Explicit expressions for the third-order aberrations of thin lenses which have a pair of mutually orthogonal planes of symmetry are derived. Provided that the power of a lens in each of its two planes of symmetry is fixed, the aberration coefficients are polynomials of at most the third degree in the principal curvatures cy and cz of one of the surfaces of the lens.
P. J. Sands, "Thin double-plane-symmetric lenses," J. Opt. Soc. Am. 63, 431-434 (1973)