Perturbations of the point characteristic

Abstract

A particular perturbation expansion of the point characteristic V(x′, y′, z′, x, y, z) is examined. If V0. is the notionally known point characteristic of an optical system K0, defined by the refractive-index function N = N0(ξ, η, ζ) let the refractive-index function of a system of interest K be N = N0 +∊N*, granted that |∊N*|≪ N0 Then one may contemplate V, written as a Taylor series in the perturbation parameter ∊, with Vr multiplying ∊r in this series. A sequence of recursive equations is obtained for the derivatives dVr/ds0, where d/ds0 denotes differentiation along the unperturbed ray, so that at no stage do the perturbations of the ray have to be determined explicitly. Two detailed examples are given.