After having shown in the previous section that an anticipatory smooth eye movement distorts the perceived space when tested with a short flash, we wondered whether we could reveal the temporal evolution of the flash-lag effect. Therefore, we performed the following regression analysis independently for both FF and FP conditions and for each time step during gaze orientation:
The results of the regression in
Equation 3 are represented in
Figure 7. Individual regression coefficients for each time step and FF or FP condition ranged from R = 0.1393…0.7597 (
p < .001…0.023). The nonzero offset α in the early orientation (
Figure 7A) was essentially due to the saccadic undershoot strategy (
Gellman & Fletcher, 1992) and the system compensated for this error later on in the orientation process.
Figure 7B shows the evolution of the error dependence on EV
flash over time. Interestingly, in the earlier orientation process, there was no difference between FP and FF relationships (
p >.05). Indeed,
Blohm et al. (2003) showed that the first orientation saccade did not take into account the smooth eye displacement. Therefore, at this time, the gain element β(t) is the same in the FP and FF condition (
t test,
p >.05). However, afterwards, the
p level that quantifies the difference of the regression parameter β(
t) between FP and FF conditions decreased. After 450 ms, the regression parameters β(
t) became significantly different (
p <.05) and even highly significantly different after 650-ms (
p<.001). Furthermore, in
Figure 7, the 95% confidence intervals of the regressions for FP and FF conditions separately also decrease, which indicates that individual regressions improve over time. Hence, although
Equation 3 is not a signature of the flash-lag effect, the resulting separation of both FP and FF populations in
Figure 7B shows the relevance of this analysis in characterizing the temporal evolution of the flash-lag effect.