Optic systems with spherical, cylindrical, and toric surfaces

A simple analytical method for tracing rays in an optical system that is made up of spherical, cylindrical, and toric surfaces with an arbitrary rotation of its meridian plane with respect to the reference system is described. An analytical procedure is also given for obtaining the spot diagram on an arbitrarily oriented section, as well as for relating the diagram obtained for the plane of this section as a plane z = 0. Finally, as an application of this procedure, several graphic representations of the spot diagrams in the planes perpendicular or nonperpendicular to the axis are presented.