We investigated the effect of attention on the flash-lag effect (FLE) in order to determine whether the FLE can be used to estimate the effect of visual attention. The FLE is the effect that a flash aligned with a moving object is perceived to lag the moving object, and several studies have shown that attention reduces its magnitude. We measured the FLE as a function of the number or speed of moving objects. The results showed that the effect of cueing, which we attributed the effect of attention, on the FLE increased monotonically with the number or the speed of the objects. This suggests that the amount of attention can be estimated by measuring the FLE, assuming that more amount of attention is required for a larger number or faster speed of objects to attend. On the basis of this presumption, we attempted to measure the spatial spread of visual attention by FLE measurements. The estimated spatial spreads were similar to those estimated by other experimental methods.

^{2}) on a gray background (28 cd/m

^{2}). The stimuli moved along a circular path with a radius of 7° while the observer fixated on the center of the circle. The flash stimuli were a pair of black disks with a diameter of 0.7° (<0.01 cd/m

^{2}). The flash disks were presented briefly (one frame of 6 ms) near the target disk (1.6° between the centers), so that the observer was able to judge the alignment between the target and the flash stimuli. The number of moving disks was one, two, or six (disk separation was 180° or 60° for the two- or six-disk condition, respectively; see Figure 1B). All disks moved at the same speed in the same direction. The speed of the moving disks was 0.33 rps (15.0°/s in terms of the linear motion in visual angle). A demonstration movie can be seen in Figure 1C.

*t*-test showed that the difference was not statistically significant (

*t*(4) = 0.05,

*p*= 0.96). In contrast, the difference was larger in the case of six disks. The same statistical test showed that the difference was highly significant (

*t*(4) = 13.9,

*p*< 0.001).

*F*(4, 40) = 7.32,

*p*< 0.001;

*F*(1, 40) = 18.7,

*p*< 0.001), while the interaction between the two factors was not significant (

*F*(4, 40) = 1.43,

*p*> 0.1).

*t*(4) = 5.24,

*p*< 0.01). The temporal delay that was shortened by cuing the target was less than 10 ms for the slowest motion (0.08 rps) and increased to more than 30 ms for the fastest motion (0.88 rps).

*i*, the PSE

_{ i }can be expressed as follows:

*m*

_{A}and

*m*

_{B}are the means of the two normal distribution functions and

*k*

_{ i }is the relative weights of the two functions in condition

*i*, which varies between 0 and 1. Similarly, the standard deviation of a mixed function, which we call the slope (SL

_{ i }) of the psychometric function, is expressed as follows:

*σ*

_{A}and

*σ*

_{B}are the standard deviation of the two normal distribution functions.

*k*

_{ i }in each condition,

*m*

_{A},

*σ*

_{A},

*m*

_{B}, and

*σ*

_{B}are required. The values of

*m*

_{A}and

*σ*

_{A}were parameters of the probability distribution function of the 100% on condition. They are estimated from the psychometric function in the target condition, where the flashes were presented only at the target disk, ignoring the other disks. We estimated the parameters,

*m*

_{B}and

*σ*

_{B}of the distribution for the 100% off condition and the weights,

*k*

_{ i }s for the five conditions in terms of a least square method. The difference in PSE and SL between the prediction from the model and experimental results was minimized in the method (there are ten equations, two for each of five conditions and seven unknowns).

*z*-score). The shape of the function is similar for the three estimations. This confirms that the spatial distribution of attention effect on the FLE reflects the spatial spread of attention, instead of any effect specific to the FLE measurements. We can assume that the observers' attentional state is similarly controlled in the three experiments because the three experiments used similar tasks of attentive tracking. The consistency across studies is shown in Figure 9. Figure 9 indicates that the measurements of attentional state using the three techniques are similarly

*reliable*. In terms of task simplicity, the flash-lag technique has an advantage. Judgments of relative location of a flash is easier than detecting a probe at threshold level and the measurement does not need special equipment such as an eye tracker. The flash-lag effect can be used conveniently to investigate states of visual attention

*in many cases*.