An aberration function that is closely related to the transverse-ray aberration but which remains meaningful under all circumstances is described. As a preliminary to deriving computing formulas for the change in aberration with refraction, it is shown first how this function can be expanded in terms of refractive indices and quantities invariant with refraction, and second how these invariants can be expanded as functions of the object space coordinates of the incident ray. Refraction at both spherical and aspheric surfaces is considered and the expansions are taken as far as is necessary to calculate the primary and secondary aberrations, although they are capable of being taken further. The convergence of the expansions is discussed.
E. F. DENBY, "Monochromatic Aberrations of Symmetrical Optical Systems. I. Expansion of the Aberration Function," J. Opt. Soc. Am. 52, 20-24 (1962)