The angular resolution of ground-based telescopes is usually not limited by
the quality of the telescope optics, but rather by the atmospheric
turbulence. This phenomenon, called seeing, is due to random temperature
fluctuations in the atmospheric layers which induce local variations of the
index of refraction resulting in distortions of the incoming wavefront
(Roddier 1981). Regardless of the telescope aperture, the ultimate
resolution is rarely better than 0.5
even in good astronomical
sites. Another effect of the seeing is to degrade the imaging sensitivity,
by spreading the collected photons over a much larger area. A posteriori
techniques have been developed to overcome the effects of the atmospheric
turbulence on the image quality, using digital post-processing: speckle
interferometry, deconvolution from wavefront sensing, etc. Nevertheless a
more promising approach is to compensate in real-time the atmospherically
induced wavefront distortion by an adaptive optics (AO) system. In this
technique the light coming from the object under study, or from a nearby
reference star, is analyzed by a wavefront sensor. Using this information,
the surface of a deformable mirror is modified in real-time by a servo
control system. The resulting wavefront is nearly planar and the
resolution becomes close to the diffraction limit of the telescope (Alloin
& Mariotti 1994).
Collecting information close to a star implies the use of small masks.
Theoretical calculations enable the expected performance of coronographic
techniques to be simulated (Malbet et al. 1996), and the influence
of the respective shapes of the occulting mask and of the Lyot stop to be
explored. Basically, the critical parameter is the relative size of the
occulting mask to the point source response extension. It strongly affects
the rejection capability of the system, as well as the efficiency of the
Lyot stop. For instance, we have calculated that the use of a 0.8\
occulting mask leads to simulated rejection rates of 335 in the case of a
perfectly flat wavefront, 215 for AO corrected images, but only 50 for
tip-tilt corrected images, and 5 in case of no correction. In other
words, to obtain the same rejection rate as the AO corrected images would
require the use of a mask that is two times larger with tip-tilt corrected
images, and 3.5 times larger without correction. This particular numerical
example (Fig. 1 (click here)) is calculated for the case of 1 seeing
and with a 3.6 meter telescope at 2.2 
m.
Figure 1: Simulated profiles of PSF obtained with a 3.6 meter telescope
at 2.2 m under atmospheric Kolmogorov turbulence conditions (seeing
= 1) and different correction modes. The full line indicates
the profile that the adaptive optics system should generate on a bright
star, compared to the profile in a perfect case of flat wavefront
(long-dashed line) and the case of the tip-tilt correction (dashed
line) and no correction at all (dotted line). Note that the
discrepancy between the calculated feature for the perfectly flat
wavefront and the Airy pattern only comes from the numerical
calculation, and has no link with atmospheric turbulence