Introduction

Extra-solar planets (Mayor &Queloz 1995, Marcy & Butler 1996) can, in principle, be seen in ground-based images using the light cancellation in dark speckles to remove the halo of star light (Labeyrie 1995). Long-exposures with high-performance adaptive optics and a correction of the seeing-induced shadow pattern on the telescope's pupil are also proposed by Angel (1994). A less extreme atmospheric correction is needed with the dark-speckle method. Both methods are expected to reach the 10^-9 relative intensity needed to detect a Jupiter-like planet near its parent star. Related space-based techniques are also considered ([Malbet et al. 1995], [Gezari et al 1997]). In the longer term, resolved images of detected exo-planets will in principle be obtainable even from the ground with long-baseline interferometric arrays ([Labeyrie 1996]).
The "dark-speckle" method exploits the light cancellation effect occuring in random coherent fields according to the Bose-Einstein statistics. Although adaptive optics can reconstruct the Airy peak, and possibly the first few rings, in the focal image of a bright star, the degree of "seeing" correction which it provides cannot be good enough to remove the fluctuating speckles in the surrounding zone of the Airy pattern. Coronagraphic devices ([Lyot 1930], [Bonneau et al. 1975], [Mauron 1980], [Malbet 1996], Gay & Rabbia 1996, Roddier & Roddier 1997) can remove the steady and organized part of the straylight, i.e. the first few Airy rings if they emerge from the boiling speckled halo, and even if they are burried but remain detectable with the dark speckle analysis.
One is therefore left with the problem of extracting as much information as possible from this speckled halo. Destructive interference in the star light occasionally causes a dark speckle to appear here and there. When this happens at the position of the planet's own faint Airy peak, the darkening cannot be as deep as elsewhere. The planet's Airy peak, also restored by the adaptive optics, indeed has a rather stable intensity, which adds to the star's local intensity. The intensity histogram is therefore locally distorted, and suitable algorithms can display the local distorsions in the form of a cleaned image. The exposures must be shorter than the turbulence life time. With a large telescope and hours of integration, a planet, typically 10⁹ times fainter than the parent star, is expected to become visible.