A study of light and charged-particle optical systems with inversion, reflection, rotation, translation, and/or glide symmetries is presented. The constraints imposed by the various symmetries on the first-order properties of a lens are investigated. In particular, the mathematical structures of the deflection vectors and the transfer matrices are described for various symmetrical systems. In the course of studying the translation and the glide symmetries, a simple technique for characterizing a general system of N identical components in series (or cascade) is also developed, based on the linear algebra theory of factoring matrices into Jordan canonical forms. Applications of these results are presented in a follow-up paper [ J. Opt. Soc. Am. A12, 2760 ( 1995)].
© 1995 Optical Society of America
Original Manuscript: February 3, 1995
Manuscript Accepted: June 16, 1995
Published: December 1, 1995
M. Szilagyi and P. H. Mui, "Symmetries in geometrical optics: theory," J. Opt. Soc. Am. A 12, 2753-2759 (1995)