Multi-focal spherical media and geodesic lenses in geometrical optics

This paper presents a general approach to designing the isotropic spherical media with complex spatial structure that provide different types of imaging for different light rays. It is based on equivalence of the spherical medium and the corresponding geodesic lens. We use this approach to design multi-focal gradient- index lenses embedded into an optically homogeneous region and multi-focal absolute instruments that provide perfect imaging of three-dimensional domains.