Flat disc, radially nonhomogeneous, lenses

A plane surfaced lens can be constructed through the use of radially nonhomogenous medium, with axial symmetry. The rays from an axial source are incident on the plane front surface, perpendicular to the axis, where the assumption is made that the rays obey Snell´s laws locally as for an infinite uniform medium. The curved ray paths are then given by the standard ray integral and are taken up to the point where each ray becomes horizontal. For certain polynomial functions describing the refractive index, the ray integral is an incomplete elliptic integral of the first kind, and trial functions can be inserted, such that the rays have become horizontal all at a second plance surface, thus creating a flat disc lens. The total sysmmetry of the design provides for many advantageous properties.