Helmholtzian Strategy To Stay In Focus With Binocular Vision

We study problems that can be applied to controlling the rotational motion of a pair of human eyes. Eyes move to acquire a point target and the control task is to direct the eye-pair towards the general target direction and, if the target is close by, to focus on the target. Roughly speaking, the former task is accomplished by versional eye movements and the latter task of pinpointing the eyes on a specific point is accomplished by vergence eye movements. We assume that the versional movement rotates the eye-pair identically whereas the vergence movements are specific to each eye with the goal of focusing. Although it is commonly believed and evidenced by collected data that 'versional eye movements satisfy Listing's Law', we show in this paper that Listing's eye movements do not maintain focus. Perhaps surprisingly, we show that if the eye controller maintains a Donders' surface originally proposed by Helmholtz, eye movements away from points on the Transverse Plane maintains focus. For points above or below the Transverse Plane, we show by simulation that rotations satisfying the Helmholtz condition maintain focus as well. Recorded data from human eye movement satisfying Listing's law supports the observation presented here.