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

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