Abstract
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.
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Dragt, A.J., Forest, E., Wolf, K.B. (1986). Foundations of a Lie algebraic theory of geometrical optics. In: Sánchez Mondragón, J., Wolf, K.B. (eds) Lie Methods in Optics. Lecture Notes in Physics, vol 250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16471-5_4
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DOI: https://doi.org/10.1007/3-540-16471-5_4
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