Sigma smooth pursuit eye tracking: constant k values revisited.

Effective sigma tracking, i.e., apparent movement perception when slow eye movements are made across a stationary repetitive pattern under stroboscopic illumination, has been shown to be a function of the distance between sequential stimuli (P(s)) and the flash frequency (f(s)). The relationship between these factors and eye velocity ( V (e)) has been formally specified as V (e)= k P(s)f(s)[deg s(-1)], where it has been argued that the value of k, which defines the rate limit for eye velocity, is normally 1, or exceptionally 2 or 3. However, theoretically the limitations on the maximum value for k are the maximum optimal pursuit speed for eye tracking (V(max)) and the minimum values which P(s) and f(s) can assume while preserving target discrimination, and since the values for V(max) are known to lie well beyond 20 deg/s and those for P(s) and f s) well below 0.3 deg and 10 Hz respectively, it should be possible to demonstrate empirically that k can assume integer values considerably larger than the indicated maximum of 3. To test this prediction, three subjects performed seven series of five EOG-monitored trials producing sigma-pursuit, with values of k ranging from 1 to 7. All subjects evidenced smooth pursuit eye tracking for every condition and reported experiencing sigma-type apparent motion in 95% of the trials. The results confirm theoretical expectations and unequivocally demonstrate that sigma tracking can be readily effected under conditions where k significantly exceeds the maximal values previously reported, in conformity with theory.