  Following the tracks of Malbet, Yu, & Shao (1995} on dark hole algorithms, we
present analytical methods to measure and correct the speckle noise behind an
ideal coronagraph. We show that, in a low aberration regime, wavefront sensing
can be accomplished with only three images, the next image being fully
corrected (no iterative process needed). The only hardware required is the
coronagraph deformable mirror and an imaging detector in the focal plane, thus
there are no non-common path errors to correct. Our first method, speckle field
nulling, is a fast FFT-based algorithm requiring the deformable mirror
influence functions to have identical shapes. Our second method, speckle energy
minimization is more general and based on matrix inversion. Numerical
simulations show that these methods can improve the contrast by several orders
of magnitude.
