The first and second order dynamics of accommodative convergence and disparity convergence

Main sequences, the function describing the relationship between eye movement amplitude and velocity, have been used extensively in oculomotor research as an indicator of first-order dynamics yet it is difficult to find main sequence analyses for accommodative vergence or for disparity vergence in isolation when all mitigating factors have been well controlled and there are no studies in which accommodative vergence and disparity vergence main sequences have been generated for the same group of subjects. The present study measured main sequences in: (1) accommodative vergence with disparity vergence open loop, (2) disparity vergence with accommodation open loop, and (3) combinations of accommodative and disparity vergence. A dynamic AC/A ratio was defined and was found to be similar to the traditional static AC/A ratio. Vergence acceleration was measured for all conditions. A pulse-step model of accommodation and convergence was constructed to interpret the dynamics of the crosslinked interactions between the two systems. The model supports cross-coupling of both the pulse and step components and simulates the primary empirical findings that: (1) disparity vergence has a higher main sequence slope than accommodative vergence, (2) both accommodative and disparity vergence acceleration increase with response amplitude whereas accommodation acceleration does not.