The time-averaged electric energy density near the focus of a lens or mirror system with annular aperture is calculated. The distribution shows greater difference from the paraxial approximation than for the full circular aperture. The vector distribution of the polarisation after focusing greatly affects the field near the focus. In particular, a mirror with annular aperture which deflects a plane-polarised wave through a small angle gives a distribution in the focal plane which exhibits bright rings around a dark centre. The field distribution of an annular system is found to consist of just two modes of free space.