The spatial distribution and the temporal dynamics of attention are well understood in isolation, but their interaction remains an open question. How does the shape of the attentional focus evolve over time? To answer this question, we measured spatiotemporal maps of endogenous and exogenous attention in humans (more than 140,000 trials in 23 subjects). We tested the visibility of a low-contrast target presented (50 ms) at different spatial distances and temporal delays from a cue in a noisy background. The cue was a non-informative salient peripheral (5°) stimulus for exogenous attention and a central arrow cue (valid 66.6%) pointing left or right for endogenous attention. As a measure of attention, we determined, for each distance and delay, the background contrast compensation required to keep performance at 75%. The spatiotemporal mapping of exogenous attention revealed a significant enhancement zone from 150 to 430 ms, extending up to 6° from the cue. Endogenous attention maps showed a peak at the cued side at 400 ms and between 8 and 10° from the cue. Modeling suggests that the data are compatible with a constant spotlight shape across time. Our results represent the first detailed spatiotemporal maps of both endogenous and exogenous attention.

*exogenous attention*and goal-driven orienting or

*endogenous attention*(Cheal & Lyon, 1991; Chica & Lupiañez, 2009; Corbetta & Shulman, 2002; Egeth & Yantis, 1997; Hein, Rolke, & Ulrich, 2006; Nakayama & Mackeben, 1989; Yantis & Jonides, 1990; Yeshurun, Montagna, & Carrasco, 2008).

*a global contrast function*(Cglob),

*an eccentricity function*(Cecc), and

*a spatiotemporal attention function*(Att) as follows:

*global contrast function*compensated for intersubject variability, acting as a gain function. This function was a constant that modulated background contrast over the entire screen area (Figure 1b). Contrast threshold was determined by one pair of staircases (one initiated at a low-contrast value and the other at a high-contrast value) in order to maintain performance at 75% no matter the eccentricity, the cue–target distance, or its SOA from cue onset.

*eccentricity function*compensated for visual acuity differences between fovea and periphery. This was a function of distance from fixation point (

_{f}) and modulated the background contrast independently over 7 concentric segments centered at the center of the screen (Figure 2), updating its contrast depending on target eccentricity from fixation point in each trial. The contrast threshold for each segment was determined by a pair of staircases in order to maintain performance at 75% along all eccentricities.

*spatiotemporal attention function*compensated for the effects of attention in both space and time. This was a function of distance (

*d*) and delay (

*t*) from cue, dynamically modulating the background contrast at different distances and delays from the cue (Figures 3 and 4). The screen area was divided in discrete segments centered at the cue position (spatial sampling) and trial duration was divided as well in discrete time steps (temporal sampling). The contrast threshold was determined independently using one staircase pair for each spatiotemporal coordinate, in order to maintain performance at 75% at every cue–target presentation distance and delay.

*X*-axis corresponds to target delay from cue onset and the

*Y*-axis to target distance from the cue. Attentional effects (percentage of background contrast compensation, see Equation 1) are color coded (from red to yellow representing attention enhancement, from blue to cyan representing inhibition, and black corresponding to the baseline). We then calculated the grand average across all subjects. Figure 7a shows the grand-average attention map for exogenous attention over 13 subjects. A progressive enhancement of attention can be seen from 50 to 150 ms. This enhancement attains a plateau from 200 to 350 ms, peaking at the spatial region extending up to 3° from the cue.

*C*

_{13}

^{2}= 78) was

*r*= 0.2574. We compared this result to the null hypothesis that the measured attention pattern was simply due to noise. To do this, we randomly scrambled the attention map of each subject (in its original 7 × 8 or 14 × 11 format, later interpolated over a 100 × 100 grid) and we calculated the Pearson correlation between all subject pairs as previously. This procedure was repeated 10,000 times and revealed that the probability of obtaining a correlation coefficient

*r*= 0.2574 due to chance was less than

*p*< 10

^{−4}. Thus, the measured spatiotemporal attentional pattern is not simply due to noise but is consistent across subjects.

^{4}times and found no cluster size equal or larger than 1695 points. Therefore, this bootstrap analysis reveals that attentional enhancement effects above 3% can be considered highly significant (

*p*< 10

^{−4}). These significant enhancing effects include the zone from 150 to 430 ms after cue onset and up to 6° of eccentricity.

*r*= 0.3193 and across the groups,

*r*= 0.2430. Bootstrap analysis (shuffling the assignment of subjects to the control or test group and repeating the pairwise correlation

*n*= 10

^{4}times) showed no significant difference between control and test groups (

*t*-test,

*p*= 0.104). Thus, even if semi-random target placement could have provided information to anticipate the target position, test subjects did not appear to use it in a significant manner.

*X*-axis corresponds to time from cue onset and the

*Y*-axis to distance from the cue. Attentional effects are color-coded (red/yellow representing attention enhancement, blue/green representing inhibition, and black corresponding to the baseline). We then calculated the grand average across all subjects. Figure 8a shows the grand-average attention map for endogenous attention over 10 subjects. The average map shows an early (100 ms) enhancing effect centered on the cue, with a later deployment of attention at the cued side peaking between 8 and 10° at around 400 ms after cue onset.

*C*

_{10}

^{2}= 45) was

*r*= 0.184. We compared this result to the null hypothesis that the measured attention pattern was simply due to noise. To do this, we randomly scrambled the attention map of each subject (in its original 7 × 10, later interpolated over a 100 × 100 grid) and we calculated the Pearson correlation between all subject pairs as previously. This procedure was repeated 10,000 times and revealed that the probability of obtaining a correlation coefficient

*r*= 0.184 due to chance was less than

*p*< 10

^{−4}. Thus, the measured spatiotemporal pattern of endogenous attention is not simply due to noise but is consistent across subjects.

^{4}. Therefore, this analysis reveals that attentional enhancement effects above 3% can be considered highly significant (

*p*= 10

^{−4}).

_{(s,t)}is decomposed in two parts: one spatial subfunction

*S*

_{(s)}that corresponds to the shape of the attentional focus and one activation function

*M*

_{(t)}that reflects the magnitude of attentional modulation as a function of time. The constant

*b*represents baseline (i.e., average value of the spatiotemporal attention function), and

*k*is a constant of proportionality obtained as follows:

*S*and

*M*as

*p*= 0.8 and

*p*= 0.7, respectively), suggesting that the spatial attention deployment pattern does not change significantly over time but only modulates its amplitude.

*x, y*coordinates) instead of one (i.e., only Euclidean cue–target distance) would be necessary. However, the introduction of another spatial dimension would multiply the number of trials required and make the study impractical. All in all, our results can be taken as a good approximation to a spatiotemporal map of exogenous and endogenous attention, since many of the abovementioned undesirable manifestations of the spatial heterogeneity of attention will average out due to our counterbalancing the target presentation over all possible locations (i.e., the same cue–target distance but oriented in all directions, presenting cue and target in the same or in different hemifields, etc.).