Adaptive optics is a powerful method to study big (D > 100 km) asteroids. In particular, the VLT/SPHERE instrument with ZIMPOL imaging polarimeter offers a diffraction-limited image, with an angular resolution of 20 mas, albeit with a complex and variable point-spread function (PSF), reaching the Strehl ratio 0.095 (in V). Moreover, a myopic deconvolution with a stellar PSF and additional priors is used to improve the resolution further. The pixel scale 3.6 mas corresponds to 3 km to at the distance of 1 au. Consequently, we obtain not only the overall shape, absolute size, and volume, but also surface topography and craters counts (D_c > 30 km).   

 With the goal to resolve several tens of big asteroids, this represents an important observational constraint for the main asteroid belt, its overall collisional evolution, and also for individual asteroid families, because families--craters identifications are now possible. We demonstrate this for the asteroid (89) Julia and its family (Vernazza etal. 2018). A 70-km crater (called Nonza) was identified on the AO images, with the help of lightcurve inversion, occultations, and shape reconstruction. A series of hydrodynamical/collisional/orbital models was then used to compare the excavated volume, the ejected volume, the largest fragment and the SFD of family members. The dynamical age of the Julia family is from 10 to 120 Myr. Additional asteroids with (or without) families are under investigation.