BINOCULAR EYE ORIENTATION DURING FIXATIONS - LISTINGS LAW EXTENDED TOINCLUDE EYE VERGENCE

Any eye position can be reached from a position called the primary pos ition by rotation about a single axis. Listing's law states that for t argets at optical infinity all rotation axes form a plane; the so-call ed Listing plane. Listing's law is not valid for fixation of nearby ta rgets. To document these deviations of Listing's law we studied binocu lar eye positions during fixations of point targets in the dark. We te sted both symmetric (targets in a sagittal plane) and asymmetric verge nce conditions. For upward fixation both eyes showed intorsion relativ e to the position that would have been taken if each eye followed List ing's law. For downward fixation we found extorsion. The in- or extors ion increased approximately linearly with the vergence angle. The dire ction of the Listing axis and the turn angle about this axis can be de scribed by rotation vectors. Our observations indicate that for fixati on of nearby targets the rotation vectors of the two eyes become diffe rent and are no longer located in a single plane. However, we find tha t it is possible to decompose the rotation vector of each eye into the sum of a symmetric and an anti-symmetric part, each with its own prop erties. (1) The symmetric part is associated with eye version. This co mponent of the rotation vector is identical for both eyes and lies in Listing's plane. In contrast to the classical form of Listing's law, t his part of the rotation vector lies in Listing's plane irrespective o f the fixation distance. (2) The anti-symmetric part of the rotation v ector is related to eye vergence. This component is of equal magnitude but oppositely directed in each eye. The anti-symmetric part lies in the mid-sagittal plane, also irrespective of fixation distance. For fi xation of targets at optical infinity the anti-symmetric part equals z ero and the eye positions obey the classical form of Listing's law. Th us, the symmetric and anti-symmetric parts of the rotation vectors are restricted to two perpendicular planes. Combining these restrictions in a model, with the additional restriction that the vertical vergence equals zero during fixation of point targets, we arrive at the predic tion that the cyclovergence is proportional to the product of elevatio n and horizontal vergence angles. This was well born out by the data. The model allows to describe the binocular eye position for fixation o f any target position in terms of the bipolar coordinates of the targe t only (i.e. using only three degrees of freedom instead of the six ne eded for two eyes).