Small-signal analysis of a visual reflex in the locust

Small-signal frequency-response measurements of a locust visual reflex in the range 0.0014 cps to 6 cps suggest description via special departures from ordinary linear-system characterization, at both low and high frequencies.At low frequency the response is similar to that of an adapting system having the formal characteristics of fractional-order differentiation. Adjustment of test-pattern luminance from 0.00025 to 1 lambert increases the order of this differentiation by about 0.37. Comparison of intensity-dependent properties of the reflex with related electrophysiological studies of photoreception implies that the frequency dependence of the optomotor response is dominated by receptor dynamics.At high frequency, phase lag is less than that required by minimum-phase linear description of the gain curves. In order to avoid the question of “predictive tracking” by the locust, a time-and frequency-dependent gain modulation is suggested to account for the less-than-minimum phase property, and shown to be qualitatively compatible with transients in gain at the start of sinusoidal pattern motion.The motion-perception model of Hassenstein and Reichardt, shown previously to predict the gross gain and phase relations of the small-signal locust response, is apparently an inappropriate description of these data since the decisive gain and phase measurements are more plausibly accounted for by intensity-dependent adaptation than by the properties of the model underlying the original prediction. An abstraction of the fundamental properties of their multiplicative interaction of ommatidia, however, can assist electrophysiological search for neural correlates of motion perception; it is shown that, under certain conditions, interaction of receptor channels via lateral shunting inhibition is (a) indistinguishable from the multiplicative motion-perception topology, and (b) formally related to a nonlinear property of inhibition in the eye of Limulus.