Experimental paradigm and analysis pipeline.

(A) Task design. Each trial contained a brief, filtered-noise stimulus (8 ms) presented to the right or left of fixation with equal probability. Half of the trials had a target Gabor (2 cycles per degree, 0° orientation) embedded in the noise (stimulus present) and the other half were only noise (target absent). Participants reported the presence of the target with concurrent confidence judgments followed by a question probing the possibility that what they had seen (either target or just noise) had been imagined (see supplemental materials). (B) Task performance. The contrast level of the target was titrated across task blocks to maintain a d’ value between 1.2 and 1.8. The individual subject d’ and criterion values are plotted in lighter circles; the grand average d’ (1.54) and criterion (0.25) are the darker circles with error bars indicating ± 1 standard error of the mean (SEM). (C) Phase effects on criterion and/or sensitivity in the signal detection theory (SDT) framework. Criterion and sensitivity changes may arise from various underlying mechanisms. A criterion change is indicative of a concurrent increase (or decrease) in hits and false alarms, with no change in separability between distributions. The first model (from left to right) indicates a phase effect on criterion as a result of a change in the internal decision criterion, whereas the second model shows a criterion effect from an additive gain applied to both the noise and signal+noise distributions (note that these two different criterion mechanisms would produce identical changes in behavior). A sensitivity shift induces a disproportionate change in hits compared to false alarms, leading to a change in overlap between distributions. The third model demonstrates multiplicative gain, whereby each distribution is multiplied by a small constant leading to a relatively small increase in the noise distribution (more false alarms) and a greater increase in the signal+noise distribution (even more hits). The final model shows the variance reduction account in which the variability of both distributions decreases, leading to more hits and fewer false alarms during the optimal phase. (D) The analysis pipeline illustrated for a single example participant. To quantify the coupling between alpha phase and behavior (in this example, d’), we computed the instantaneous phase using a Hilbert transform on the filtered (IAF ± 2 Hz) and (post-stimulus) tapered EEG data. For each time point and electrode, the single-trial phase angles were binned into 8 phase bins and d’ was computed using those subset of trials. These measurements were then vectorized by assigning d’ as the vector length and the bin center as the vector angle. The resultant vector length was then computed to quantify the alpha phase-d’ coupling magnitude at each point in time while the angle points in the direction of the optimal phase. This example subject showed significant phase-d’ coupling in the ∼100 ms preceding stimulus onset.

Alpha phase modulates perceptual sensitivity through phase-dependent fluctuations in internal noise.

(A) Alpha phase predicts sensitivity up to 426 ms before the stimulus presentation. The time course of the resultant vector lengths characterizing the alpha phase-d’ coupling shows significant cluster-corrected coupling from −220ms until stimulus onset, as indicated by the black bar. A significant (uncorrected) effect was present as early as −426 ms pre-stimulus, as seen by the gray bar. The dashed line indicates the permutation threshold of the 95th percentile and the error bars represent ± 1 SEM. (B) The phasic modulation of d’ arose from the inverse phasic relationship of hits and false alarms, supporting a model in which the variability of internal responses changes in a phase-dependent manner. The first graph (from left to right) shows the underlying change in d’ across phase bins. The data have been aligned across participants so that each individual’s highest d’ was assigned to bin 8 (omitted from the plot), with the remaining data circularly shifted, and is averaged across −450 ms to stimulus onset. Error bars represent ± 1 SEM. The pattern shows a clear phasic modulation of d’ across bins. The second graph shows the similarly aligned and averaged hit rate (HR) and false alarm rate (FAR). This revealed an inverse phasic relationship between HR and FAR, consistent with the prediction made by the variance reduction model. (C-D) No evidence for the coupling of criterion to pre-stimulus alpha-band phase. Graph C reveals the time course of the resultant vector lengths for alpha phase-criterion coupling, whereas graph D shows the underlying shifted c across phase bins (shifted to participants’ optimal phase, as in graph B). We did not observe any significant phase-dependant relationship between phase and criterion. (E) Responses to pairs of identical stimuli occurring over the course of the experiment were more consistent with one another when both stimuli were presented during the best phase. This supports the notion that the internal representations of the stimulus were less variable during one’s optimal phase. Error bars represent ±1 within-subjects SEM. (F) The topography of phase-d’ coupling averaged over −450 - 0 ms showed significant effects (black dots) over frontal and occipital electrodes. The angular difference between the frontal (AFz) and occipital (Oz) optimal phases suggests a single dipole source as they are significantly clustered around ∼180° (i.e., phase opposition). Gray lines are individual subject phase difference vectors and the orange line is the circular average.

Alpha phase sharpens sensory tuning during the optimal phase.

(A) The analysis pipeline for a single example participant. To create the classification images (CI) for each participant’s optimal and suboptimal phase, we extracted the normalized energy profiles of each stimulus, quantifying the amount of energy in each orientation and spatial frequency (SF) combination. The single-trial energy at each SF and orientation was then regressed on the participant’s binary response (i.e., “target” or “noise”) resulting in a beta value. The beta values of a given SF and orientation characterize the influence that energy changes have on a participant’s response and reveal perceptual tuning. (B) CI of participant’s optimal and suboptimal phase. The bootstrapped CI of optimal and suboptimal phase with two example contours of the 2-D Gaussian fit depicted in black circles. The marginals of the CI averaged across orientations (above) and SF (on the right) are shown alongside each CI with the model fit. Error bars indicate 1 bootstrapped SEM. (C) The difference CI reveals broader tuning for the suboptimal phase around the target features. The difference CI was created by subtracting the optimal CI from the suboptimal CI for each bootstrapped iteration. The black outlines represent SF and orientation combinations that show significant (p < 0.05) changes in beta values between the optimal and suboptimal phase. The differences reveal greater beta values for off-target features (target SF = 2, orientation = 0°) during one’s suboptimal phase, broadening perceptual tuning. (D) Variance in sensory tuning is reduced during one’s optimal phase. To quantify changes in sensory tuning between optimal and suboptimal phase, we fit a 2-D Gaussian to the optimal phase CI and modulated three parameters to account for the fit of the suboptimal phase CI. We found a significant modulation in the SD parameter, characterizing the variance of the Gaussian across both the SF and orientation dimensions. No significant modulation for the gain or offset parameters were found. Taken together, this suggests that sensory tuning during one’s optimal phase sharpens towards the relevant stimulus features.

Alpha phase shows a weak relationship with confidence and no relationship with judgements of imagination.

(A) The time course from the coupling of alpha phase and confidence shows a significant (uncorrected) relationship from −220 to −153 ms. The dashed line indicates the permutation threshold of the 95th percentile and the error bars represent ± 1 SEM. (B) There was no significant relationship in the coupling of alpha phase and imagination judgements at any timepoint.

Alpha power only shows a modulation of confidence.

(A) The relationship between alpha power and behavior (in this instance, d’) was quantified by first binning all of the trials into 8 quantiles of descending power and then computing d’ for each bin using the corresponding subset of trials. We then fit a line to d’ across bins and analyzed the slope of this line at each timepoint, which is the time course depicted in each of the graphs. We found no significant linear relationship between alpha power and d’ at any time point. The dashed lines indicate the lower (2.5th percentile) and upper (97.5th percentile) permutation thresholds and the error bars represent ± 1 SEM. (B) The time course illustrating the linear relationship between alpha power and criterion similarly showed no significant association. (C) Alpha power was significantly negatively associated with confidence, such that higher pre-stimulus alpha power predicted reduced confidence in the judgment of the grating’s presence or absence. This relationship was robust, with a significant cluster-corrected effect spanning –400 to –50 ms, and a weaker, uncorrected effect observed between –630 and –590 ms. (D) We observed no significant relationship between alpha power and the proportion of imagination judgements reported.