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 <i>c</i><i><sub>y</sub></i> and <i>c</i><i><sub>z</sub></i> of one of the surfaces of the lens.
P. J. Sands, "Thin double-plane-symmetric lenses," J. Opt. Soc. Am. 63, 431-434 (1973)