Conditions for having identical aberration behaviors of various thick lenses

Two optical lenses with the same focal length but different lens thicknesses and principal plane locations can provide equivalent first-order optics on imagery if the marginal and chief ray heights and slope angles at their principal planes are equal, resulting in the same system magnification, object and image distances. In this paper, we will prove that if these lenses have the same primary aberrations (including Seidel aberrations, chromatic aberrations, and secondary spectrum) corresponding to the same marginal and chief rays then they must have the same new aberrations for any same new rays. This theorem is useful when designers would like to redesign a lens group in a system. The influence on the movements among lens groups, the special aberration properties of plane parallel plates, and afocal lens groups are also discussed.