Pupil filters can modify the three dimensional response of an optical system. In this paper, we study different pupil symmetries that produce a predictable image behavior. We show that different pupil-filters that satisfy certain symmetry conditions can produce axial responses which are either identical or mirror reflected. We also establish the differences in the symmetry properties between amplitude-only filters and phase-only filters. In particular, we are interested in phase filters that produce transverse superresolution with axial superresolution or high depth of focus. ©2004 Optical Society of America.