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 , defined by the refractive-index function N = N0(ξ, η, ζ) let the refractive-index function of a system of interest 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.
© 1990 Optical Society of America
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