Ab initio Binocular Formulation of Listing's Law

Abstract Human eyes do not have perfectly aligned optical components; the fovea is displaced from the posterior pole, and the crystalline lens is tilted away from the optical axis. Although important in the study of vision quality, it is used here in binocular and oculomotor vision research. In the binocular system with the eye’s misaligned optics, changes in visual axis direction (torsion-free) and torsional position are computed in the framework of Rodrigues’ vector and visualized in GeoGebra simulations. It leads to the first consistently formulated binocular Listing’s law, important in oculomotor control by constraining the eye's redundant torsional degree of freedom. It resolves some shortcomings associated with the original Listing’s law. The binocular formulation modifies the Listing plane, indispensable ingredient of Listing’s law, by replacing it with the binocular eyes’ posture corresponding to the eye muscles’ natural tonus resting position, which serves as a zero-reference level for convergence effort. Supported by ophthalmology studies, it revises the elusive neurophysiological significance of the Listing plane. Furthermore, the binocular constraints couple 3D changes in the eyes’ torsional positions in the binocular extension of Listing’s law, which is important in oculomotor control and previously unavailable. Lastly, the first formulation of a simple noncommutativity rule underlying Listing’s law is derived by specifying the configuration space of binocularly constrained eyes’ fixations, which is visualized in GeoGebra simulations. The results obtained in this study should be a part of the answers to the questions posted in the literature on the relevance of Listing’s law to clinical practices.