  The phase diversity technique is a useful tool to measure and pre-compensate
for quasi-static aberrations, in particular non-common path aberrations, in an
adaptive optics corrected imaging system. In this paper, we propose and
validate by simulations an extension of the phase diversity technique that uses
long exposure adaptive optics corrected images for sensing quasi-static
aberrations during the scientific observation, in particular for high-contrast
imaging. The principle of the method is that, for a sufficiently long exposure
time, the residual turbulence is averaged into a convolutive component of the
image and that phase diversity estimates the sole static aberrations of
interest. The advantages of such a procedure, compared to the processing of
short-exposure image pairs, are that the separation between static aberrations
and turbulence-induced ones is performed by the long-exposure itself and not
numerically, that only one image pair must be processed, that the estimation
benefits from the high SNR of long-exposure images, and that only the static
aberrations of interest are to be estimated. Long-exposure phase diversity can
also be used as a phasing sensor for a segmented aperture telescope. Thus, it
may be particularly useful for future planet finder projects such as EPICS on
the European ELT.
