. 2026 Oct 15;29(11):117870. doi: 10.1016/j.isci.2026.117870

Phase-dependent EEG decoding of continuous visual stimuli

Michele Deodato ^1,^2,^3,^∗, David Melcher ^1,²

PMCID: PMC13694887 PMID: 42927217

Summary

Neural oscillations support cognition and perception by organizing information across oscillatory cycles. Although animal studies support this view, evidence in humans is mixed and largely based on transient stimuli. We tested whether alpha oscillations, the dominant human brain rhythm, periodically modulate the strength of visual representations. EEG was recorded while participants viewed long-lasting (2 s) Gabor patches. Using a phase-dependent decoding approach, we quantified stimulus decoding accuracy at specific alpha phases. Decoding performance varied systematically with alpha phase, following a smooth unimodal profile that peaked over occipito-parietal electrodes. These effects emerged well after stimulus onset and generalized to earlier time points, indicating a modulation of visual processing during continuous input. Our findings demonstrate that visual information is represented more accurately at specific alpha phases. This provides strong evidence that sensory processing is shaped by intrinsic brain dynamics and introduces a generalizable decoding pipeline for linking oscillatory phase to neural information processing.

Keywords: neural oscillations, visual processing, EEG decoding, alpha phase

Graphical abstract

Highlights

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Stimulus-locked visual decoding is dominated by transient onset responses
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Phase-locked visual decoding varies systematically across the oscillatory cycle
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Phase-dependent effects are specific to alpha oscillations and strongest over posterior sites
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Cross-phase decoding shows representational strength, not content, varies by phase

Health sciences; Medicine; Medical specialty; Internal medicine; Neurology

Introduction

It is widely accepted that our experience of visual space is actively constructed by the brain. Despite sharp color vision being limited to the fovea and blind spots lacking any input, we perceive a seamless and detailed visual field. Likewise, while we experience vision as continuous, many temporal aspects of sensory processing may be influenced by spontaneous rhythmic patterns of neural activity.¹^,² Much evidence suggest that the processing of sensory information is shaped by neural oscillations in the alpha frequency range (8–13 Hz).²^,³ These rhythmic fluctuations in neural excitability act as dynamic gates, modulating neural firing and thus creating temporal windows during which sensory input is preferentially processed.⁴^,⁵^,⁶ By segmenting sensory processing, the visual system optimizes the extraction of relevant information from a continuous sensory stream under constraints due to eye movements and limits in attentional and neural processing capacity.

In support of this account, several studies have shown that the phase of pre-stimulus alpha oscillations influences the perception of phosphenes,⁷ illusory flashes,⁸ and near-threshold flashes,⁹ as well as temporal integration¹⁰^,¹¹ and order and timing judgments¹²^,¹³ of brief visual events. Additionally, intra- and inter-individual differences in the frequency of alpha oscillations have been linked to the temporal resolution of perception.¹⁴^,¹⁵^,¹⁶ However, findings are mixed,¹⁷ with recent work challenging the reliability and generalizability of these effects.¹⁸^,¹⁹ More critically, three major limitations have hindered a deeper understanding of the relationship between oscillations and sensory processing. First, effects are largely confined to transient stimuli, limiting their explanatory power for continuous, naturalistic visual processing. Second, research has focused almost exclusively on pre-stimulus phase, leaving open the question of whether sensory information is dynamically modulated during sustained visual input. Finally, rhythmic processing is typically assessed via subjective reports rather than neural measures of information processing, potentially being influenced by decision-making factors.

Here, we address these gaps by shifting focus from perceptual reports of brief flashes to neural signal dynamics of continuous stimuli. We recorded EEG from participants viewing long-lasting (2 s) Gabor patches while performing an unrelated task designed to maintain fixation and stable visual input (Figure 1). The Gabor stimuli could vary in orientation (−45° and 45°) and spatial frequency (1.85 and 7.5 cpd) and were entirely task-irrelevant, allowing us to examine visual processing in the absence of attention or behavioral relevance. The functional significance of neural oscillations rests on the idea that different phases of the cycle correspond to distinct neural activations, a notion well supported by animal studies.⁵^,²⁰ To test that neural processing of continuous stimuli fluctuates rhythmically, we developed a phase-dependent decoding approach that quantifies how accurately visual information can be read from neural signals as a function of the phase of ongoing oscillations. This approach tests whether the readout quality of visual representations fluctuates with intrinsic oscillatory dynamics, without requiring a subjective perceptual report about the Gabor stimulus. Our results demonstrate that neural decoding of continuous visual input varies unimodally across the alpha cycle, providing evidence that neural processing of spatial frequency is rhythmically modulated in time, in synchrony with brain oscillations.

Results

Distinct temporal stages in EEG representations of continuous stimuli

To quantify neural decoding of stimulus features, we applied time-resolved multivariate pattern analysis, training a linear discriminant analysis (LDA) classifier to decode orientation and spatial frequency from EEG topographies at each time point (–500 to 2,000 ms relative to stimulus onset).

Decoding accuracy peaked around 100 ms for both orientation (peak accuracy = 86.5%) and spatial frequency (peak accuracy = 54.7%). Orientation decoding remained at chance level afterward and was generally lower than spatial frequency decoding (Figure 2A), consistent with previous report on the EEG decoding of different visual features from EEG signals.²¹ It should be noted that orientation accuracy in the 1,000–2,000 ms range was significant when pooling data across multiple time points (see Figure 2B, random condition). Decoding accuracy for spatial frequency remained significantly above chance throughout the 2-s presentation (Figure 2A) and showed an exponential decay characterized by an early encoding stage with transient peaks of high accuracy, followed by a later maintenance stage during which accuracy declined (<60%) but remained above chance (Figure 2A), even when considering narrowband power (Figure S1). A temporal generalization analysis (Figure 2A) showed significant generalization across the whole stimulus duration, thus this decrease in decoding accuracy does not necessarily imply a change in the content of neural representations and could simply reflect a decrease in overall activation of the representational content.²² Previous research has linked changes in neural activity, in particular in alpha band power, to microsaccades.²³ To verify that this residual decoding performance was not driven by ocular artifacts, we conducted two control analyses: decoding using only horizontal and vertical eye-position data, and a comparison of microsaccade rates between low and high spatial frequency trials. Both analyses yielded no significant results, confirming that the observed EEG effects were not driven by eye movements. This suggests that while visual features are strongly encoded immediately after stimulus onset, they continue to be represented in a sustained format during prolonged visual stimulation.²² These results establish that continuous, unattended visual stimuli elicit robust and temporally extended neural responses that can be tracked using EEG.

EEG decoding locked to stimulus onset, alpha phase, and their generalization

(A) Left: decoding accuracy for stimulus orientation (red) and spatial frequency (blue) over time, locked to stimulus onset (time = 0). Topographies of the activation patterns²⁴ at the most prominent decoding peaks. Black dots indicate significant (p < 0.05, Student’s t test, cluster corrected) channels. Shaded areas indicate ±1 SEM across participants. Horizontal lines indicate significant decoding accuracy. Right: temporal generalization for spatial frequency decoding. The white outline indicates areas of significant decoding accuracy.

(B) Same as (A) but data are locked to spontaneous alpha phase of channel POz instead of stimulus onset. See also Figure S2.

(C) Cross-decoding accuracy when training on phase-locked data and testing on time-locked data (top) and vice versa (bottom).

Phase-dependent decoding reveals rhythmic enhancement of visual information

To test whether neural processing of continuous visual input fluctuates rhythmically with alpha phase, we performed decoding analyses on EEG data selectively sampled at distinct points within the alpha cycle (Figure 3A). We restricted this analysis to a late time window, between 1,000 and 2,000 ms after stimulus onset, when the stimulus was still present but transient onset-related activity had long subsided. This choice is essential, since onset responses elicit pronounced alpha desynchronization that compromises a precise and meaningful estimation of alpha phase (see STAR Methods). Decoding accuracy for spatial frequency differed systematically between alpha peaks and troughs (p_cluster < 0.05). Over posterior sensors, spatial frequency was decoded more accurately at the alpha trough than at the peak, whereas frontal sensors showed the opposite phase relationship (Figure 3B). No effect was found for orientation decoding (Figure 2B). This pattern remained robust with respect to a control analysis using randomly sampled phases, confirming that the effect was phase-specific (Figure 3B). Notably, the phase characterized by poor accuracy was not different from a random condition (Figure 3B) suggesting that the effect is driven by enhancement at specific phases, not by suppression at others, at least with respect to a phase-agnostic decoding. Additionally, this modulation disappeared when considering the phase of theta (4–7 Hz) oscillations, showing that the effect is also frequency specific. These findings demonstrate that the strength of neural representations is not constant over time, even when visual input remains unchanged, but instead varies systematically with the phase of ongoing alpha oscillations, suggesting that visual processing is shaped by the intrinsic temporal structure of ongoing neural activity.

Phase-dependent EEG decoding

(A) Schematic of the phase-dependent decoding approach. For each trial, scalp voltage topographies were extracted at specific points of the alpha cycle (e.g., troughs) and used to train a linear decoder to classify stimulus identity.

(B) Decoding accuracy was compared between alpha peaks, troughs, and random phases (see STAR Methods). The violin plots show that posterior channels (POz) showed significantly higher decoding accuracy at the trough (t(21) = 3.33, p = 0.003, d = 0.72), while frontal channels (Fz) showed higher accuracy at the peak (t(21) = −2.33, p = 0.029, d = −0.5). The topographic map displays the t values from paired comparisons across electrodes (peak vs. trough), with significant clusters (black dots) identified via permutation testing (N = 1,000, p < 0.05). Accuracy at both sites exceeded that observed when phase samples were selected randomly (∗p < 0.05, ∗∗p < 0.01, Student’s t test, N = 22).

(C) The color map shows tuning of decoding accuracy as a function of alpha phase (18 bins) and scalp location (64 channels). The plot on the right side shows the tuning curve corresponding to one row of the map (blue arrow, channel POz) with the corresponding harmonic regression fit (dotted line). Shaded area is the SEM across participants. See also Figure S2. The topographic map shows the amplitude of the fitted sinusoid, reflecting the strength of phase-dependent modulation across the scalp and peaking over posterior electrodes.

Using 18 equally spaced phase bins spanning 0–2π, decoding accuracy formed smooth unimodal tuning curves (Figures 3C and S2). A harmonic regression model confirmed the significance of this rhythmic modulation. Specifically, the model explained a substantial portion of variance in decoding accuracy across the whole scalp (mean R² = 0.57, range = [0.47, 0.69], p_cluster < 0.001), with a mean modulation amplitude of 1.5% (SD = 0.22%) (Figure 3C). Preferred phases were consistent across participants within occipital and frontal clusters (Rayleigh test p < 0.05), although this phase alignment did not survive correction for multiple comparisons (see STAR Methods). This variability is expected as it reflects individual differences in cortical geometry, the location and orientation of cortical alpha generators. Lack of alignment of preferred phases across participants also account for the small effect sizes in Figure 3B as can be seen from participants individual tuning curves (Figure S2). For example, the average difference between each participant preferred and unpreferred phase at channel POz was 6.1% (std = 2.7; Figure S2). Although restricted to spatial frequency, these results confirm that decoding accuracy is rhythmically modulated by ongoing alpha phase, with a single optimal phase for visual processing.

Generalization of neural representations across the alpha cycle

Next, we investigated the similarity of neural representations across the alpha cycle. Activation patterns 24 at the phase trough exhibited a strong and spatially structured topography with multiple significant channels, whereas patterns at the peak were comparatively weaker and did not reach significance (Figure 2B). Despite these differences, temporal generalization analysis on the phase-resolved data revealed significant decoding across the entire matrix, indicating that discriminative information generalized across all phases (Figure 2B). To further examine the relationship between phase- and time-resolved representations, we performed cross-decoding between phase-locked and time-locked data. Classifiers trained at the preferred alpha phase generalized maximally to earlier time points in the time-locked data, showing that the information expressed at the phase peak corresponds to a representation that is also present earlier in time (Figure 2C), and suggest a periodic reactivation of this pattern. Notably, this generalization was observed even though the phase-based model was trained exclusively on later time points. These results are consistent with a shared representational structure whose expression varies as a function of oscillatory phase, rather than a qualitative reorganization of the neural code. In this framework, alpha phase modulates the fidelity or accessibility of neural representations.

Phase-dependent decoding depends on anti-phase signals

The presence of opposite phase-dependent decoding effects at frontal and posterior sites raises the question of whether these patterns reflect two interacting sources. While conclusions from scalp EEG data can only be tentative, to address this question we estimated the phase relationship between each pair of significant anterior-posterior EEG channels by computing cross-spectral density in the alpha band.

Circular V-tests showed that 215 out of 243 anterior-posterior channel pairs (88.5%) exhibited significant clustering around 180° (p_Bonferroni < 0.05; mean phase offset = 179.34°) (Figure 4). Additionally, the phase-slope index (PSI), a measure of information flow robust to volume conduction,²⁵ between frontal and posterior channels was not different from 0 (p_permutations > 0.05), suggesting no interaction between these regions (Figure 4).

Distribution of alpha phase differences between anterior and posterior clusters

(Left) Scalp map showing significant frontal (red) and occipito-parietal (blue) channels identified in the phase-dependent (peak vs. trough) decoding analysis. Black arrows indicate anterior-posterior channel pairs. For each possible pair, we computed the average phase difference in the alpha frequency range (8–13 Hz) and the PSI. (Middle) Polar histogram showing the distribution of alpha phase differences across all channel pairs (N = 243) averaged across participants. The distribution is tightly clustered around 180°. (Right) Random distribution of the PSI. The observed PSI (averaged across anterior-posterior pairs, red dotted line) was not significant with respect to the upper and lower distribution limits (black dotted lines), indicating no evidence for information transfer between channels. See also Figure S3.

These results do not support interacting sources in distal areas but are consistent with previous work identifying posterior alpha generators, likely within the occipito-parietal cortex, as a dominant generator of rhythmic visual processing.¹⁰^,²⁶ Source reconstruction revealed overlapping cortical distributions at alpha peaks and troughs, with opposite source orientations, consistent with the recruitment of a common set of generators across the alpha cycle (Figure S3). However, given the limited spatial resolution and inherent volume conduction in sensor-level EEG data, we cannot exclude the presence of multiple interacting sources within these areas or more complex network dynamics contributing to the observed phase patterns.

Discussion

Oscillatory brain activity is a core organizing principle of neural function and a well-established marker of dysfunction in a range of clinical conditions.²⁷ Understanding how these rhythms influence sensory processing is therefore central to neuroscience. Here, by showing that decoding of spatial frequency fluctuates with ongoing alpha phase, we demonstrate that rhythmic influences on sensory processing persist throughout continuous visual input, rather than being limited to initial encoding. In the absence of changes in the visual stimulus, our results do not necessarily imply changes in representational content, but rather fluctuations in the strength or accessibility of an underlying stable representation, thereby affecting how well stimulus information can be decoded from population activity.

Although our approach differs from using EEG phase as a feature for classification of conscious perception⁹^,²⁸^,²⁹^,³⁰ or prediction of the statistics of neural firing,³¹ it still provides a strong neural foundation for the idea that perception is shaped not only by what is seen, but also by when it is seen within the brain’s intrinsic temporal structure.

Much of the existing research on phase-dependent visual processing has relied on participants’ subjective reports of bistable stimuli,⁸^,¹⁰^,²⁹ leaving open questions about whether these rhythmic fluctuations also shape objective neural representations. While some studies have shown that pre-stimulus alpha phase can modulate early sensory responses, such as evoked potentials and global field power,³²^,³³^,³⁴ these effects reflect the initial encoding of stimuli. In contrast, our analyses reveal that alpha phase continues to modulate neural representations well beyond stimulus onset, during sustained visual processing. This distinction is critical, as our results highlight meaningful differences between initial encoding and maintenance stages of processing. We reveal a persistent, spontaneous oscillatory influence on neural processing that would be masked in more conventional paradigms. Our focus on continuous visual input aligns with growing efforts to shift experimental paradigms toward the temporal dynamics of natural vision.³⁵^,³⁶ Furthermore, because stimulus onset can elicit phase resetting,³⁷ and feature-specific changes in fixational eye movements,³⁸ isolating the maintenance period allowed us to reveal ongoing, spontaneous rhythmic influences on neural processing that would otherwise be obscured by evoked responses. Notably, the poor replicability of some of the original findings may stem from the influence of stimulus onset and offset responses, the artificial and technically demanding setups required to precisely control millisecond-scale transients and the participants effort (or lack thereof) in detecting subtle differences, rather than from a lack of underlying rhythmicity. By demonstrating phase-dependent neural decoding during continuous viewing, we provided a robust and more ecologically valid test of the relationship between neural oscillations and visual processing. Nevertheless, this effect was observed only for spatial frequency and that extension to other visual features remains to be established.

Over the past century, different interpretations of this relationship have gained traction, often motivated by compelling psychological phenomena.³⁹ Yet, enthusiasm has repeatedly waned due to the lack of definitive neural evidence.¹^,² One of the earliest formalizations of this idea came from Pitts and McCulloch, who proposed a “cortical scanning” theory in which cortical layers cyclically fluctuate in receptivity to incoming input.⁴⁰ More recently, the framework of rhythmic perception proposed that perception is not uniformly continuous, but modulated by the phase of ongoing brain rhythms such that certain phases promote more efficient sensory processing, while opposite phases impair it.⁴ Importantly, and consistent with our findings, this rhythmicity does not imply discrete, frame-like snapshots of perception, but rather continuous fluctuations in neural excitability that modulate the fidelity of sensory information over time.

Rhythmic fluctuations are often attributed to attentional sampling, rather than intrinsic periodicity within sensory processing per se.¹²^,³⁹^,⁴¹^,⁴² In this context, oscillatory effects arise from rhythmic modulations of sensory gain driven by fluctuations in attentional focus. However, growing evidence indicates that attentional and sensory rhythms coexist and operate at distinct frequencies, with attention often linked to slower theta rhythms (4–7 Hz),⁴³ and early sensory encoding associated with faster alpha-band oscillations (8–13 Hz).⁴⁴ This supports the idea that multiple, coexisting oscillatory mechanisms coordinate different aspects of perception and cognition at different temporal scales.¹⁰^,⁴⁴^,⁴⁵

In the present study, the stimuli were entirely task-irrelevant, and participants were not instructed to attend to them. This makes it unlikely that fluctuations in decoding performance were driven by rhythmic attentional enhancement. Instead, these results may reflect a form of rhythmic suppression, where sustained attention to fixation periodically inhibits processing of irrelevant inputs, leading to phase-dependent modulations in visual processing.⁴²^,⁴³

An alternative explanation that does not invoke attention is that alpha phase reflects the responsivity of spatial frequency-selective neural populations. For example, recent work suggests that alpha oscillations could reflect differential involvement of the magnocellular and parvocellular pathways,⁴⁶^,⁴⁷ which could explain why phasic effects are often observed with transient, low-contrast stimuli that predominantly engage the magnocellular pathway.⁹^,²⁸ More generally, posterior alpha troughs have been associated with periods of heightened cortical excitability in sensory cortex, supporting enhanced sensory processing.⁶^,⁴⁸ Correspondingly, fluctuations in the balance between synaptic excitation and inhibition have been shown to modulate the strength of alpha-band rhythmic inhibition⁴⁹ and its impact on perception.⁵⁰ Overall, these interpretations support the central conclusion that visual processing of continuous stimuli fluctuates rhythmically as a function of alpha phase.

On a final methodological note, our phase-dependent decoding technique offers a flexible and generalizable approach for probing how oscillatory dynamics shape cognitive processing across diverse experimental contexts. By isolating specific moments in the oscillatory cycle, such as peaks and troughs, we demonstrate that neural processing of visual input fluctuates systematically, revealing when decoding from EEG is most effective. Beyond its theoretical implications, this approach is especially promising for brain-computer interface (BCI) applications, where timing decoding to optimal oscillatory phases could significantly enhance performance. We showed that not all moments in the EEG signal are equally informative: decoding accuracy can vary markedly with ongoing oscillatory phase, offering a principled way to enhance predictions of perception from continuous EEG activity.

Limitations of the study

Although our results support the central conclusion that visual processing of continuous stimuli fluctuates rhythmically as a function of alpha phase, there are various limitations of this study. For example, the visual features were task-irrelevant, and participants did not provide perceptual reports or decisions concerning them. Although this design allowed us to examine neural stimulus information independently of task-related decision processes, it does not establish whether the observed phase-dependent modulation also affects perception or behavior. Additionally, phase-dependent modulation was observed for spatial frequency but not orientation. Whether the effect generalizes to other visual features, stimulus classes, or tasks therefore remains to be established.

Resource availability

Lead contact

Requests for further information and resources should be directed to and will be fulfilled by the lead contact, Michele Deodato (deodato.mic@gmail.com).

Materials availability

This study did not generate new unique reagents.

Data and code availability

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EEG and decoding data have been deposited at https://osf.io/9na4m/ and are publicly available as of the date of publication.
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All original code has been deposited at https://osf.io/9na4m/ and is publicly available as of the date of publication. The code to reproduce the phase-dependent decoding analysis is available at https://github.com/DeoMiche/PDD-toolbox.
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Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request (deodato.mic@gmail.com).

Acknowledgments

This research was carried out on the High-Performance Computing resources at New York University Abu Dhabi. This work was supported by the NYUAD Center for Brain and Health, funded by Tamkeen under NYU Abu Dhabi Research Institute grant CG012.

Author contributions

Conceptualization, M.D. and D.M.; methodology, M.D.; formal analysis, M.D.; software, M.D.; visualization, M.D.; funding acquisition, D.M.; writing – original draft preparation, M.D.; writing – review and editing, M.D. and D.M.; supervision, D.M.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data

EEG data	This Paper	https://osf.io/9na4m/

Software and algorithms

MATLAB (R2024b)	Mathworks, Natick, MA, USA	https://www.mathworks.com
Phase-Dependent Decoding Toolbox	This Paper	https://github.com/DeoMiche/PDD-toolbox
ADAM toolbox	Fahrenfort et al.⁵¹	https://github.com/fahrenfort/ADAM
EEGLAB (v2023.1)	Delorme and Makeig⁵²	https://sccn.ucsd.edu/eeglab/
Fieldtrip (v20241025)	Oostenveld et al.⁵³	https://www.fieldtriptoolbox.org/

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Experimental model and study participant details

Participants

Twenty-two participants (12 females) between 18 and 35 years old (age mean: 23.13 years; SD: 3.6) participated in the experiment and received compensation. Inclusion criteria were normal or corrected to normal vision and English fluency. Data were collected in accordance with the Declaration of Helsinki, and the study protocol was approved by the local ethics committee (New York University Abu Dhabi IRB, HRPP-2023-163).

Method details

Experimental procedure

The experiment took place in a dark, magnetically shielded room. Stimuli were projected with a PROPixx projector (VPixx Technologies) set to a refresh rate of 100 Hz, displayed on a 65 cm × 36 cm screen. The experiment was implemented using MATLAB (The MathWorks) and the psychophysics toolbox.⁵⁴ Participants laid their head on a chin rest at a distance of 90 cm. Eye data were recorded with an Eyelink 1000 eye-tracker (SR Research, Ontario, Canada) in desktop mount mode with a sampling rate of 1000 Hz.

Upon arrival to the laboratory, participants were instructed on the good practices to follow during EEG experiments (e.g., limit body movements and blinking) and were prepared for EEG recording.

Each trial began with a central fixation cross presented for 1000 ms, with an added temporal jitter of ±250 ms. This was followed by the appearance of a centrally presented Gabor patch. The Gabor stimuli varied across trials in orientation (–45° or 45°) and spatial frequency (1.85 or 7.5 cycles per degree, cpd). All Gabors were presented at 100% contrast and occupied ∼3 degrees of visual angle. After 2000 ms, a brief stimulus pair was presented while the Gabor remained on screen. This was either a 30 ms, 2000 Hz tone paired with a 30 ms white luminance flash, or two successive flashes, implemented by changing the fixation cross to white. The temporal order (flash-first or beep-first) and stimulus onset asynchrony (SOA) varied randomly across trials. For audiovisual pairs, SOAs ranged from 0 to 360 ms in 30 ms steps; for double-flash trials, SOAs ranged from 50 to 230 ms in 20 ms steps. The Gabor remained on screen for an additional 500 ms after the stimulus pair, after which participants reported whether the flash and beep were synchronous or asynchronous, or indicated the number of flashes perceived. We refer to the stimulus as continuous or sustained to highlight the uninterrupted presentation of a stable visual stimulus over an extended period (see²²^,³⁵ for a similar approach), in contrast to brief, transient stimuli typically used in the literature. Contrary to a fully passive paradigm (e.g., free-viewing), adding this task allowed us to minimize variability due to, for example, attentional disengagement and mind-wandering while preserving the task-irrelevant nature of the stimulus.

Participants were instructed to blink only after the Gabor had disappeared. The experiment consisted of 7 blocks (100 trials each) with audiovisual stimulus pairs, followed by 3 blocks (107 trials each) of flash-flash trials. Short breaks were provided between blocks. The full session lasted approximately 2.5 hours.

EEG recording and preprocessing

EEG data were recorded using a 64-channel active electrode system (BrainProducts GmbH) arranged according to the international 10–10 system (Fp1, Fz, F3, F7, FT9, FC5, FC1, C3, T7, TP9, CP5, CP1, Pz, P3, P7, O1, Oz, O2, P4, P8, TP10, CP6, CP2, Cz, C4, T8, FT10, FC6, FC2, F4, F8, Fp2, AF7, AF3, AFz, F1, F5, FT7, FC3, C1, C5, TP7, CP3, P1, P5, PO7, PO3, POz, PO4, PO8, P6, P2, CPz, CP4, TP8, C6, C2, FC4, FT8, F6, AF8, AF4, F2, Iz). Signals were acquired using BrainVision Recorder (BrainProducts GmbH), with a sampling rate of 1000 Hz and an online reference at FCz. Electrode impedances were kept below 10 kΩ throughout the session.

Offline preprocessing was conducted using eeglab⁵² and custom scripts in MATLAB. The data were band-pass filtered between 0.5 and 45 Hz. Channels exhibiting excessive noise (average of .86 channels per participant) were removed and subsequently interpolated using spherical splines. The continuous signal was epoched with respect to the gabor onset, re-referenced to the common average and oculomotor artifacts were identified and removed using independent component analysis (ICA). Finally, trials containing residual artifacts were visually inspected and rejected (average of 35.36 trials excluded per participant). Unless otherwise specified, all statistical tests were two-sided, and cluster-based permutation tests used an alpha threshold of .05 and 1,000 permutations.

Quantification and statistical analysis

EEG multivariate pattern analysis

To determine whether features of the visual stimulus were reliably decodable from EEG, we performed time-resolved multivariate pattern analysis (MVPA) using the Amsterdam Decoding and Modeling (ADAM) toolbox.⁵¹ The analysis focused on decoding separately spatial frequency and orientation of the stimulus from the preprocessed EEG data, aligned to stimulus onset.

For each participant, EEG epochs were down-sampled to 250 Hz and entered into a backward decoding model (BDM) with 10-fold cross-validation. A linear discriminant analysis (LDA) classifier was trained to discriminate between classes based on the scalp-wide voltage patterns at each time point. Classification performance was quantified using the area under the receiver operating characteristic curve (AUC), and decoding was performed and generalized at each time point from -500 ms to 2000 ms relative to stimulus onset.

Group-level statistical inference was performed using cluster-based permutation testing⁵⁵ implemented in the ADAM toolbox (1000 permutations, alpha = .05). This method controls the family-wise error rate while retaining sensitivity to temporally extended effects.

Eye-movements control analyses

Eye-tracking analyses were conducted on the subset of 19 participants with reliable data (i.e., <20% missing samples). To rule out the possibility that decoding performance during the maintenance period reflected subtle eye movements, we first performed a control analysis in which only horizontal and vertical eye-position traces were used as features in the decoding model. Second, we detected microsaccades using a velocity-based algorithm⁵⁶ and compared microsaccade rates across spatial frequency conditions. For both analyses, multiple comparisons in the temporal domain were corrected using a permutation-based cluster correction (N = 1000).

Phase-dependent decoding

We computed decoding for each phase of the alpha cycle to investigate how neural representations of visual features vary as a function of the instantaneous phase of a signal. Scripts to implement phase-dependent decoding are available on github (https://github.com/DeoMiche/PDD-toolbox/).

Continuous EEG data were first band-pass filtered in the alpha range (8–12 Hz) (or in the theta range (4–7 Hz) for a control analysis) using FieldTrip’s⁵³ ‘firws’ filter, a zero-phase, non-causal windowed-sinc finite impulse response filter that preserves phase information. From the filtered signal, instantaneous phase and amplitude were extracted via the Hilbert transform.

To ensure robust phase estimation and improve computational efficiency, time points with alpha amplitude below the 66th percentile were excluded. For each phase angle of interest (e.g., peak or trough), we identified all timestamps across all trials where the instantaneous alpha phase matched that angle. Around each timestamp, we extracted scalp voltage data spanning ±5% of the full phase cycle and averaged these surrounding points to enhance the signal-to-noise ratio. This yielded a set of composite voltage maps representing neural activity specifically at that phase. As a control condition for the specificity of phase effects, scalp voltage data was selected with random timestamps (see Figure 3B). The whole algorithm was repeated with random timestamps to keep the increase of SNR due to averaging and increasing the number of samples per condition in the MVPA.

Separate datasets for peak and trough phases were then created for each channel, and multivariate decoding of spatial frequency was performed using the ADAM toolbox. Decoding accuracy was then compared across peak and trough datasets with a two-tailed paired t-test. This procedure was repeated for every channel in the scalp and cluster-based permutation correction (N=1000, alpha=.05) accounted for multiple comparisons across channels. This approach yields a spatial map of peak vs trough modulation of decoding accuracy (Figure 3B).

Harmonic regression

Phase-dependent decoding was computed across 18 equally spaced phase bins spanning the full oscillatory cycle (0 - 2π), including generalization from each phase bin to the others. To asses rhythmic modulation of accuracy with respect to phase, we fit a harmonic regression to the resulting phase–accuracy profiles following the methods outlined in.⁵⁷ For each participant and electrode, decoding accuracy was modelled as a linear combination of sine and cosine terms:

y (ϕ) = β_{0} + β_{1} \sin (ϕ) + β_{2} \cos (ϕ) + ϵ

where ϕ denotes the phase bin centers (ranging from 0 to 2π), and ε is residual error. From the regression coefficients, we derived the amplitude modulation as:

A = \sqrt{β_{1}^{2} + β_{2}^{2}}

reflecting the strength of phase-dependent modulation, and the preferred phase as:

θ = atan 2 (β_{1}, β_{2})

indicating the phase at which decoding accuracy peaks.

Then, we generated null distributions of amplitude and phase estimates by randomly permuting (N=1000) the phase labels and re-fitting the harmonic model. Because amplitude values are strictly non-negative, we computed robust z-scores using the median absolute deviation (MAD) of the null distribution:

Z = 0.6745 \cdot \frac{A_{obs} - median (A_{perm})}{MAD (A_{perm})}

This provided a normalized, outlier-robust effect size for each participant and electrode that can be meaningfully tested against zero.

For phase, we quantified phase alignment across participants using the cosine similarity between each subject’s preferred phase and the group mean phase (i.e., the circular average): $d_{i} = \cos (θ_{i} - \bar{θ})$ .

This measure is the equivalent of a dot-product in circular space and reflects phase consistency across subjects: values near 1 indicate close alignment with the group mean and values near –1 indicate opposite phase preference. We again computed robust z-scores for this alignment measure using the corresponding null distribution from the permuted data, yielding per-participant, per-channel phase alignment scores. At the group level, we tested the z-scores for both amplitude and phase alignment against zero using a one-sample t-test. To correct for multiple comparisons across electrodes, we applied a cluster-based permutation test.

Phase-lag analysis

For each subject, we identified the electrodes within the significant frontal and occipito-parietal clusters (as determined by the cluster-based permutation test on peak–trough decoding differences) and computed all pairwise combinations between them (N = 243 pairs). EEG data were segmented from 1000 to 2000 ms post-stimulus and bandpass filtered in the alpha range (8–13 Hz). For each channel pair, we computed the cross-spectral density (CSD), and the phase difference was derived from the angle of the resulting complex-valued CSD. This yielded an estimate of phase differences for each channel pair and participant.

To assess whether phase differences were non-uniformly distributed and clustered around 180°, we applied a circular V-test (from the CircStat toolbox⁵⁸) to each channel pair across participants, testing against a mean direction of 180°. The resulting p-values were Bonferroni-corrected for multiple comparisons across the 243 channel pairs.

Additionally, we computed the phase-slope index (PSI) between the same channel pairs, following the procedure described in.²⁵ The PSI quantifies the consistency of phase differences across neighboring frequencies: when one signal systematically leads another in phase across frequencies, the PSI becomes positive, indicating a directed influence from the leading to the lagging site. Positive PSI values therefore indicate that anterior channels lead posterior ones, whereas negative values indicate the opposite direction of information flow. To assess statistical significance, a null distribution was generated by randomly sign-flipping the PSI across iterations (N=1000), and the observed value was compared against this distribution.

Footnotes

Supplemental information can be found online at https://doi.org/10.1016/j.isci.2026.117870.

Supplemental information

Document S1. Supplemental methods and Figures S1–S3

mmc1.pdf^{(444.9KB, pdf)}

References

1.White P.A. Academic Press Inc.; 2018. Is Conscious Perception a Series of Discrete Temporal Frames? Preprint at. [DOI] [PubMed] [Google Scholar]
2.VanRullen R., Koch C. Is perception discrete or continuous? Trends Cogn. Sci. 2003;7:207–213. doi: 10.1016/S1364-6613(03)00095-0. [DOI] [PubMed] [Google Scholar]
3.Brickwedde M., Limachya R., Markiewicz R., Sutton E., Postzich C., Shapiro K., Jensen O., Mazaheri A. Cross-modal interaction of Alpha Activity does not reflect inhibition of early sensory processing: A frequency tagging study using EEG and MEG. bioRxiv. 2022 doi: 10.7554/eLife.106050.3. Preprint. [DOI] [PMC free article] [PubMed] [Google Scholar]
4.VanRullen R. Perceptual Cycles. Trends Cogn. Sci. 2016;20:723–735. doi: 10.1016/j.tics.2016.07.006. [DOI] [PubMed] [Google Scholar]
5.Haegens S., Nácher V., Luna R., Romo R., Jensen O. α-Oscillations in the monkey sensorimotor network influence discrimination performance by rhythmical inhibition of neuronal spiking. Proc. Natl. Acad. Sci. USA. 2011;108:19377–19382. doi: 10.1073/pnas.1117190108. [DOI] [PMC free article] [PubMed] [Google Scholar]
6.Jensen O., Mazaheri A. Shaping Functional Architecture by Oscillatory Alpha Activity: Gating by Inhibition. Front. Hum. Neurosci. 2010;4 doi: 10.3389/fnhum.2010.00186. [DOI] [PMC free article] [PubMed] [Google Scholar]
7.Dugué L., Marque P., VanRullen R. The Phase of Ongoing Oscillations Mediates the Causal Relation between Brain Excitation and Visual Perception. J. Neurosci. 2011;31:11889–11893. doi: 10.1523/JNEUROSCI.1161-11.2011. [DOI] [PMC free article] [PubMed] [Google Scholar]
8.Gulbinaite R., İlhan B., VanRullen R. The Triple-Flash Illusion Reveals a Driving Role of Alpha-Band Reverberations in Visual Perception. J. Neurosci. 2017;37:7219–7230. doi: 10.1523/JNEUROSCI.3929-16.2017. [DOI] [PMC free article] [PubMed] [Google Scholar]
9.Busch N.A., Dubois J., VanRullen R. The Phase of Ongoing EEG Oscillations Predicts Visual Perception. J. Neurosci. 2009;29:7869–7876. doi: 10.1523/JNEUROSCI.0113-09.2009. [DOI] [PMC free article] [PubMed] [Google Scholar]
10.Ronconi L., Balestrieri E., Baldauf D., Melcher D. Distinct Cortical Networks Subserve Spatio-temporal Sampling in Vision through Different Oscillatory Rhythms. J. Cogn. Neurosci. 2024;36:572–589. doi: 10.1162/jocn_a_02006. [DOI] [PubMed] [Google Scholar]
11.Valera F.J., Toro A., Roy John E., Schwartz E.L. Perceptual framing and cortical alpha rhythm. Neuropsychologia. 1981;19:675–686. doi: 10.1016/0028-3932(81)90005-1. [DOI] [PubMed] [Google Scholar]
12.Kristofferson A.B. Successiveness Discrimination as a Two-State, Quantal Process. Science. 1967;158:1337–1339. doi: 10.1126/science.158.3806.1337. [DOI] [PubMed] [Google Scholar]
13.Milton A., Pleydell-Pearce C.W. The phase of pre-stimulus alpha oscillations influences the visual perception of stimulus timing. Neuroimage. 2016;133:53–61. doi: 10.1016/j.neuroimage.2016.02.065. [DOI] [PMC free article] [PubMed] [Google Scholar]
14.Samaha J., Postle B.R. The Speed of Alpha-Band Oscillations Predicts the Temporal Resolution of Visual Perception. Curr. Biol. 2015;25:2985–2990. doi: 10.1016/j.cub.2015.10.007. [DOI] [PMC free article] [PubMed] [Google Scholar]
15.Deodato M., Melcher D. Correlations between Visual Temporal Resolution and Individual Alpha Peak Frequency: Evidence that Internal and Measurement Noise Drive Null Findings. J. Cogn. Neurosci. 2024;36:590–601. doi: 10.1162/JOCN_A_01993. [DOI] [PubMed] [Google Scholar]
16.Wutz A., Melcher D., Samaha J. Frequency modulation of neural oscillations according to visual task demands. Proc. Natl. Acad. Sci. USA. 2018;115:1346–1351. doi: 10.1073/PNAS.1713318115/-/DCSUPPLEMENTAL. [DOI] [PMC free article] [PubMed] [Google Scholar]
17.Keitel C., Ruzzoli M., Dugué L., Busch N.A., Benwell C.S.Y. Rhythms in cognition: The evidence revisited. Eur. J. Neurosci. 2022;55:2991–3009. doi: 10.1111/ejn.15740. [DOI] [PMC free article] [PubMed] [Google Scholar]
18.Buergers S., Noppeney U. The role of alpha oscillations in temporal binding within and across the senses. Nat. Hum. Behav. 2022;6:732–742. doi: 10.1038/s41562-022-01294-x. [DOI] [PMC free article] [PubMed] [Google Scholar]
19.Ruzzoli M., Torralba M., Morís Fernández L., Soto-Faraco S. The relevance of alpha phase in human perception. Cortex. 2019;120:249–268. doi: 10.1016/j.cortex.2019.05.012. [DOI] [PubMed] [Google Scholar]
20.Gupta N., Singh S.S., Stopfer M. Oscillatory integration windows in neurons. Nat. Commun. 2016;7 doi: 10.1038/ncomms13808. [DOI] [PMC free article] [PubMed] [Google Scholar]
21.Grootswagers T., Robinson A.K., Shatek S.M., Carlson T.A. Mapping the dynamics of visual feature coding: Insights into perception and integration. PLoS Comput. Biol. 2024;20 doi: 10.1371/journal.pcbi.1011760. [DOI] [PMC free article] [PubMed] [Google Scholar]
22.Broday-Dvir R., Norman Y., Harel M., Mehta A.D., Malach R. Perceptual stability reflected in neuronal pattern similarities in human visual cortex. Cell Rep. 2023;42 doi: 10.1016/j.celrep.2023.112614. [DOI] [PubMed] [Google Scholar]
23.Liu B., Nobre A.C., van Ede F. Functional but not obligatory link between microsaccades and neural modulation by covert spatial attention. Nat. Commun. 2022;13:3503. doi: 10.1038/s41467-022-31217-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
24.Haufe S., Meinecke F., Görgen K., Dähne S., Haynes J.-D., Blankertz B., Bießmann F. On the interpretation of weight vectors of linear models in multivariate neuroimaging. Neuroimage. 2014;87:96–110. doi: 10.1016/j.neuroimage.2013.10.067. [DOI] [PubMed] [Google Scholar]
25.Nolte G., Ziehe A., Nikulin V.V., Schlögl A., Krämer N., Brismar T., Müller K.R. Robustly estimating the flow direction of information in complex physical systems. Phys. Rev. Lett. 2008;100:234101. doi: 10.1103/PhysRevLett.100.234101. [DOI] [PubMed] [Google Scholar]
26.Zhigalov A., Jensen O. Perceptual echoes as travelling waves may arise from two discrete neuronal sources. Neuroimage. 2023;272 doi: 10.1016/j.neuroimage.2023.120047. [DOI] [PMC free article] [PubMed] [Google Scholar]
27.Ippolito G., Bertaccini R., Tarasi L., Di Gregorio F., Trajkovic J., Battaglia S., Romei V. The Role of Alpha Oscillations among the Main Neuropsychiatric Disorders in the Adult and Developing Human Brain: Evidence from the Last 10 Years of Research. Biomedicines. 2022;10:3189. doi: 10.3390/biomedicines10123189. [DOI] [PMC free article] [PubMed] [Google Scholar]
28.Mathewson K.E., Gratton G., Fabiani M., Beck D.M., Ro T. To See or Not to See: Prestimulus Phase Predicts Visual Awareness. J. Neurosci. 2009;29:2725–2732. doi: 10.1523/JNEUROSCI.3963-08.2009. [DOI] [PMC free article] [PubMed] [Google Scholar]
29.ten Oever S., Sack A.T. Oscillatory phase shapes syllable perception. Proc. Natl. Acad. Sci. USA. 2015;112:15833–15837. doi: 10.1073/pnas.1517519112. [DOI] [PMC free article] [PubMed] [Google Scholar]
30.Karimi-Rouzbahani H. Evidence for Multiscale Multiplexed Representation of Visual Features in EEG. Neural Comput. 2024;36:412–436. doi: 10.1162/neco_a_01649. [DOI] [PubMed] [Google Scholar]
31.Ng B.S.W., Logothetis N.K., Kayser C. EEG Phase Patterns Reflect the Selectivity of Neural Firing. Cereb. Cortex. 2013;23:389–398. doi: 10.1093/cercor/bhs031. [DOI] [PubMed] [Google Scholar]
32.Dou W., Morrow A., Iemi L., Samaha J. Pre-stimulus alpha-band phase gates early visual cortex responses. Neuroimage. 2022;253 doi: 10.1016/j.neuroimage.2022.119060. [DOI] [PubMed] [Google Scholar]
33.Iemi L., Busch N.A., Laudini A., Haegens S., Samaha J., Villringer A., Nikulin V.V. Multiple mechanisms link prestimulus neural oscillations to sensory responses. Elife. 2019;8 doi: 10.7554/eLife.43620. [DOI] [PMC free article] [PubMed] [Google Scholar]
34.Naruse Y., Matani A., Hayakawa T., Fujimaki N. Influence of seamlessness between pre- and poststimulus alpha rhythms on visual evoked potential. Neuroimage. 2006;32:1221–1225. doi: 10.1016/j.neuroimage.2006.04.222. [DOI] [PubMed] [Google Scholar]
35.Deodato M., Melcher D. Continuous temporal integration in the human visual system. J. Vis. 2024;24:5. doi: 10.1167/jov.24.13.5. [DOI] [PMC free article] [PubMed] [Google Scholar]
36.Chen L., Cichy R.M., Kaiser D. Alpha-frequency feedback to early visual cortex orchestrates coherent naturalistic vision. Sci. Adv. 2023;9 doi: 10.1126/sciadv.adi2321. [DOI] [PMC free article] [PubMed] [Google Scholar]
37.Min B.-K., Busch N.A., Debener S., Kranczioch C., Hanslmayr S., Engel A.K., Herrmann C.S. The best of both worlds: Phase-reset of human EEG alpha activity and additive power contribute to ERP generation. Int. J. Psychophysiol. 2007;65:58–68. doi: 10.1016/j.ijpsycho.2007.03.002. [DOI] [PubMed] [Google Scholar]
38.Bonneh Y.S., Adini Y., Polat U. Contrast sensitivity revealed by microsaccades. J. Vis. 2015;15:11. doi: 10.1167/15.9.11. [DOI] [PubMed] [Google Scholar]
39.Macdonald J.S.P., Cavanagh P., VanRullen R. Attentional sampling of multiple wagon wheels. Atten. Percept. Psychophys. 2014;76:64–72. doi: 10.3758/s13414-013-0555-5. [DOI] [PubMed] [Google Scholar]
40.Pitts W., McCulloch W.S. How we know universals the perception of auditory and visual forms. Bull. Math. Biophys. 1947;9:127–147. doi: 10.1007/BF02478291. [DOI] [PubMed] [Google Scholar]
41.Fiebelkorn I.C., Kastner S. A Rhythmic Theory of Attention. Trends Cogn. Sci. 2019;23:87–101. doi: 10.1016/j.tics.2018.11.009. [DOI] [PMC free article] [PubMed] [Google Scholar]
42.Landau A.N., Fries P. Attention Samples Stimuli Rhythmically. Curr. Biol. 2012;22:1000–1004. doi: 10.1016/j.cub.2012.03.054. [DOI] [PubMed] [Google Scholar]
43.Landau A.N., Schreyer H.M., van Pelt S., Fries P. Distributed Attention Is Implemented through Theta-Rhythmic Gamma Modulation. Curr. Biol. 2015;25:2332–2337. doi: 10.1016/j.cub.2015.07.048. [DOI] [PubMed] [Google Scholar]
44.Michel R., Dugué L., Busch N.A. Distinct contributions of alpha and theta rhythms to perceptual and attentional sampling. Eur. J. Neurosci. 2022;55:3025–3039. doi: 10.1111/ejn.15154. [DOI] [PubMed] [Google Scholar]
45.Benedetto A., Binda P., Costagli M., Tosetti M., Morrone M.C. Predictive visuo-motor communication through neural oscillations. Curr. Biol. 2021;31:3401–3408.e4. doi: 10.1016/j.cub.2021.05.026. [DOI] [PMC free article] [PubMed] [Google Scholar]
46.Pilipenko A., Samaha J. Selective Effects of Ongoing Alpha-Band Activity on Magno- and Parvo-Mediated Detection. Psychophysiology. 2025;62 doi: 10.1111/psyp.70070. [DOI] [PMC free article] [PubMed] [Google Scholar]
47.Sewards T.V., Sewards M.A. Alpha-band oscillations in visual cortex: part of the neural correlate of visual awareness? Int. J. Psychophysiol. 1999;32:35–45. doi: 10.1016/S0167-8760(98)00062-2. [DOI] [PubMed] [Google Scholar]
48.Kelley C., Slater C., Sorrentino M., Noone D., Hung J., Sajda P., Wang Q. Alpha modulation of spiking activity across multiple brain regions in mice performing a tactile selective detection task. Eur. J. Neurosci. 2025;62 doi: 10.1111/ejn.70356. [DOI] [PMC free article] [PubMed] [Google Scholar]
49.Lozano-Soldevilla D. On the Physiological Modulation and Potential Mechanisms Underlying Parieto-Occipital Alpha Oscillations. Front. Comput. Neurosci. 2018;12 doi: 10.3389/fncom.2018.00023. [DOI] [PMC free article] [PubMed] [Google Scholar]
50.Deodato M., Melcher D. Aperiodic EEG Predicts Variability of Visual Temporal Processing. J. Neurosci. 2024;44 doi: 10.1523/JNEUROSCI.2308-23.2024. [DOI] [PMC free article] [PubMed] [Google Scholar]
51.Fahrenfort J.J., van Driel J., van Gaal S., Olivers C.N.L. From ERPs to MVPA Using the Amsterdam Decoding and Modeling Toolbox (ADAM) Front. Neurosci. 2018;12 doi: 10.3389/fnins.2018.00368. [DOI] [PMC free article] [PubMed] [Google Scholar]
52.Delorme A., Makeig S. EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J. Neurosci. Methods. 2004;134:9–21. doi: 10.1016/j.jneumeth.2003.10.009. [DOI] [PubMed] [Google Scholar]
53.Oostenveld R., Fries P., Maris E., Schoffelen J.-M. FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data. Comput. Intell. Neurosci. 2011;2011:156869. doi: 10.1155/2011/156869. [DOI] [PMC free article] [PubMed] [Google Scholar]
54.Brainard D.H. The Psychophysics Toolbox. Spat. Vis. 1997;10:433–436. doi: 10.1163/156856897X00357. [DOI] [PubMed] [Google Scholar]
55.Maris E., Oostenveld R. Nonparametric statistical testing of EEG- and MEG-data. J. Neurosci. Methods. 2007;164:177–190. doi: 10.1016/j.jneumeth.2007.03.024. [DOI] [PubMed] [Google Scholar]
56.Engbert R., Mergenthaler K. Microsaccades are triggered by low retinal image slip. Proc. Natl. Acad. Sci. USA. 2006;103:7192–7197. doi: 10.1073/pnas.0509557103. [DOI] [PMC free article] [PubMed] [Google Scholar]
57.Henry M.J., Obleser J., Crusey M.R., Fuller E.R., Lee Y.S., Meyer M., Acosta E.A.M., Van Hedger S.C., Inbar M., Oderbolz C., et al. How strong is the rhythm of perception? A registered replication of Hickok et al. (2015) R. Soc. Open Sci. 2025;12 doi: 10.1098/rsos.220497. [DOI] [PMC free article] [PubMed] [Google Scholar]
58.Berens P. CircStat : A MATLAB Toolbox for Circular Statistics. J. Stat. Softw. 2009;31:1–21. doi: 10.18637/jss.v031.i10. [DOI] [Google Scholar]

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