  Quasi-static aberrations in coronagraphic systems are the ultimate limitation
to the capabilities of exoplanet imagers both ground-based and space-based.
These aberrations - which can be due to various causes such as optics alignment
or moving optical parts during the observing sequence - create light residuals
called speckles in the focal plane that might be mistaken for a planets. For
ground-based instruments, the presence of residual turbulent wavefront errors
due to partial adaptive optics correction causes an additional difficulty to
the challenge of measuring aberrations in the presence of a coronagraph. In
this paper, we present an extension of COFFEE, the coronagraphic phase
diversity, to the estimation of quasi-static aberrations in the presence of
adaptive optics-corrected residual turbulence. We perform realistic numerical
simulations to assess the performance that can be expected on an instrument of
the current generation. We perform the first experimental validation in the
laboratory which demonstrates that quasistatic aberrations can be corrected
during the observations by means of coronagraphic phase diversity.
