  Context . Initially designed to detect and characterise exoplanets, extreme
adaptive optics (AO) systems open a new window onto the Solar System by
resolving its small bodies. Nonetheless, their study remains limited by the
accuracy of the knowledge of the AO-corrected point spread function (AO-PSF)
that degrades their image and produces a bright halo, potentially hiding faint
moons in their close vicinity. Aims . To overcome the random nature of AO-PSFs,
I aim to develop a method that blindly recovers the PSF and its faint
structured extensions directly into the data of interest, without any prior on
the instrument or the object's shape. The objectives are both to deconvolve the
object and to properly estimate and remove its surrounding halo to highlight
potential faint companions. Methods . My method first estimated the PSF core
via a parametric model fit, under the assumption of a sharp-edged flat object.
Then, the resolved object and the PSF extensions were alternatively deconvolved
with a robust method, insensitive to model outliers, such as cosmic rays or
unresolved moons. Finally, the complex halo produced by the AO system was
modelled and removed from the data. Results . The method is validated on
realistic simulations with an on-sky AO-PSF from the SPHERE/ZIMPOL instrument.
On real data, the proposed blind deconvolution algorithm strongly improves the
image sharpness and retrieves details on the surface of asteroids. In addition,
their moons are visible in all tested epochs despite important variability in
turbulence conditions. Conclusions . My method shows the feasibility of
retrieving the complex features of AO-PSFs directly from the data of interest.
It paves the way towards more precise studies of asteroid surfaces and the
discovery and characterisation of Solar System moons in archival data or with
future instruments on extremely large telescopes with ever more complex
AO-PSFs.
