Abstract

A derivation of the fifth-order aberrations for a system of centered spherical surfaces is presented. The fifth-order aberrations are partitioned into surface contributions. The method contains two novel features. First, the theory is based rigorously on the concept of the angle characteristic function (eikonal) for a single surface only. Starting from the single-surface eikonal, expressions for third-and fifth-order aberrations, as well as third-order pupil aberrations, are formulated. Second, the problem of finding the aberration coefficients for a system of surfaces is reshaped into the problem of solving a set of coupled nonlinear equations. Application of Lagrange's theorem up to fifth order then yields the expressions for the third-and fifth-order aberration coefficients at once. In this way, Buchdahl’s iteration procedure can be avoided.

© 1987 Optical Society of America