Chromatic coordinates in aberration theory

In the computation of the chromatic-aberration coefficients of a specified optical system, it is crucial that the chromatic behavior of the materials in the system be closely approximated by truncated Taylor series in one coordinate. The form of this chromatic coordinate determines the quality of the resulting approximations and is therefore of central importance. Four different forms are proposed, each being appropriate to different circumstances. The approximation of dispersive properties by polynomials in these coordinates is considered in detail. Although this method was devised solely for use in the context of aberration theory, it is found to be among the most effective means for the approximation of dispersion curves in general.