The formalism for the prolate apodized coronagraphs is shortly outlined. A presentation of the numerical
computation of the circular prolate apodization is given, and a comparison is made between the exact prolate
and the solution obtained by Guyon & Roddier (2000), with an iterative algorithm. The agreement is excellent
between the two solutions, provided a sufficient sampling of the mask.
Numerical simulations are presented for circular apertures with prolate apodizations and compared to the
classical unapodized technique: off-axis response, effect of mask size, central obscuration and chromatism.