Figure 1.

Double-detection functions can reveal periodicities even when the phase varies across trials. (A) Protocol. Let us assume that the probability of detecting a stimulus (i.e., the system's sensitivity) fluctuates periodically along with the phase of an ongoing oscillatory process. By definition, this process bears no relation with the timing of each trial, and thus the phase will differ on each trial. On successive trials, not one but two stimuli are presented, with a variable delay between them. (B) Expected results. Because the phase of the oscillatory process at the moment of stimulus presentation is fully unpredictable, the average probability of detecting each stimulus as a function of time (using an absolute reference, such as the trial onset) will be constant (left). The probability of detecting the second stimulus will also be independent of the time elapsed since the first one (middle). However, the probability of detecting both stimuli (albeit smaller) will oscillate as a function of the delay between them, and the period of this oscillation will be equal to the period of the original ongoing oscillatory process (adapted from Latour, 1967).