A system matrix for astigmatic optical systems: I. Introduction and dioptric power relations

A single 4 X 4 system matrix is used to represent the para-axial properties of optical systems consisting of separated obliquely crossed spherocylindrical lenses. The 4 X 4 system matrix is a generalization and combination of the 2 X 2 Gaussian system matrix for spherical optical systems, and the 2 X 2 dioptric power matrix for a single spherocylindrical lens or for obliquely crossed spherocylindrical lenses in contact with each other. The 4 X 4 system matrix approach simplifies both the conceptual and numerical analysis of complicated astigmatic systems.