We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.

A new class of gradient refractive index (GRIN) lens is introduced and analyzed. The interior iso-indicial contours mimic the external shape of the lens, which leads to an invariant geometry of the GRIN structure. The lens model employs a conventional surface representation using a coincoid of revolution with a higher-order aspheric term. This model has a unique feature, namely, it allows analytical paraxial ray tracing. The height and the angle of an arbitrary incident ray can be found inside the lens in a closed-form expression, which is used to calculate the main optical characteristics of the lens, including the optical power and third-order monochromatic aberration coefficients. Moreover, due to strong coupling of the external surface shape to the GRIN structure, the proposed GRIN lens is well suited for studying accommodation mechanism in the eye. To show the power of the model, several examples are given emphasizing the usefulness of the analytical solution. The presented geometry-invariant GRIN lens can be used for modeling and reconstructing the crystalline lens of the human eye and other types of eyes featuring a GRIN lens.

The atmosphere introduces chromatic errors that may limit the performance of adaptive optics (AO) systems on large telescopes. Various aspects of this problem have been considered in the literature over the past two decades. It is necessary to revisit this problem in order to examine the effect on currently planned systems, including very high-order AO on current 8-10 m class telescopes and on future 30-42 m extremely large telescopes. We review the literature on chromatic effects and combine an analysis of all effects in one place. We examine implications for AO and point out some effects that should be taken into account in the design of future systems. In particular we show that attention should be paid to chromatic pupil shifts, which may arise in components such as atmospheric dispersion compensators.

We present a practical method for reconstructing the optical system of the human eye from off-axis wavefront measurements. A retinal beacon formed at different locations on the retina allows probing the optical structure of the eye by the outgoing beams that exit the eye through the dilated pupil. A Shack-Hartmann aberrometer measures the amount of wave aberrations in each beam at the exit pupil plane. Wavefront data obtained at different oblique directions is used for tomographic reconstruction by optimizing a generic eye model with reverse ray-tracing. The multi-configuration system is constructed by tracing pre-aberrated beams backwards from each direction through the exit pupil into the optical system of the aberrometer followed by the generic eye model. Matching all wave aberrations measured at each field point is equivalent to minimizing the size of the beacon spots on the retina. The main benefit of having a personalized eye model is the ability to identify the origin of the ocular aberrations and to find the optimal way for their correction.