Healthy human eyes misaligned optical components: Binocular Listings law

The healthy human eyes optical components are misaligned. Although important in studying vision quality, it has been overlooked in research on binocular and oculomotor vision. This study presents the construction of ocular torsion in the binocular system that incorporates the fovea displaced from the posterior pole and the lens tilted away from the eyes optical axis. When the eyes binocular posture changes, each eyes torsional position transformations, computed in the framework of Rodrigues vector, are visualized in GeoGebra simulations. Listings law, important in oculomotor control by constraining a single eye redundant torsional degree of freedom, is ab initio formulated for bifoveal fixations in the binocular system with misaligned optical components for the fixed upright head. It leads to the configuration space of binocularly constrained eyes fixations, including the noncommutativity rule. This formulation modifies the Listing plane of the straight-ahead eyes primary position by replacing it with the binocular eyes posture corresponding to the empirical horopters abathic distance fixation, a unique bifoveal fixation for which the longitudinal horopter is a straight frontal line. Notably, it corresponds 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 orientation and, hence, torsional positions during simulations with GeoGebras dynamic geometry. The binocular Listings law developed here can support this coupling, which is important in oculomotor control. The results obtained in this study should be a part of the answers to the questions posted in the literature on the relevance of Listings law to clinical practices. Author summaryOur eye optical components are misaligned: the fovea is displaced from the eyes posterior pole, and the lens is tilted away from the optical axis. Listings law, important in oculomotor control, has not only overlooked the misaligned eyes optics but was also formulated for a single eye, with a later ad hoc extension added for binocular vision. The purpose of Listings law is to constrain the eyes redundant torsional degrees of freedom, thereby supporting neural processing in the development of our spatial understanding by controlling the noncommutativity of the eyes rotations. This goal cannot be fully met because Listings law is monocular, but we acquire an understanding of the scene through bifoveal fixations on objects. In this work, I construct ocular torsion that accounts for the eyes misaligned optics and incorporate it into Listings law. It directly leads to its first ab initio consistent binocular formulation, which is visualized in a computer simulation. Supported by ophthalmological studies, it revises the still elusive neurophysiological significance of the Listing plane, the basic ingredient of Listings law. It also resolves the persistent lack of a generally accepted explanation for Listings law. The results of this study are likely to be important in the ongoing discussion in the literature regarding the relevance of Listings law to clinical practices.