The aberrations of systems having (1) two axes of symmetry, (2) one axis of symmetry, (3) no axis of symmetry are investigated via Hamilton's mixed characteristic functionW. The mixed characteristicWis also the aberration function in the Luneberg-Kirchhoff diffraction integral. The result is employed to obtain the (incoherent) transfer function for a circular aperture in the presence of these aberrations as well as the point spread function (distribution of illuminance). Typical numerical results are discussed.