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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 12, Iss. 12 — Dec. 1, 1995
  • pp: 2753–2759

Symmetries in geometrical optics: theory

M. Szilagyi and P. H. Mui  »View Author Affiliations

JOSA A, Vol. 12, Issue 12, pp. 2753-2759 (1995)

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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. A 12, 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)

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  1. M. Szilagyi, Electron and Ion Optics (Plenum, New York, 1988). [CrossRef]
  2. S. Bhagavantam, T. Venkatarayudu, Theory of Groups and Its Application to Physical Problems (Academic, New York, 1969).
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  10. P. H. Mui, M. Szilagyi, “Synthesis of monopole-and-quadrupole focusing columns,” J. Vac. Sci. Technol. B 12, 3036–3045 (1994). [CrossRef]
  11. M. Szilagyi, P. H. Mui, “Synthesis of focusing-and-deflection columns,” J. Vac. Sci. Technol. B 13, 375–382 (1995). [CrossRef]
  12. Y. Li, “Application of group theory to electron optics,” Adv. Electron. Electron Phys. 85, 231–258 (1993). [CrossRef]
  13. D. C. Carey, The Optics of Charged Particle Beams (Harwood, New York, 1987).
  14. S. Humphries, Principles of Charged Particle Acceleration (Wiley, New York, 1986).
  15. M. Szilagyi, P. H. Mui, “Symmetries in geometrical optics: applications,” J. Opt. Soc. Am. 12, 2760–2766 (1995). [CrossRef]
  16. Results in this section are not generally valid for systems with magnetic components.
  17. Results for cases (1), (2), and (4) in this section are not generally valid for systems with magnetic components.
  18. P. W. Milonni, J. H. Eberly, Lasers (Wiley-Interscience, New York, 1988).
  19. C.-T. Chen, Linear System Theory and Design (Holt, Rinehart & Winston, New York, 1970).

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