  To detect Earth-like planets in the visible with a coronagraphic telescope,
two major noise sources have to be overcome: the photon noise of the diffracted
star light, and the speckle noise due to the star light scattered by
instrumental defects. Coronagraphs tackle only the photon noise contribution.
In order to decrease the speckle noise below the planet level, an active
control of the wave front is required. We have developed analytical methods to
measure and correct the speckle noise behind a coronagraph with a deformable
mirror. In this paper, we summarize these methods, present numerical
simulations, and discuss preliminary experimental results obtained with the
High-Contrast Imaging Testbed at NASA's Jet Propulsion Laboratory.
