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 eyes optical axis. The ocular torsion computation involves Eulers rotation theorem in the framework of Rodrigues vector. When the eyes binocular posture changes, each eyes torsional orientation transformations are visualized in GeoGebras dynamic geometry environment. Listings law, which originally restricts single-eye torsional positions and has imprecise binocular extensions, is formulated ab initio for binocular fixations using Eulers rotation theorem. It replaces Listings plane and related perpendicular primary direction with the empirical horopters 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 Listings plane. Thus, Listings law use in clinical diagnosis and management of strabismus should be updated.