[en] Images of simple objects produced by a perfect lens and a phase plate have been calculated by use of Abbe theory for Foucault, Hilbert and Zernike phase plates. The results show that with a Zernike plate, white outlines and ringing like those observed previously can be caused by the beam hole, which limits the low-spatial-frequency response of the system even when the lens behaves perfectly. When the change of phase added by the phase plate is distributed over a range of radius rather than a simple step, the unwanted effects are substantially reduced. (paper)