Third-order aberration contributions of aspheric surfaces are derived from the point of view of wave theory. The design of a double aspheric curved field anastigmat based on third-order theory is then presented and its performance compared to a similar (Petzval) system consisting solely of spherical surfaces. The control of higher order aberrations and the possibility of increasing the relative aperture of the system with the aid of aspherics are discussed.
JOSEPH MEIRON, "On the Design of Optical Systems Containing Aspheric Surfaces," J. Opt. Soc. Am. 46, 288-292 (1956)