A possible method of pupil apodization using Zernike's phase contrast is presented. I recall the phase contrast principle and show through numerical simulations that it may be used to generate an apodization using very simple optics in the monochromatic case. I also demonstrate that the general formalism for Lyot and Roddier & Roddier coronagraphy can be extended to the Zernike case. This may improve the quality of the simulations undertaken to demonstrate the technique's performances.