Using bilinear transformations to estimate the ratios of accommodation and vergence responses of binocular vision

Abnormal binocular vision occurs in a broad range of disorders including strabismus, amblyopia, heterophorias, large fixation disparities, and anomalous refractive conditions. The examination and treatment of these problems are the major tasks in optometry clinics. However, the concepts and parameters used in clinic are not closely related to the parameters in the interactive model of the accommodative and vergence systems. In this paper we study the ratio accommodative response and vergence response of the system. We show that the ratio of accommodative and vergence responses is a classical Mobius transformation (bilinear transformation). We then determine the derivatives, composite structures, and fixed points of ratios. The results of this study will greatly improve our insight in the oculomotor system and its mechanisms related with different types of abnormal binocular vision.