Third-Order Aberrations of `Doubly Symmetric' Systems

The third-order geometric aberrations of non-rotationally symmetric imaging systems are classified, and their characteristics given diagrammatically for the case of a circular exit aperture. The systems are `doubly symmetric', that is, they retain symmetry about each of two mutually perpendicular planes. Eleven new aberrations occur, three of which are third-order distortions, three give curved image surfaces, three are analogous to coma, and two to spherical aberration.