Abstract
A dispersive model of a gradient refractive index (GRIN) lens is introduced based on the idea of iso-dispersive contours. These contours have constant Abbe number and their shape is related to iso-indicial contours of the monochromatic geometry-invariant GRIN lens (GIGL) model. The chromatic GIGL model predicts the dispersion throughout the GRIN structure by using the dispersion curves of the surface and the center of the lens. The analytical approach for paraxial ray tracing and the monochromatic aberration calculations used in the GIGL model is employed here to derive closed-form expressions for the axial and lateral color coefficients of the lens. Expressions for equivalent refractive index and the equivalent Abbe number of the homogeneous equivalent lens are also presented and new aspects of the chromatic aberration change due to aging are discussed. The key derivations and explanations of the GRIN lens optical properties are accompanied with numerical examples for the human and animal eye GRIN lenses.
Highlights
The experimental studies have shown a spatial change in chromatic dispersion of the gradient index (GRIN) eye lens
The paraxial ray-tracing will be the basis for calculating chromatic aberration of the GRIN structure, provided that the dispersion model for the surface and the center of the GRIN lens is given by experimental measurements
In the geometry-invariant GRIN lens model, the refractive index distribution is based on the power law profile, which was originally proposed by Pierscionek [4] and later supported by several studies [5,6,7,8,9]
Summary
The experimental studies have shown a spatial change in chromatic dispersion of the gradient index (GRIN) eye lens. The paraxial ray-tracing will be the basis for calculating chromatic aberration of the GRIN structure, provided that the dispersion model for the surface and the center of the GRIN lens is given by experimental measurements. In this paper we employ the geometry-invariant GRIN lens (GIGL) monochromatic model [3] and introduce wavelength dependence of the refractive index. This allows us to obtain a chromatic model matching experimental data on dispersion of the GRIN lens as well as to retain all properties of the GIGL mode including the analytical description for paraxial raytracing. Optical design sign convention, we introduce ‘−’ in front of Ta and Rp
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