Abstract

Given an optical system with a plane of symmetry and an arbitrarily chosen ray contained in this plane, it is shown that it is possible to determine exact analytic formulas for a set of aberration coefficients characterizing the image-forming properties of bundles of rays in the neighborhood (but not necessarily centered on) the given ray. The foundations of the theory are laid, all formulas needed to compute the coefficients of orders one, two, and three are derived, and those simplifications which arise when a surface is a sphere are considered in detail.

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