Geometry-invariant GRIN lens: iso-dispersive contours

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.