On the linearity of accommodation dynamics

Available experimental data on the gain and phase lags in the closed-loop accommodation responses to stimuli whose dioptric vergence changes sinusoidally with time are examined. It is shown that both phase lags and gain change almost linearly with the temporal frequency of the stimulus. This implies that the phase lags correspond to a frequency-independent time delay and that, if the system is linear, the impulse response should take a symmetrical (sin x/x)(2) form, with a corresponding standard form of step response. Comparison of this derived step response with the quasi-exponential results found experimentally underlines the limitations of attempting to generalize dynamic accommodation performance from responses obtained with predictable sinusoidally-changing stimuli and the application of a linear model. Consideration of the frequency response which would lead to an exponential step response supports the argument that, although the gain results obtained with sinusoidal stimuli are reasonably representative of those applying with other forms of stimulus, the predictable nature of sinusoidally-changing stimuli makes the derived phase lags inapplicable to non-predictable step or other stimuli. Other limitations in linear models of the response are discussed.