  High-contrast imaging provided by a coronagraph is critical for the direction
imaging of the Earth-like planet orbiting its bright parent star. A major
limitation for such direct imaging is the speckle noise that is induced from
the wave-front error of an optical system. We derive an algorithm for the
wave-front measurement directly from 3 focal plane images. The 3 images are
achieved through a deformable mirror to provide specific phases for the optics
system. We introduce an extra amplitude modulation on one deformable mirror
configuration to create an uncorrelated wave-front, which is a critical
procedure for wave-front sensing. The simulation shows that the reconstructed
wave-front is consistent with the original wave-front theoretically, which
indicates that such an algorithm is a promising technique for the wave-front
measurement for the high-contrast imaging.
