ABSTRACT
The symmetrical optical system, that is a system with symmetry about an axis of revolution, is the type of system most frequently met as a design problem; this includes systems folded by means of plane mirrors or prisms, since it is trivial to unfold them for optical design purposes. However, non-symmetrical systems are not uncommon, example, some kinds of spectacle lens, spectrographic systems, anamorphic projection systems and systems containing holographic optical elements. The treatment is based mainly on the geometrical optics model but there will be occasional references to physical optics in the form of scalar wave theory; this is needed for dealing with aberration tolerances. The more detailed theory of involutions and collineations is not important in geometrical optics, but they are mentioned to establish the point that the most general one-to-one correspondences take this form; on the other hand, it is seen that in real optical image formation the relationship between object and image entities is more complex.
