Abstract

We are considering an extension of ray matrices to cover situations of reduced symmetry. Examples of the cases considered include paraxial rays with rotated cylindrical and toroidal lenses and rays that make a small angle with any general skew ray. Here 4×4 matrices are necessarily required. In addition to the usual translation and refraction matrices we also need a rotation matrix to provide a proper system description. Even when point sources are initially used the images are often astigmatic images. In this paper the basic matrices are reviewed and single surface imaging equations for astigmatic line derivations outlined. These equations are compared to the wave trace equations for describing optical fields propagating through an optical system.

© 1991 Optical Society of America