  We present an analysis of self-imaging in a regime beyond the paraxial, where
deviation from simple paraxial propagation causes apparent self-imaging
aberrations. The resulting structures are examples of aberration without rays
and are described analytically using post-paraxial theory. They are shown to
relate to, but surprisingly do not precisely replicate, a standard integral
representation of a diffraction cusp. Beyond the Talbot effect, this result is
significant as it illustrates that the effect of aberration -- as manifested in
the replacement of a perfect focus with a cusp-like pattern -- can occur as a
consequence of improving the paraxial approximation, rather than due to
imperfections in the optical system.
