In a paper probably to be published in Optika i Spektroskopiya the wave aberration for sagittal focus for the arbitrary surface of rotational symmetry has been carried out on the base of the astigmatic beam invariant Ds = nusds. The resulting expression for the wave aberration has been reformulated into three terms which, in the Seidel region, go over into astigmatism (the first) and into the Petzval curvature (the second) while the third disappears.
Miron Gaj, "Generalization of Seidel Astigmatism and Petzval Curvature," Appl. Opt. 5, 1045-1049 (1966)