Ab Initio Binocular Formulation of Listing’s Law

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 eye's optical axis. Important in the study of vision quality, it is included here in binocular and oculomotor research. In the binocular system, with the eye's optical asymmetry, all axes differ. The eye's posture change is decomposed into the torsion-free part that gives the change in visual axis direction and the torsional part that best approximates the rotation about the lens's optical axis. This geometric formulation, supported by computer simulations and modern ophthalmology studies, leads to binocular Listing's law and the related half-angle rule, important for oculomotor control by constraining the eye's redundant torsional degree of freedom. The eye's primary position and the Listing plane, indispensable ingredients of Listing's law, are replaced with the binocular eyes' posture corresponding to the eye muscles' natural tonus resting position, which serves as a zero-reference level for convergence effort. Further, the binocular constraints couple 3D changes in the torsional positions of the eyes within the ab initio formulation of Listing's law here, which was previously proposed ad hoc. Finally, the noncommutativity rule underlying Listing's law and the half-angle rule are discussed by specifying the configuration space of sequences of fixations of binocularly constrained eyes, which are visualized in 3D 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.