On-Line Long-Exposure Phase Diversity: a Powerful Tool for Sensing   Quasi-Static Aberrations of Extreme Adaptive Optics Imaging Systems
  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. 
L. M. Mugnier, J.-F. Sauvage, T. Fusco, A. Cornia and S. Dandy