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The phase diversity technique is a useful tool to measure and pre-compensatefor quasi-static aberrations, in particular non-common path aberrations, in anadaptive optics corrected imaging system. In this paper, we propose andvalidate by simulations an extension of the phase diversity technique that useslong exposure adaptive optics corrected images for sensing quasi-staticaberrations during the scientific observation, in particular for high-contrastimaging. The principle of the method is that, for a sufficiently long exposuretime, the residual turbulence is averaged into a convolutive component of theimage and that phase diversity estimates the sole static aberrations ofinterest. The advantages of such a procedure, compared to the processing ofshort-exposure image pairs, are that the separation between static aberrationsand turbulence-induced ones is performed by the long-exposure itself and notnumerically, that only one image pair must be processed, that the estimationbenefits from the high SNR of long-exposure images, and that only the staticaberrations of interest are to be estimated. Long-exposure phase diversity canalso be used as a phasing sensor for a segmented aperture telescope. Thus, itmay be particularly useful for future planet finder projects such as EPICS onthe European ELT.

On-Line Long-Exposure Phase Diversity: a Powerful Tool for Sensing Quasi-Static Aberrations of Extreme Adaptive Optics Imaging Systems