The use of third-order (Seidel) aberration coefficients has been well established in lens design for very many years. The ability to determine which surface is responsible for the introduction of a certain aberration is almost essential if the designer is to intelligently correct that aberration, and Seidel coefficients form the basis of intelligent lens design. However, for lenses at higher numerical apertures and field sizes, third-order aberrations are insufficient for describing all of the aberrations. In fact, for the majority of lenses, higher-order aberrations need to be included in their design and analysis.
Several authors have developed schemes for calculating the fifth-order and even the seventh-order coefficients. The equations developed by Buchdahl seem to be the most popular, partly due to Rimmer, who described the Buchdahl method in a master's thesis from the University of Rochester. The equations discussed below follow those published by Rimmer, but they are exactly equivalent to Buchdahl's equations. These equations also include the seventh-order spherical aberration coefficients, and we will refer to the fifth-order aberration coefficients and seventh-order spherical aberration coefficients collectively as Buchdahl coefficients.
Online access to SPIE eBooks is limited to subscribing institutions.