Dynamic modeling of Haidinger's brush phenomenon and analysis of the cornea effect based on the model

Abstract

Starting from the dynamic feature of the vision process and taking into account the time constants of the polarization-dependent process of cones, this study proposed a physical model that can mathematically describe the transient nature of Haidinger's brushes (HB). A saturated exponential growth function was proposed to describe the dynamic process, and the corresponding formulas were derived and discussed. The sensitivities of both static and rotating HB were considered in the model, and the visibility of HB was also investigated. Additionally, the impact of the cornea on the visions of HB was examined by using this model. Analytical results reveal that there exist two types of patterns in the rotating HB phenomenon. The visual perception of the rotating HB is related to the magnitude and interaction of these two patterns, as well as the corneal phase shift. The rotation orientation reversal at large corneal phase shifts observed by some researchers can also be explained by the model. The results are consistent with experimental observations and might help with the clinical diagnosis of macula disorders and corneal abnormalities.

Keywords: Birefringence; Cornea; Haidinger’s brushes (HB); Phase shift; Polarization; Time constant; Transition process.