ABSTRACT
By a finite aberration formula one can mean first an expression for the whole of the aberration for particular aperture and field coordinates, as opposed to the primary aberration expressions. Finite aberration expressions, of which there is a considerable variety, were developed for one or more of three different purposes. To show the contributions to the aberration from each surface. To obtain, from considerations of symmetry, information about extra-axial aberrations from raytraces of axial pencils. And to facilitate computation by reducing the number of significant figures to be carried, just as the primary aberration formulae do. Historically, expressions for total optical path aberration were developed first for axial pencils, then for off-axis pencils in a meridian plane and finally for skew rays. The derivation for skew rays is actually quite straightforward and it is easy to derive the more specialized cases from the skew ray formula.
