Does the foveal shape influence the image formation in human eyes?

A fovea, the retinal pitted invagination in the area centralis, is found in many vertebrates such as fish, reptiles, birds and in higher primates including humans. Because of the refractive index step between the retinal tissue and vitreous, the fovea defines an optically effective interface with aspherical characteristics, which influences the ray propagation to the receptor layer buried about 250 μm within the retinal layers [1]. In principle, two basic foveal shapes can be distinguished [2]. On the one hand, the convexiclivate type of fovea is a deep, funnel-shaped depression with a convex slope of the side walls and is observed in birds, some lizards, and certain deep-sea teleosts. On the other hand, the concaviclivate type of fovea is shallow and gradually shaped; the human fovea is of this type. Previous examinations on the influence of the fovea on the image-forming process have mainly been focused on the steep foveae types in which increasing magnification and directional-dependent distortion effects were predicted [3], [4], [5], [6], [7]. These investigations have been restricted to simple geometrical descriptions of the foveal shape, such as spheres and paraboloids. Real geometrical foveal structures from living creatures have not yet been examined. Moreover, the ray-trace considerations have been partly reduced to a few selected rays approaching the vitreo-retinal interface, and very limited numbers of incidence directions and wavelength-dependent effects have been investigated. Studies on the refracting characteristics of human foveae types are even more rare [2], [8]. C. Ross analyzed the optical functionality of the foveae of tarsiers, neglecting the influence of the anterior part of the eye and regarding only position shifts of three single rays. This contribution aims to answer the question on whether a comprehensive human eye model, which takes all optical components and their aberrations into account, leads to more detailed findings. In particular, field- and wavelength-dependent influences on spot sizes and positions, based on actual ray-bundle-cones are considered, which allow the estimation of aberration effects. With the current investigation, we address this issue by combining a realistic anatomical model of the anterior parts of the eye with real human fovea geometries. For the anterior eye, the human eye model of Liou and Brennan [9], with a gradient index profile of the crystalline lens, was used. To investigate the influence of actual fovea geometries on image formation, two selected and different foveal shapes (average and extraordinary), based on in vivo optical coherence tomography (OCT) measurements of a human eye were used. We analyzed the ray-optical behavior and implemented additional considerations that involve the variation of the observed field position, pupil diameter, chromatic effects, and especially the imaging behavior of peripheral colors in the receptor plane when the primary color is focused on this theoretical surface. These simulations validate and expand the knowledge about the correlation between aperture size and real and theoretical spot size, the effect of the foveal shape on either spot size and axial spot position, and, finally, the lateral spot position and color dependency of the incident angle.