The relationship between absolute disparity and ocular vergence

The relationship between disparity and ocular vergence was investigated under closed-loop as well as under open-loop viewing conditions. First we examined whether vergence responded similarly to disparity presented under open-loop and closed-loop conditions. Similar response were observed in both conditions. The direct relationship between disparity and vergence was examined by presenting constant disparities between 0.2° and 4° under open-loop viewing conditions. Such vergence responses are described as the outputs of first-order low-pass filters with different filter characteristics for each amplitude of disparity. By analyzing the latency of vergence responses induced by constant disparities with help of the transfer function of disparitycontrolled vergence, the time delay of disparity processing in the vergence loop was estimated. We suggested that the time delay was approximately between 80 and 120 ms instead of 160 ms as is generally assumed. The relationship between the rate of disparity change and vergence was examined by comparing responses to ramp and stepwise changes in target vergence. From the similar responses to ramp and staircase changes in disparity we concluded that vergence is not sensitive to the velocity of target vergence as such. On the basis of these findings we developed a model of disparity-controlled vergence. In this model disparity is processed through several parallel, imperfect integrators with slightly different low-pass filter characteristics, each of them susceptible to a limited range of disparities. Gains as well as phase lags of vergence responses to sinusoidal disparities are accurately simulated by this model. As a consequence of the limited working range of the low-pass filters, the model correctly simulates the alterations of fast and slow phases in response to step and ramps of target vergence, which are characteristic of real vergence responses.