Sigma smooth pursuit eye tracking: constant k values revisited

Abstract

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.