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Coronagraphy is a very efficient technique for identifying and characterizingextra-solar planets orbiting in the habitable zone of their parent star,especially when used in a space environment. An important family ofcoronagraphs is based on phase plates located at an intermediate image plane ofthe optical system, that spread the starlight outside the "Lyot" exit pupilplane of the instrument. In this communication we present a set of candidatephase functions generating a central null at the Lyot plane, and study how itpropagates to the image plane of the coronagraph. These functions includelinear azimuthal phase ramps (the well-known optical vortex), azimuthallycosine-modulated phase profiles, and circular phase gratings. Numericalsimulations of the expected null depth, inner working angle, sensitivity topointing errors, effect of central obscuration located at the pupil or imageplanes, and effective throughput including image mask and Lyot stoptransmissions are presented and discussed. The preliminary conclusion is thatazimuthal cosine functions appear as an interesting alternative to theclassical optical vortex of integer topological charge.

Analysis of nulling phase functions suitable to image plane coronagraphy