We present a new processing technique aimed at significantly improving the angular differential imaging method (ADI) in the context of high-contrast imaging of faint objects nearby bright stars in observations obtained with extreme adaptive optics (EXAO) systems. This technique, named SFADI for Speckle-Free ADI, allows to improve the achievable contrast by means of speckles identification and suppression. This is possible in very high cadence data, which freeze the atmospheric evolution. Here we present simulations in which synthetic planets are injected into a real millisecond frame rate sequence, acquired at the LBT telescope at visible wavelength, and show that this technique can deliver low and uniform background, allowing unambiguous detection of $10^{-5}$ contrast planets, from $100$ to $300$ mas separations, under poor and highly variable seeing conditions ($0.8$ to $1.5$ arcsec FWHM) and in only $20$ min of acquisition. A comparison with a standard ADI approach shows that the contrast limit is improved by a factor of $5$. We extensively discuss the SFADI dependence on the various parameters like speckle identification threshold, frame integration time, and number of frames, as well as its ability to provide high-contrast imaging for extended sources, and also to work with fast acquisitions.
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