Foundations of a Lie algebraic theory of geometrical optics

  • Alex J. Dragt
  • Etienne Forest
  • Kurt Bernardo Wolf
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 250)


We present the foundations of a new Lie algebraic method of characterizing optical systems and computing their aberrations. This method represents the action of each separate element of a compound optical system —including all departures from paraxial optics— by a certain operator. The operators can then be concatenated in the same order as the optical elements and, following well-defined rules, we obtain a resultant operator that characterizes the entire system. These include standard aligned optical systems with spherical or aspherical lenses, models of fibers with polynomial z-dependent index profile, and also sharp interfaces between such elements. They are given explicitly to third aberration order.

We generalize a previous result on the factorization of the optical phase-space transformation due to a refraction interface. We also present a group-theoretical classification for aberrations of any order of systems with axial symmetry, applying it to the problem of combining aberrations; new insights are thus provided on the origin and possible correction of these aberrations. We give a fairly complete catalog of the Lie operators corresponding to various simple optical systems. Finally, there is a brief discussion of the possible merits of constructing a computer code, RAYLIE, for the Lie algebraic treatment of geometric ray optics.


Poisson Bracket Geometrical Optic Aberration Coefficient Wigner Coefficient Simple Transit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Alex J. Dragt
  • Etienne Forest
  • Kurt Bernardo Wolf

There are no affiliations available

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