5The aperture stop of the iris is subject to refraction by the cornea, and thus an outside observer sees a virtual image: the "entrance pupil" of the eye. When viewed off-axis, the entrance pupil has an elliptical form. The precise appearance of the entrance pupil is a consequence of the anatomical and optical properties of the eye, and the relative positions of the eye and the observer. This paper presents a ray-traced model eye that provides the parameters of the entrance pupil ellipse for an observer at an arbitrary location. The model is able to reproduce empirical measurements of the shape of the entrance pupil with good accuracy. I demonstrate that accurate specification of the entrance pupil of a stationary eye requires modeling of corneal refraction, the misalignment of the line-of-sight and optical axis, and the non-circularity of the aperture stop. The model, including a three-dimensional ray-tracing function through quadric surfaces, is implemented in open-source MATLAB code. 6 Introduction 7When viewed from the outside, the aperture stop of the iris is seen through corneal refraction. The image of the stop is the 8 entrance pupil of the eye. The precise appearance of the entrance pupil depends upon the anatomical and optical properties 9 of the eye, as well as the relative positions of the eye and the observer. Characterization of the entrance pupil is relevant for 10 modeling the off-axis image-forming properties of the eye (1), optimizing corneal surgery (2), and performing model-based 11 eye-tracking (3).
12The appearance of the entrance pupil as a function of horizontal viewing angle has been the subject of empirical measurement 13 over some decades (4; 5). As an observer views the eye from an increasingly oblique angle, the pupil takes on an ever-more 14 ellipitical appearance. Mathur and colleagues (6) measured the shape of the entrance pupil as a function of the nasal and 15 temporal visual field positions of a camera moved about a stationary eye. The ratio of the minor to major axis length of the 16 pupil ellipse (essentially the horizontal-to-vertical aspect ratio) was well-fit by a decentered and flattened cosine function of 17 viewing angle. Fedtke and colleagues (7), using optical software, obtained a function with similar form by ray trace simulation 18 of a rotationally symmetric cornea (8). As will be developed, the fit of this previous model to empirical data is imperfect.
19Here I present a ray-traced model eye that provides the ellipse parameters of the entrance pupil as seen by an observer 20 at an arbitrary location. The model accounts for individual variation in biometric parameters, including spherical refractive 21 error. The location of the fovea is specified and used to derive the line-of-sight of the eye. The open-source MATLAB 22 code (https://github.com/gkaguirrelab/gkaModelEye) implements an invertible ray-tracing solution that can 23 incorporate artificial lenses (e.g., spectacles, contacts) in the optical path between eye and observer. I simulate the circumstances 24 of ...