Derivation of aberration coefficients for single-element plane-symmetric reflecting systems using Mathematica(trademark)

摘要

The definition of the generalized optical path function for a grating or mirror with a single plane of symmetry is reviewed. The generalized optical path function is then expanded in a series of wavefront aberration terms using only a few lines of code in the Mathematica(trademark) scientific programming environment. The use of the algebraic capabilities of the Mathematica(trademark) environment allows straightforward calculation of aberration coefficients that would normally require considerable effort if undertaken by paper and pencil. In addition, the derivation can be carried out to higher order aberration terms, limited only by the capabilities of the computer platform used.