Detection of apparent motion in random dot patterns requires correlation across time and space. It has been difficult to study the temporal requirements for the correlation step because motion detection also depends on temporal filtering preceding correlation and on integration at the next levels. To specifically study tuning for temporal interval in the correlation step, we performed an experiment in which prefiltering and postintegration were held constant and in which we used a motion stimulus containing coherent motion for a single interval value only. The stimulus consisted of a sparse random dot pattern in which each dot was presented in two frames only, separated by a specified interval. On each frame, half of the dots were refreshed and the other half was a displaced reincarnation of the pattern generated one or several frames earlier. Motion energy statistics in such a stimulus do not vary from frame to frame, and the directional bias in spatiotemporal correlations is similar for different interval settings. We measured coherence thresholds for left–right direction discrimination by varying motion coherence levels in a Quest staircase procedure, as a function of both step size and interval. Results show that highest sensitivity was found for an interval of 17–42 ms, irrespective of viewing distance. The falloff at longer intervals was much sharper than previously described. Tuning for temporal interval was largely, but not completely, independent of step size. The optimal temporal interval slightly decreased with increasing step size. Similarly, the optimal step size decreased with increasing temporal interval.

^{2}) displayed in a window of 400 × 400 pixels. The standard number of dots was 5,000, yielding a dot density of 80 dots/deg

^{2}. In two control experiments, we tested the effect of different dot densities and different viewing distances on the step size and interval tuning for an optimal interval and step size, respectively.

*X*-axis. The

*Y*-axis represents time, with each line of dots corresponding to a monitor frame. The left-hand column shows examples of dynamic noise and 100% coherent motion, for different combinations of step size and interval. A coherence value of 100% in these stimuli corresponds to coherent displacement of all relocated dots in combination with randomly refreshing the other half of the dots. All combinations (1/1, 2/2, 4/4, and 8/8 pixels/frames) represent the same mean velocity. Coherent motion shows up as an oriented pattern in such space–time plots, with the orientation representing the velocity. In comparison, apparent motion with unlimited dot lifetime would give a noiseless, oriented pattern, with correlations across all time steps in the display. In contrast, a horizontal line in Figure 1 correlates only with a line preceding or following it by the specified interval. There is no correlation bias across smaller or larger intervals. What is important is that the directional correlation bias in the stimulus is the same on every frame of the monitor and does not vary with the specified temporal interval for displacements. As noted previously by Morgan and Ward (1980), apparent motion generated in this way looks surprisingly continuous, irrespective of the specified temporal interval. Observers have the impression of a rigidly moving pattern within dynamic noise rather than a dynamically and discretely changing pattern.

*T*) to a sensitivity measure, in which sensitivity (

*S*) was defined on a logarithmic axis:

*f*(

*s*) describes tuning as function of step size (

*s*) and

*g*(

*t*) describes tuning as function of interval (

*t*).

*μ*

_{S}and

*μ*

_{T}are the optimal values, and

*σ*

_{S}and

*σ*

_{T}represent tuning width.

*R*

^{2}value, which quantifies the fraction of the total squared error that is explained by the model. All procedures were implemented in MATLAB, using custom and standard Matlab functions.

*R*

^{2}values were .931, .822, .925, .881, and .841 for subjects R.B., S.S., M.L., M.S., and E.S., respectively). Oval-shaped tuning as for R.B. and asymmetric spatial tuning as for observer M.S. are reproduced accurately. Independent step size and temporal interval tuning, however, fail to capture any oblique effects, such as observed for S.S. The fourth column in Figure 3 quantifies the differences between experimental data and separable tuning. Differences are given as log values. The maximum difference of about 0.6 log unit for observer S.S. corresponds to a factor of 4.0 in sensitivity. Although deviations from independence are relatively small, the data do show a general trend. Sensitivities for combinations of large temporal intervals (16–90 ms) and small step sizes, as well as small temporal intervals and larger step sizes (6–30 arcmin), were underestimated. Combinations of large intervals and large steps, as well as small intervals and small steps, were overestimated. To assess the nature and significance of spatiotemporal interactions, we extended the model to include spatiotemporal interactions. We used an

*F*test to compare the fits of the two models ( http://www.graphpad.com/curvefit). It provides a quantitative estimate of the significance of the increase in

*R*

^{2}value, given the change in degrees of freedom due to additional parameters. The test calculates the chance (

*p*value) that the data set fits the more complicated model better, if the simpler model is, in fact, correct.

*p*values are based on the

*F*ratio, given by

*df*denotes the degrees of freedom, and the subscripts identify the simpler model (subscript 1) or the more complicated model (subscript 2).

*p*values below .05 were taken to indicate significant improvements of the model fits.

*μ*

_{ S}) with temporal interval, as well as a shift of the temporal optimum (

*μ*

_{ T}) with step size. We compared first-order (linear), second-order (quadratic), and third-order (cubic) shifts of spatial and temporal optima. For all observers, except M.L., increasing the order resulted in significantly better fits.

*R*

^{2}values increased from an average value of .880 for no interactions to .922, .941, and .957 for linear, quadratic, and cubic interactions, respectively. Results for fits with a third-order shift of optimal interval as well as optimal step size are shown in Figure 3 (third column). The last column in Figure 3 quantifies the fit errors for the interaction model. In general, temporal optima decreased with increasing step sizes, although the decrement was less for larger step sizes. For observer M.S., the temporal optimum was constant, irrespective of step size. Spatial optima tended to decrease with increasing temporal interval, except for M.L., who showed little interactions.

*μ*parameter, did provide significant improvements, but these improvements were smaller than for the shift in

*μ*

_{ S}and

*μ*

_{ T}.

^{2}per frame, at a monitor refresh rate of 120 Hz, in an 8° × 8° window. Morgan and Ward used a relatively low dot density (13,000 points per 728 ms, in a 2.25° × 2.25° window). A single point subtended 2.4 arcmin and was present for less than 56 μs. Fredericksen et al., on the other hand, used much higher dot densities. Variations in dot density might, therefore, play a role in comparing our data to those of others. To gain insight into the effects of dot density in our stimulus, we performed several control experiments at different dot densities. Figure 4A shows measurements of temporal tuning curves for densities ranging from 5 to 160 dots/deg

^{2}. Figure 4B shows similar measurements for spatial tuning curves. Temporal tuning was measured at the optimal step size of 7.2 arcmin, and spatial tuning was measured at the optimal temporal interval of 33 ms. Measurements for 80, 40, and 20 dots/deg

^{2}did not differ substantially. A dot density of 80 dots/deg

^{2}thus seemed sufficient to reach optimal sensitivity. An increase to 160 dots/deg

^{2}dots resulted in a sharper falloff for intervals above 16.7 ms. Yet, for intervals of 16.7 ms and lower, thresholds were similar to the condition with 80 dots/deg

^{2}. A reduction to 10 and 5 dots/deg

^{2}had little effect for intervals beyond 42 ms. Threshold for intervals smaller than 42 ms were higher when compared with the condition of 80 dots/deg

^{2}. Nonetheless, the optimal interval was not affected. Figure 4B shows that step size tuning for 80 and 40 dots/deg

^{2}was similar. For higher and lower dot densities, thresholds were raised and optimal step sizes shifted toward lower values. In summary, we conclude that dot density may affect both spatial and temporal tuning. However, the value of 80 dots/deg

^{2}did not seem to limit performance in our experiments.

^{2}), which was practically comparable to the mean luminance in the study by Fredericksen et al. (50 cd/m

^{2}). If anything, we might have expected slightly longer optimal intervals and step sizes. The discrepancy cannot be explained by differences in dot density or viewing distance either. Our control experiments showed that the shape of the temporal tuning curves for coherence detection did not vary drastically with viewing distance. Similar to previous reports in which

*D*

_{max}measurements were found to depend on various stimulus parameters, including dot density, varying the dot density in our experiments did affect both spatial and temporal tuning. However, increasing the dot density reduced rather than increased the high temporal falloff. We conclude, therefore, that low thresholds for long intervals in the study of Fredericksen et al. are a result of the presence of multiple correlations in their stimuli with long intervals. Because patterns remained stationary between displacements in their stimuli, at large temporal intervals, correlations were also present at shorter intervals. This might very well explain why observers remained highly sensitive to long intervals in their stimulus, whereas in our stimuli, sensitivity for long time intervals sharply declined.