  As the performance of coronagraphs improves, the achievable contrast is more
and more dependent of the shape of the pupil. The future generation of space
and ground based coronagraphic instruments will have to achieve high contrast
levels on on-axis and/or segmented telescopes. To correct for the high
amplitude aberrations introduced by secondary mirror structures and
segmentation of the primary mirror, we explore a two deformable mirror (DM)
method. The major difficulty of several DM methods is the non-linear relation
linking actuator strokes to the point spread function in the coronagraph focal
plane. The Active Compensation of Aperture Discontinuities (ACAD) method is
achieving this minimization by solving a non linear differential Monge Ampere
equation. Once this open loop method have reached the minimum, a close-loop
stroke minimization method can be applied to correct for phase and amplitude
aberrations to achieve the ultimate contrast. In this paper, I describe the
results of the parametric analysis that that I have undertaken on this method.
After recalling the principle of the method, I will described the explored
parameter space (deformable mirror set-up, shape of the pupil, bandwidth,
coronagraph designs). I will precisely described the way I simulated the Vortex
coronagraph for this numerical simulation. Finally I will present the
preliminary results of this parametric analysis for space telescope pupils
only.

Instrumentation and Methods for Astrophysics