the two locations are part of the same visual object (Fiebelkorn, Saalmann, & Kastner, 2013). Even when only one possible target location is to be monitored, spontaneous fluctuations in detection performance reveal an underlying periodic process (VanRullen et al., 2007).

Such discrete perceptual episodes seem at odds with our day-to-day experience of continuous visual awareness. However, basic cinematography shows us that a sequence of discrete samples can be perceived as continuous. Furthermore, although visual awareness might appear continuous, periodic fluctuations of awareness have in fact been linked to oscillatory brain activity (Song, Meng, Lin, Zhou, & Luo, 2014; Spaak, de Lange, & Jensen, 2014; de Graaf et al., 2013; Busch, Dubois, & VanRullen, 2009; Mathewson, Gratton, Fabiani, Beck, & Ro, 2009), indicating that periodic neural mechanisms do indeed result in discrete episodes in perceptual processing.

To date, studies investigating discrete attentional processes have considered perception during fixations. On the one hand, this is an unsurprising methodological choice, because visual input is interrupted every time we make saccadic eye movements (Krekelberg, 2010). As such, saccades already split visual input into discrete episodes, which would make it difficult to conclude at which stage of the visual hierarchy processing might be discrete. On the other hand, however, studying the way the visual system handles the discrete sensory episodes delineated by saccades might be informative about discrete perceptual processes more generally. For example, we do not perceive the transients introduced by saccadic eye movements. Instead, the visual system is able to stitch together input across saccades into a continuous stream of visual awareness, revealing that the neural mechanisms to integrate discrete samples into a continuous stream of awareness do in fact exist.

Furthermore, it is well established that the neural circuitries for the preparation of eye movements and for the deployment of attention are closely linked (e.g., Moore, Armstrong, & Fallah, 2003; Schall & Thompson, 1999). For example, attention is preallocated to future saccade targets (Rizzolatti, Riggio, Dascola, & Umiltá, 1987), and attention has been proposed to be involved in remapping visual space in anticipation of the new retinotopic locations (Melcher, 2007). There is evidence that ongoing oscillatory brain activity affects the preparation of saccadic eye movements in humans (Hamm, Dyckman, McDowell, & Clementz, 2012; Drewes & VanRullen, 2011), and saccadic eye movements in primates have been shown to synchronize low-frequency oscillations in the hippocampus (Hoffman et al., 2013; Jutras, Fries, & Bufallo, 2013), but the relationship between periodic attentional processes and saccadic eye movements in humans remains unstudied.

To address this question, in two experiments, observers made voluntary saccades back and forth between two positions while eye movements were recorded. Observers detected subtle targets that were briefly flashed at each saccade target at a range of latencies with respect to the saccade. Our results reveal a rhythmic oscillation of detection performance both before and after the saccadic eye movement, indicating that the preparation of saccadic eye movements depends on the phase of the ongoing attentional rhythm.

METHODS

Experiment 1

The author and four naive observers, all men with normal or corrected-to-normal vision, participated in the experiment after giving informed consent. I anticipated that, if they existed, oscillations in detection performance would be evident in individual observers. Because possible interindividual difference might contaminate an across-observer average, I elected to collect a large number of trials in relatively few observers. Because trials were to be binned post hoc in a time-resolved manner, obtaining sufficient trials to allow the results of individual observers to be interpreted at all required a large number of trials and a substantial time commitment from the observer (approximately 8 hr in total).

Stimuli were presented on a 21-in. LaCie 321 LCD monitor at 60 Hz and 1600 × 1200 resolution at a distance of 60 cm from the observer, controlled by an Apple G5 computer running MATLAB 7.5 with Psychtoolbox 3.0.8 extensions. Eye movements were recorded using an EyeLink II eyetracker (SR Research, Mississauga, Canada). The position of the left pupil was sampled at a rate of 250 Hz, and saccades were detected using the proprietary EyeLink algorithm.

Stimuli consisted of two fixation points (diameter = 0.45° of visual angle) separated horizontally by 11.24°. Around each fixation point, a drifting grating was presented within an annulus (outer diameter = 3.38°, inner diameter = 0.67°). Each grating had a spatial frequency of 2.23 cycles per degree of visual angle and drifted at a rate of 2 Hz (0.90° of visual angle per second). At the start of each block, both gratings drifted rightward. To avoid inducing a motion aftereffect, the drift direction of each grating changed over time at a rate of 10° polar angle per second, with the right grating changing direction clockwise and the left grating changing direction counterclockwise. Stimuli were presented at maximum contrast on a medium gray background (Figure 1).

Figure 1. 

Stimulus. The stimulus consisted of two fixation points surrounded by drifting gratings. The fixation points gradually switched color at the start of every trial; observers made voluntary eye movements to fixate the black fixation dot. Observers' task was to monitor the fixated grating for the presentation of a contrast decrement target (shown here in exaggerated contrast in the right grating).

Figure 1. 

Stimulus. The stimulus consisted of two fixation points surrounded by drifting gratings. The fixation points gradually switched color at the start of every trial; observers made voluntary eye movements to fixate the black fixation dot. Observers' task was to monitor the fixated grating for the presentation of a contrast decrement target (shown here in exaggerated contrast in the right grating).

Observers were instructed to maintain fixation on the black fixation point and to monitor the surrounding drifting grating for the appearance of a target. Targets consisted of brief (33 msec) contrast decrements in the grating. The contrast decrement was a 2-D Gaussian with width of 0.45° (FWHM), presented within the grating at a random polar angle at a distance of 0.90° from the center of the fixation dot. The magnitude of the contrast decrement was established independently for each observer before the main experiment by a separate staircase procedure such that observers detected roughly 50% of targets. Because the target was presented at a random polar angle within the grating, there was no systematic relationship between the phase of the sine function within the grating and the phase of the sine function at the target position.

Stimuli were presented continuously over the course of an entire block, which consisted of 120 trials. At the start of each block, one of the two fixation points was black; and the other, white. Each trial started by the black fixation point gradually changing to white and then the white fixation point gradually changing to black. This transition took place gradually, ending 333 msec after trial start. During each trial, a single target was presented, at 1 of 120 random intervals from 0 to 2 sec (in steps of 16.7 msec) after trial start. Because this interval overlapped with the fixation transition period, in some trials, the target was presented during the fixation point change. The target was always presented in the grating in which the fixation point was black or transitioning into black. The trial continued for a random duration between 3.75 and 4.25 sec, before a new trial initiated by the black fixation point changing location again. Trials moved into each other seamlessly, without interruption or breaks.

Observers were instructed to maintain fixation on the black fixation dot and to shift their gaze to follow it when it changed location. A fixation window was not enforced by eye tracking. In addition, observers were instructed to monitor the fixated grating for the appearance of the target and report detecting it as rapidly as possible by means of a button press. Only responses within 1000 msec of target presentation were accepted. Observers received no feedback about their responses. Observers were instructed after the initial staircase procedure that they would see targets on only some trials. There were no catch trials.

Each observer completed 15 blocks for 1800 trials per observer.

Experiment 2

The experimental setup was the same in Experiment 2 as in Experiment 1, with the following exceptions: The author and three naive observers, all men with normal or corrected-to-normal vision, participated in this experiment after giving informed consent. All but one of the observers had previously participated in Experiment 1. Because it was observed in Experiment 1 that oscillations were clearly evident in individual observers, and in light of the time commitment required from observers, I elected to include four observers in Experiment 2.

As in Experiment 1, observers made voluntary eye movements back and forth between two drifting gratings, each time monitoring the fixated grating for the appearance of a contrast decrement target. However, whereas in Experiment 1, the target was only presented at one of the two gratings, in Experiment 2, the target was presented simultaneously in both gratings. Because detecting the target required fixating the corresponding grating, it was impossible for observers to perceive the target at both locations simultaneously. In addition, whereas in Experiment 1, the target was presented only after fixation point change (0–2000 msec), in Experiment 2, the target could be presented either before or after the fixation point change (833 msec before to 1166 msec after).

Observers' task was the same as in Experiment 1, with the exception that observers reported in which of the two grating they detected a target, using one of two buttons corresponding to the left and right gratings (rather than merely reporting the presence of the target with a single button, as in Experiment 1).

As in Experiment 1, each observer completed 15 blocks of 120 trials each, for 1800 trials per observer.

RESULTS

Experiment 1

Five observers made voluntary saccades back and forth between two drifting gratings, each time monitoring the fixated grating for the presentation of a threshold-level luminance decrement (Figure 1). For each trial, the temporal offset between the end of the saccade that the observer made to fixate that trial's fixation point and the presentation of the target was calculated. Only trials in which precisely one saccade was extracted within 2 sec of target presentation (either before or after) were included in the analysis. All valid trials were collapsed across all observers (for 8550 valid trials of 9000) and sorted into 4-msec bins (from 500 msec before to 2000 msec after the end of the saccade). The proportion of correctly detected targets was calculated for each bin, and the resulting time series was smoothed with a moving average window 7 bins (28 msec) wide (Figure 2).

Figure 2. 

Experiment 1 results: Detection performance as a function of time relative to saccade offset. Gray bars denote raw proportion correct, binned in 4-msec bins. The thick dashed line represents the same data, smoothed with a moving average window 7 bins (28 msec) wide. Light dashed lines represent bootstrapped 95% confidence intervals of this smoothed time course. The solid line denotes a dampened oscillation function optimized to fit the data (see main text).

Figure 2. 

Experiment 1 results: Detection performance as a function of time relative to saccade offset. Gray bars denote raw proportion correct, binned in 4-msec bins. The thick dashed line represents the same data, smoothed with a moving average window 7 bins (28 msec) wide. Light dashed lines represent bootstrapped 95% confidence intervals of this smoothed time course. The solid line denotes a dampened oscillation function optimized to fit the data (see main text).

Furthermore, 95% confidence intervals were estimated for the smoothed time series data using bootstrapping (Efron & Tibshirani, 1994). Ten thousand new data sets were generated by drawing 9000 trials at random with replacement from the original available data. Each data set was analyzed in the identical way, and 95% confidence intervals were calculated for each time point in the smoothed time series by finding the 2.5 and 97.5 percentile points in the resulting distributions.

To describe oscillation evident in the smoothed time series both qualitatively and quantitatively, detection performance was modeled as a function of time with five free parameters:
formula
formula

This function defines detection performance y as a function of time t, whereby the first term denotes the asymptotic performance level well after saccade landing, the second term denotes a Gaussian function to model the initial increase in performance after saccade landing, and the third term represents a cosine oscillation with a Gaussian window to model any oscillations immediately after saccade landing. All values for before saccade landing were set to zero. The function was fitted to data from the interval ranging from 400 msec before saccade landing to 1600 msec after saccade landing. This particular function was chosen to model several key properties:

  • 1. 

    Performance must be zero when the eyes are fixating elsewhere or in flight.

  • 2. 

    Performance must ramp up gradually after saccade landing to reach a certain approximately constant level of performance. To model a sigmoidal increase with nondiscontinuous second derivative, I chose a half-Gaussian, inverted so as to ramp up to a constant.

  • 3. 

    A cosine term is included to identify any oscillation. Because this oscillation is expected to be time-locked to the saccade and because any trial-by-trial or intersubject variability in oscillation frequency will introduce de-phasing of the oscillation, the oscillation needs to be dampened proportional to the temporal distance from the saccade. For parsimony, a half-Gaussian was chosen to model this dampening.

An optimization procedure (Nelder–Mead multidimensional unconstrained nonlinear minimization) was used to minimize mean squared error by optimizing parameters x0 (the center of both the Gaussian ramp and the Gaussian window modulating the cosine oscillation), σ1 (the width of the Gaussian ramp), σ2 (the width of the Gaussian window modulating the cosine oscillation), λ (the wavelength of the cosine oscillation), and ϑ (the phase of the cosine oscillation). Of particular interest were the wavelength and phase of the cosine oscillation—applying the optimization procedure to the complete original data set generated an optimal period of 264 msec (3.78 Hz) with a phase of 1.5 radians for the cosine oscillation.

To generate 95% confidence intervals for the parameter estimates, the identical fitting procedure was applied to the 10,000 data sets generated previously to estimate 95% confidence intervals for the smoothed time series. For each parameter, the 2.5 and 97.5 percentile points on the resulting distribution of estimates for that parameter were taken as 95% confidence intervals. Circular statistics were used for phase estimates. This yielded a 95% confidence interval from 180 to 653 msec for the period of the oscillation and 0.17–2.9 radians for the phase of the oscillation.

Cross-validation was used to evaluate the fit of the function and also to control for overfitting. The complete data set was split into halves, fitting the function to the first half and then evaluating it on the second half. To evaluate the noise ceiling imposed by the data itself, not only the degree to which the function optimized for one half of the data could explain the other half was evaluated, but also the degree to which the first half of the data itself could explain the other half. This procedure was carried out 10,000 times, splitting the data set into different halves each time. Across all bootstrapped data sets, the function optimized for one half of the data was able to explain an average of 88.3% of the variance in the other half. The actual data of the first half of the data set were able to explain only 78.9% of the data in the other half, making overfitting unlikely.

The gradual change in the fixation point luminance was designed to prompt observers to make voluntary saccades to the opposite grating, rather than provide an exogenous cue that might itself reset an attentional rhythm as in Landau and Fries (2012). To evaluate the degree to which the observed oscillations might nonetheless be locked to the fixation point change, rather than the saccade, the entire analysis was repeated as a function of time relative to fixation point change instead of saccade landing. Across all observers, saccade landing occurred a mean of 413 msec after the start of the change in the luminance of the fixation points, with a standard deviation of 74 msec. The analysis procedure was identical, with the exception that trials were binned in 16.67-msec bins because of the temporal limits imposed by the 60-Hz refresh rate of the monitor.

As is visible in Figure 3, no oscillations in detection performance are evident when trials are binned according to time relative to fixation point change. In addition, the optimal value for λ parameter denoting the wavelength of the cosine oscillation was 1629 msec, two orders of magnitude greater than in the saccade-locked data, indicating that the ∼4-Hz oscillation evident in the saccade-locked data was not present when data were analyzed relative to fixation dot change.

Figure 3. 

Experiment 1 results: Detection performance as a function of time relative to fixation point change, rather than saccade offset, showing that no oscillations are evident when data are time-locked to fixation point change. Gray bars denote raw proportion correct, binned in 16.67-msec bins. The thick dashed line represents the same data, smoothed with a moving average window 2 bins (33.3 msec) wide. Light dashed lines represent bootstrapped 95% confidence intervals of this smoothed time course.

Figure 3. 

Experiment 1 results: Detection performance as a function of time relative to fixation point change, rather than saccade offset, showing that no oscillations are evident when data are time-locked to fixation point change. Gray bars denote raw proportion correct, binned in 16.67-msec bins. The thick dashed line represents the same data, smoothed with a moving average window 2 bins (33.3 msec) wide. Light dashed lines represent bootstrapped 95% confidence intervals of this smoothed time course.

To further confirm this, the same function was fitted to each of the 10,000 bootstrapped data sets as for the original saccade-locked data and evaluated by cross-validation. A function optimized to fit one half of the data explained an average of 92.9% of the variance in the other half. Importantly, the actual data of the first half of the data set were also able to explain an average of 90.7% of the data in the other half. This difference was substantially and significantly smaller (2.21%, 95% CI [2.17%, 2.24%]) than the additional variance explained by the fitted function in the original analysis (9.54%, 95% CI [9.47%, 9.58%]), indicating that the oscillatory function captured more systematic variance when data were analyzed relative to saccade landing than when analyzed relative to the onset of the fixation dot change. Furthermore, when results were analyzed relative to fixation dot change, there was a very wide range of optimal values for the λ parameter (oscillation wavelength) across bootstrapped data sets (mean = 14992 msec, SD = 7044 msec; 95% CI [205 msec, 14412 msec]), indicating that the oscillatory component did not capture real, systematic oscillations in the data. Altogether, the absence of oscillations in the detection performance when analyzed relative to fixation point change therefore indicates that the fixation point change did not provide an exogenous cue, which itself induced an oscillation.

Detection performance as a function of time relative to saccade landing reveals a nonmonotonic increase in detection performance after saccade landing that cannot be attributed to an attentional reset after an exogenous cue. The time course of detection performance was well fitted by a dampened oscillation with a period of 3.78 Hz. This oscillation is both qualitatively and quantitatively similar to Landau and Fries (2012), who reported that exogenously cuing one of two attended gratings induced 4-Hz oscillations in detection performance at both locations. The fact that similar oscillations in detection performance follow voluntary saccades, in the absence of an exogenous attentional cue, indicates that saccadic eye movements interact with periodic attentional sampling. However, the exogenous cues presented by Landau and Fries induced a reset of the attentional rhythm: No time-locked oscillations were evident in detection performance preceding presentation of the cue. Conversely, in the present experiment, observers made voluntary eye movements in the absence of any transient external stimuli. As such, the present finding of oscillations in detection performance time-locked to saccade landing can have two possible explanations. On the one hand, it is possible that saccadic eye movements reset the attentional rhythm in a comparable way with exogenous cues. Alternatively, saccade preparation might itself depend on the ongoing attentional rhythm. In this view, oscillations in detection performance after saccade landing would not reveal a reset of the attentional rhythm but rather the persistence of the rhythm that dictated the execution of the saccade. The following experiment was carried out to distinguish between these two possibilities.

Experiment 2

Four observers made voluntary saccades between two drifting gratings in the same way as in Experiment 1. However, in Experiment 2, targets were presented bilaterally both before and after saccades, and observers reported in which grating a target was detected, if any. Detection performance at each location was evaluated as a function of time relative to saccade landing. Smoothed time series were calculated on the basis of all 6949 valid trials (of a total of 7200) collapsed across all four observers in precisely the same way as in Experiment 1. Detection performance was calculated independently for the grating that the observer was fixating before the saccade (the saccade origin) and for the grating that the observer was making a saccade toward (the saccade destination). Results are shown in Figure 4.

Figure 4. 

Experiment 2 results: Detection performance at saccade origin (red) and saccade destination (blue) as a function of time relative to saccade offset. Shaded bars denote raw proportion correct, binned in 4-msec bins. The thick dashed lines represent the same data, smoothed with a moving average window 7 bins (28 msec) wide. Light dashed lines represent bootstrapped 95% confidence intervals of smoothed time courses. Solid lines denote dampened oscillation functions optimized to fit the data (see main text). The bottom shows only the oscillatory term from the fitted functions (without the dampening coefficient; blue denotes the fit at the destination, and red denotes the fit at the origin). Each function is shown as a solid line over the period where the function was fitted and as a dashed line as extrapolated over the remaining period. This shows vividly that the two functions have almost identical wavelength and phase.

Figure 4. 

Experiment 2 results: Detection performance at saccade origin (red) and saccade destination (blue) as a function of time relative to saccade offset. Shaded bars denote raw proportion correct, binned in 4-msec bins. The thick dashed lines represent the same data, smoothed with a moving average window 7 bins (28 msec) wide. Light dashed lines represent bootstrapped 95% confidence intervals of smoothed time courses. Solid lines denote dampened oscillation functions optimized to fit the data (see main text). The bottom shows only the oscillatory term from the fitted functions (without the dampening coefficient; blue denotes the fit at the destination, and red denotes the fit at the origin). Each function is shown as a solid line over the period where the function was fitted and as a dashed line as extrapolated over the remaining period. This shows vividly that the two functions have almost identical wavelength and phase.

To quantitatively compare the patterns of detection performance before and after the saccade to each other, as well as with the results of Experiment 1, the fitting procedure from Experiment 1 was applied to detection performance at both the saccade origin and the saccade destination (over the period between 900 msec before and 600 msec after saccade landing). Performance at the saccade destination was modeled using the identical function as in Experiment 1. For the saccade origin, the functional form remained the same, but the function was nonzero for the period before rather than after the saccade. Because mean saccade duration across all trials was 60 msec, the value of the function was set to zero from 60 msec before saccade landing onward.

At the saccade origin:
formula
formula
At the saccade destination:
formula
formula

As in Experiment 1, confidence intervals of the optimized parameters were estimated by bootstrapping. For detection performance at the saccade origin, optimal parameters for the oscillation period and phase were 254 msec (95% CI [239 msec, 279 msec]) and 1.40 radians (95% CI [0.97, 1.93]), respectively. For the saccade destination, optimal parameters for period and phase were 259 msec (95% CI [223 msec, 375 msec]) and 1.20 radians (95% CI [0.26, 2.79]), respectively. A comparison of phase angles, with confidence intervals, is shown in Figure 6 (inset). The bottom of Figure 4 shows the oscillatory term of both functions in the time domain, revealing the near-perfect match of both wavelength and phase between the fits before and after the saccade.

Fits at both the saccade origin and the saccade destination were cross-validated using split-half cross-validation with 10,000 iterations. The fitted function explained 94% of variance at the saccade origin and 91% at the saccade destination. The noise ceiling (the proportion of variance in one half that could be explained by the actual data of the second half, rather than the fitted function) was 89% at the saccade origin and 87% at the saccade destination. As in Experiment 1, this made overfitting unlikely.

As in the previous experiment, the fixation point changed luminance gradually to invite observers to initiate voluntary saccades. The mean latency of saccade landing relative to the start of the fixation point change was 510 msec, with a standard deviation of 118 msec. The fact that oscillations are already evident in performance before the average start of the fixation point change (Figure 4, thick dashed red line) already suggests that oscillations are unlikely to be time-locked to the fixation point change. Nevertheless, to ensure this change did not constitute an exogenous cue that might induce a reset of the attentional rhythm, the entire analysis was repeated as a function of time relative to fixation point change, rather than saccade landing. Trials were binned into 16.67-msec bins and analyzed using otherwise identical steps. The resulting time course of detection performance reveals no evidence of oscillatory detection performance time-locked to the start of the fixation point change (Figure 5).

Figure 5. 

Experiment 2 results: Detection performance at saccade origin (red) and saccade destination (blue) as a function of time relative to fixation point change, rather than saccade landing. Shaded bars denote raw proportion correct, binned in 16.67-msec bins. The thick dashed lines represent the same data, smoothed with a moving average window 2 bins (33.3 msec) wide. Light dashed lines represent bootstrapped 95% confidence intervals of smoothed time courses. Solid lines denote dampened oscillation functions optimized to fit the data (see main text).

Figure 5. 

Experiment 2 results: Detection performance at saccade origin (red) and saccade destination (blue) as a function of time relative to fixation point change, rather than saccade landing. Shaded bars denote raw proportion correct, binned in 16.67-msec bins. The thick dashed lines represent the same data, smoothed with a moving average window 2 bins (33.3 msec) wide. Light dashed lines represent bootstrapped 95% confidence intervals of smoothed time courses. Solid lines denote dampened oscillation functions optimized to fit the data (see main text).

The optimal values for λ parameter were 203 msec at the saccade origin and 158 msec at the saccade destination. To evaluate the stability of the oscillatory term, the same functions were fitted to each of 10,000 bootstrapped data sets and evaluated by cross-validation. Functions optimized to fit one half of the data explained an average of 90.6% (before saccade) and 89.6% (after saccade) of the variance in the other half. Importantly, the actual data of the first half of the data set were also able to explain an average of 92.9% (before saccade) and 89.0% (after saccade) of the data in the other half. As in Experiment 1, this difference was significantly smaller (before saccade: −2.23%, 95% CI [−2.28%, −2.19%]; after saccade: 0.57%, 95% CI [0.51%, 0.62%]) than in the original analysis (before saccade: 3.64%, 95% CI [3.59%, 3.70%]; after saccade: 4.83%, 95% CI [4.73%, 4.92%]). Both before and after saccade, there was a very wide range of optimal values for the λ parameter (oscillation wavelength) across bootstrapped data sets (before saccade: mean = 20538 msec, SD = 143790 msec, 95% CI [153 msec, 215760 msec]; after saccade: mean = 254 msec, SD = 785 msec, 95% CI [87 msec, 932 msec]). Together, the low amount of variance explained by the fitted function (relative to the noise ceiling) and the large range of values for the oscillation wavelength indicate that the fixation point change did not provide an exogenous cue, which itself induced an oscillation. As in Experiment 1, this rules out that the observed oscillation might be locked to an exogenous cue, rather than the saccade itself.

Finally, to verify the underlying frequency of the oscillation, detection performance relative to saccade offset at both locations over the entire period (−900 to 600 msec) was submitted to spectral analysis. This revealed a peak at 4 Hz (Figure 6). Bootstrapping was used to generate 95% confidence intervals of the estimates of spectral power by drawing 10,000 data sets from the original data set with replacement. Subsequently, bootstrapping was used to test the observed spectral amplitudes against the null hypothesis of no temporal structure in the time series. Furthermore, 10,000 data sets were generated by randomly shuffling bin labels within the −900- to 600-msec interval. Each data set was submitted to spectral analysis in the same way as was done for the original data set. For each frequency, amplitudes in the original data set exceeding the 99.5 percentile of the distribution of amplitudes in the bootstrapped data were taken as being significant at p < .01.

Figure 6. 

Power spectrum of perisaccadic detection performance. Dashed lines indicate bootstrapped 95% confidence intervals. Asterisks denote frequencies at which the observed spectral power was significantly higher than the bootstrapped null distribution (p < .01). There is a clear and significant peak at 4 Hz. (Inset) Phase angle of the oscillation in the optimized function for Experiment 1 as well as both the saccade origin and the saccade destination in Experiment 2. Shaded areas denote bootstrapped 95% confidence intervals. All three phase angles are in close agreement with each other, indicating that the attentional rhythm is not phase-shifted by the intervening saccade.

Figure 6. 

Power spectrum of perisaccadic detection performance. Dashed lines indicate bootstrapped 95% confidence intervals. Asterisks denote frequencies at which the observed spectral power was significantly higher than the bootstrapped null distribution (p < .01). There is a clear and significant peak at 4 Hz. (Inset) Phase angle of the oscillation in the optimized function for Experiment 1 as well as both the saccade origin and the saccade destination in Experiment 2. Shaded areas denote bootstrapped 95% confidence intervals. All three phase angles are in close agreement with each other, indicating that the attentional rhythm is not phase-shifted by the intervening saccade.

Individual Observers

In both experiments, observers made voluntary eye movements, and trials were binned post hoc depending on the time difference between the saccade landing and the presentation of the target. In the main analyses, results were analyzed after aggregating all trials across all observers. This was done to solve a number of problems that would have been caused by conventional grand averages across individual observers. Because of the stochastic distribution of trials over possible temporal offsets, analyzing data within individual observers required binning trials into relatively large bins. This results in a loss of temporal precision. Furthermore, because of the random distribution of trials over bins, bins varied in the amount of data included in each bin and therefore in the relative accuracy with which they estimated the true proportion correct at that latency. This relative accuracy measure is lost when within-observer averages are subsequently combined into a grand average across observers, introducing the problem that an observer with only a single trial for a given bin contributes a disproportionately extreme value to the average (1 or 0). Furthermore, except for very large bin sizes, each observer had multiple bins without any trials within the time range of interest, creating a missing data problem that would need to be addressed before applying our fitting procedure.

To solve this problem, all trials were aggregated across all observers for the main analyses. This approach however introduced the potential problem that the observed oscillations actually reflected single peaks in individual observers, at different latencies. To address this possibility, we reanalyzed the data for both experiments, binning the data into 16-msec bins within individual observers, and time courses were plotted for individual observers. Subsequently, for each of the two experiments, the average time course across all observers was calculated, with the SEM across observers for each bin. Results are shown for Experiment 1 (Figure 7) and Experiment 2 (Figure 8).

Figure 7. 

Experiment 1 results for individual observers. (A) Time course of detection performance as a function of time relative to saccade landing for five individual observers. (B) Mean time course across all five observers. The dotted line denotes the SEM at individual time points. As is evident, the main oscillatory feature in the main analysis (a trough slightly before 200 msec) is evident also in this grand average and in each of the individual observers.

Figure 7. 

Experiment 1 results for individual observers. (A) Time course of detection performance as a function of time relative to saccade landing for five individual observers. (B) Mean time course across all five observers. The dotted line denotes the SEM at individual time points. As is evident, the main oscillatory feature in the main analysis (a trough slightly before 200 msec) is evident also in this grand average and in each of the individual observers.

Figure 8. 

Experiment 2 results for individual observers. (A) Time course of detection performance as a function of time relative to saccade landing for four individual observers. For clarity, performance at the saccade origin and the saccade destination is summed into a single line for each observer. (B) Mean time course across all four observers. The red lines denote performance at the saccade origin; the blue lines denote performance at the saccade destination. The dashed line denotes the SEM at individual time points in each case. As is evident, the oscillatory features in the main analysis are evident also in this grand average and in each of the individual observers, albeit with considerable loss of resolution.

Figure 8. 

Experiment 2 results for individual observers. (A) Time course of detection performance as a function of time relative to saccade landing for four individual observers. For clarity, performance at the saccade origin and the saccade destination is summed into a single line for each observer. (B) Mean time course across all four observers. The red lines denote performance at the saccade origin; the blue lines denote performance at the saccade destination. The dashed line denotes the SEM at individual time points in each case. As is evident, the oscillatory features in the main analysis are evident also in this grand average and in each of the individual observers, albeit with considerable loss of resolution.

The results unequivocally show that the oscillations observed in the main analysis are present both in individual observers and in the grand average. This shows that the observed oscillations do in fact reflect oscillations within individual observers.

DISCUSSION

In the two experiments, observers made voluntary saccadic eye movements between two placeholders, monitoring each for the appearance of a contrast decrement target. Targets were presented before, during, and after the saccade, and detection performance at both the saccade origin (Experiment 2) and the saccade destination (Experiments 1 and 2) was evaluated as a function of time relative to saccade landing. The results reveal periodic oscillations in detection performance both before the saccade at the saccade origin and after the saccade at the saccade destination. Time–frequency decomposition of the time course of detection performance revealed oscillations at approximately 4 Hz in both locations. In both cases, the time course of detection performance was well fitted by a dampened oscillation with a period of 3.9 Hz. None of these oscillations were observed when data were time-locked to the cue prompting observers to make saccades, rather than to the saccade landing itself. Finally, the phases of the oscillations before and after the saccade in Experiment 2 did not differ and also matched the phase observed after the saccade in Experiment 1. This indicates that the saccade was executed as part of an ongoing periodic process, rather than resetting it, and furthermore, that the saccade itself did not disrupt the rhythm.

Landau and Fries (2012) and Fiebelkorn et al. (2013) demonstrated that the presentation of an exogenous cue at one of two possible target locations causes oscillations in detection performance at both locations. These oscillations were observed at around 4 Hz, with the two locations sampled roughly in counterphase. In the present experiments, no exogenous cue was presented. Instead, detection performance was evaluated at a range of latencies with respect to the end of a saccadic eye movement. Importantly, this saccadic eye movement was made voluntarily, in the deliberate absence of a transient exogenous cue that might have induced phase locking. Nevertheless, in Experiment 1, oscillations in detection performance were observed after saccade landing (later replicated in Experiment 2). Experiment 2 was carried out to distinguish whether this phase locking resulted from voluntary saccadic eye movements resetting the attentional rhythm or whether the ongoing attentional rhythm in fact dictates when saccades are prepared and executed. The results revealed phase-locked oscillations in detection performance already before saccade onset, indicating that the attentional rhythm is in fact ongoing and determines when voluntary saccades are made. In other words, saccade execution rides the attentional rhythm.

In both experiments, the fundamental frequency of the attentional rhythm was observed to be around 4 Hz. This is in line with previous observations in similar paradigms with the exception that, here, observers monitored only one possible target location, rather than two (Landau & Fries, 2012) or three (Fiebelkorn et al., 2013). The present result therefore shows that attention samples rhythmically even when it is not divided, a conclusion consistent with previous computational work (VanRullen et al., 2007). However, VanRullen and colleagues reported a sampling frequency of around 7 Hz, roughly double the frequency observed here. It is unclear whether the difference is conceptually relevant or merely because of variations in stimuli, experimental procedure, and/or observers.

On the one hand, Holcombe (2009) argues that visual processes with perception thresholds in the 4- to 8-Hz range all reflect a similar attentional requirement. Earlier studies of attentive tracking similarly consider the 4- to 8-Hz range to reflect a single process (Verstraten, Cavanagh, & Labianca, 2000). The sampling frequency might also be variable over time. Conceivably, the attentional rhythm might speed up or slow down, possibly contingent on task demands or eye movement execution. The present experiments showed no indication of oscillations at other frequencies, but it is possible that slight trial-by-trial variations in sampling rate would result in de-phasing away from the saccade offset, hiding ongoing oscillations far before or after the saccade in the final time course.

Alternatively, the 4-Hz oscillation observed here might actually reflect one half of an ongoing 8-Hz attentional sampling mechanism alternately sampling the two gratings. Such an interpretation would require that, although observers are instructed to only monitor the fixated grating, attention nevertheless continues to sample the task-irrelevant grating. Furthermore, it would require that the attentional oscillation phase-shifts during the saccade, because the first sample at the saccade destination occurs roughly 250 msec after the last sample at the saccade origin. Such an interpretation is nevertheless plausible because the deployment of attention to the foveated location does in fact stay in phase across the saccade, because in retinotopic coordinates, the saccade target replaces the saccade origin. In addition, attention has been shown to have an important role in remapping visual space across saccades (Rolfs, Jonikaitis, Deubel, & Cavanagh, 2011). Validating this interpretation will require probing the availability of attention at both the saccade origin and the saccade destination, independently before and after the saccade. If the 4-Hz oscillation observed here indeed reflects one half of an ongoing 8-Hz attentional mechanism, this should be evident as counterphase 4-Hz oscillations at performance at the two locations, with the phase relationship reversing during the saccade.

Recent work has already shown that the phase of ongoing cortical EEG oscillations is predictive of a range of perceptual processes. Interestingly, whereas the behavioral work largely reveals oscillations in the theta range (∼4 Hz), the main cortical oscillations implicated in perception are in the alpha range (∼10 Hz). For example, the phase of prestimulus alpha phase is predictive of whether an observer will detect a threshold-level stimulus (Busch et al., 2009; Mathewson et al., 2009). This effect was subsequently shown to be attributable to attentional sampling (Busch & VanRullen, 2010). Furthermore, entraining an observer to 10-Hz stimulus sequences results in sustained 10-Hz oscillations in behavioral performance (Spaak et al., 2014; de Graaf et al., 2013), and the occipital alpha rhythm has been shown to encode dynamic stimulus properties in the form of recurrent representations or echoes (VanRullen & MacDonald, 2012). The phase of ongoing EEG oscillations has also been related to the speed of motor preparation. For instance, prestimulus occipital alpha phase influenced the probability of making rapid express saccades (Hamm et al., 2012). Drewes and VanRullen (2011) later showed more generally that prestimulus EEG phase in the 11- to 17-Hz range was predictive of saccadic RT. Song et al. (2014) put forth the compelling possibility that the theta-band oscillations in behavioral performance are in fact caused by rhythmic pulses of alpha-band activity, potentially reconciling the apparent frequency divide between behavioral and neurophysiological measures. Nevertheless, more work will be necessary to understand how theta and alpha rhythms result in perceptual oscillations and how these interact with eye movements.

In summary, the present experiments reveal that we plan and execute voluntary saccadic eye movements as part of an ongoing attentional rhythm. Saccades ride this constant ebb and flow of attentional resources, with the eyes in flight during the trough of the attentional wave. This shared periodic processing architecture further supports the view that attentional allocation and saccade preparation are related, if not identical, processes. It also implies that saccadic mechanisms and perisaccadic phenomena might in some cases apply to attention—for instance, we might look to saccadic suppression mechanisms as a model for how discrete attentional samples are nonetheless stitched together into a continuous, smooth flow of conscious awareness. Furthermore, the observation that the attentional rhythm dictates voluntary motor behavior leads to a number of predictions regarding when we might and might not be able to make voluntary saccades. For example, in a double-saccade paradigm, if saccades are executed in the troughs of the attentional rhythm, this would predict a very specific distribution of intersaccade latencies.

Interestingly, the present findings extend the “Active Sensing” paradigm developed by Schroeder and colleagues (e.g., Morillon, Schroeder, & Wyart, 2014; Schroeder, Wilson, Radman, Scharfman, & Lakatos, 2010). A central theme in this paradigm is that motor activity associated with sensory effectors, such as sniffing, has sensory consequences, including synchronization of oscillatory neural activity in early sensory areas. However, the present results are inconsistent with an interpretation in which motor execution causes oscillations in perception, because oscillations are evident in perception well before the action is executed. The observed oscillations are also unlikely to be because of motor preparation (as opposed to execution), as they are observed even before the fixation point starts to change to cue observers to make a saccade. Furthermore, when data are plotted time-locked to the presentation of this cue, no oscillations are observed. As such, it is unlikely that motor preparation or execution in the strict sense induces the oscillations observed here. In a broader sense, however, attention itself has been argued to be in essence a premotor process (e.g., Rizzolatti et al., 1987), and in that sense, the ongoing attentional rhythm could be seen as an ongoing premotor rhythm. This is consistent with recent work by Tomassini, Spinelli, Jacono, Sandini, and Morrone (2015) showing that oscillations in perceptual performance might precede voluntary motor behavior more generally using a paradigm where observers made hand movements rather than saccades. It will therefore be interesting to see to what degree a single, central rhythm dictates sensorimotor behavior across different modalities. Finally, it remains an open question how the ongoing rhythm might affect real-world viewing, where exogenous and endogenous saccades are combined, and how it affects the perception of, or is itself affected by, the temporal dynamics of moving or changing stimuli such as videos.

Acknowledgments

I am grateful to two anonymous reviewers for valuable input on a previous version of this paper.

Reprint requests should be sent to Hinze Hogendoorn, Helmholtz Institute, Experimental Psychology Division, Utrecht University, Heidelberglaan 1, 3584 CS Utrecht, The Netherlands, or via e-mail: j.h.a.hogendoorn@uu.nl.

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