Optical Aberration Coefficients II The Tertiary Intrinsic Coefficients

Abstract

The algebraic method for the determination of higher-order aberration coefficients based on the notion of quasi-invariance employs a process of iteration in which the nth step yields the exact coefficients of order 2n+1. To carry out the nth step one requires at each surface (i) all p and q coefficients of order less than 2n+1, (ii) the set of intrinsic p coefficients of order 2n+1 (the latter depending solely on the surface in question and not upon the coefficients which describe the imperfections implicit in that part of the system which precedes it). The algebraic steps leading to the explicit forms of higher-order intrinsic coefficients are quite elementary but very tedious and lead to an almost unmanageable jungle of terms unless a suitable reduction is carried out once and for all. The secondary terms have been dealt with elsewhere. The present paper now throws the monochromatic tertiary (i.e., seventh order) intrinsic coefficients of spherical surfaces into a very simple form eminently suitable for computation with an ordinary desk machine. In fact, the ten unbarred intrinsic coefficients, which alone appear in a suitably constructed computing scheme, require a total of only thirteen entries per surface.