Wyatt 13 measured the average (across subject) ellipse parameters for the entrance pupil under dim and bright light conditions (with the visual axis of the eye aligned with camera axis). The stop is, however, modeled as slightly non-circular. Instead, the aperture stop is modeled as centered and fixed on the optical axis. The current model does not attempt to incorporate these measurements into the properties of the aperture stop. There is evidence that the entrance pupil is decentered nasally with respect to the optical axis, and that the center shifts temporally with dilation (reviewed in 12). The inner rim of the iris is the source of the image of the border of the entrance pupil. The iris is modeled as a plane perpendicular to the optical axis (i.e., zero “iris angle”), positioned 3.9 mm posterior to the anterior surface of the cornea, at the location of the anterior surface of the lens for the cycloplegic eye 11. The center of the back cornea ellipsoid is positioned so that there is 0.55 mm of corneal thickness between the front and back surface of the cornea at the apex, following Atchison 10. I simulate the circumstances of the Mathur and colleagues study 6 and show that their measurements can be replicated with good accuracy if the model incorporates ( i) corneal refraction, ( ii) the separation of the visual and optical axes, and ( iii) the non-circularity and tilt of the aperture stop. The open-source MATLAB code ( ) implements an invertible ray tracing solution that can incorporate artificial lenses (e.g., spectacles, contacts) in the optical path between eye and observer. The location of the fovea is specified and used to derive the visual axis and line-of-sight of the eye. The model accounts for individual variation in biometric parameters, including spherical refractive error. Here I present a ray traced model eye that provides the ellipse parameters of the entrance pupil as seen by an observer at an arbitrary location. As will be developed, the fit of this previous model to empirical data is imperfect. Fedtke and colleagues 7, using optical software, obtained a function with similar form by ray trace simulation of a rotationally symmetric cornea 8. The ratio of the minor to major axis length of the pupil ellipse (essentially the horizontal-to-vertical aspect ratio) was well-fit by a decentered and flattened cosine function of viewing angle. Mathur and colleagues 6 measured the shape of the entrance pupil as a function of the nasal and temporal visual field positions of a camera moved about a stationary eye. As an observer views the eye from an increasingly oblique angle, the pupil takes on an ever-more ellipitical appearance. The appearance of the entrance pupil as a function of horizontal viewing angle has been the subject of empirical measurement over some decades 4, 5. Characterization of the entrance pupil is relevant for modeling the off-axis image-forming properties of the eye 1, optimizing corneal surgery 2, and performing model-based eye-tracking 3. The precise appearance of the entrance pupil depends upon the anatomical and optical properties of the eye, as well as the relative positions of the eye and the observer. The image of the stop is the entrance pupil of the eye. When viewed from the outside, the aperture stop of the iris is seen through corneal refraction.
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