Binocular Listing’s Law For Human Eyes' Misaligned Optical Components

Human eyes' optical components are misaligned. This study presents the geometric construction of ocular torsion in the binocular system, in which the eye model incorporates the fovea that is not located on and the lens that is tilted away from the eye's optical axis. The ocular torsion computation involves Euler's rotation theorem in the framework of Rodrigue's vector. When the eyes' binocular posture changes, each eye's torsional orientation transformations are visualized in GeoGebra's dynamic geometry environment. Listing's law, which originally restricts single-eye torsional positions and has imprecise binocular extensions, is formulated ab initio for binocular fixations using Euler's rotation theorem. It replaces Listing's plane and related perpendicular primary direction with the empirical horopter's abathic distance fixation, which has a straight frontal line configuration at this fixation. Notably, it corresponds to the eye muscles' natural tonus resting position, which serves as a zero-reference level for convergence effort, providing the missing neurophysiological significance of Listing's plane. Thus, Listing's law use in clinical diagnosis and management of strabismus should be updated.