Healthy human eyes’ misaligned optical components: Binocular Listing’s law
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The healthy human eye’s 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 eye’s optical axis. When the eyes’ binocular posture changes, each eye’s torsional position transformations, computed in the framework of Rodrigues’ vector, are visualized in GeoGebra simulations. Listing’s 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’ rotations, including the noncommutativity rule. This formulation modifies the Listing plane of the straight-ahead eye’s primary position by replacing it with the binocular eyes’ posture corresponding to the empirical horopter’s 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 GeoGebra’s dynamic geometry. The binocular Listing’s 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 Listing’s law to clinical practices.
Author summary
Our eye optical components are misaligned: the fovea is displaced from the eye’s posterior pole, and the lens is tilted away from the optical axis. Listing’s law, important in oculomotor control, has not only overlooked the misaligned eye’s optics but was also formulated for a single eye, with a later ad hoc extension added for binocular vision. The purpose of Listing’s law is to constrain the eye’s redundant torsional degrees of freedom, thereby supporting neural processing in the development of our spatial understanding by controlling the noncommutativity of the eye’s rotations. This goal cannot be fully met because Listing’s 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 eye’s misaligned optics and incorporate it into Listing’s 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 Listing’s law. It also resolves the persistent lack of a generally accepted explanation for Listing’s law. The results of this study are likely to be important in the ongoing discussion in the literature regarding the relevance of Listing’s law to clinical practices.
