  SAXO+ is a planned enhancement of the existing SAXO, the VLT/ SPHERE adaptive
optics system, deployed on ESO's Very Large Telescope. This upgrade is designed
to significantly enhance the instrument's capacity to detect and analyze young
Jupiter-like planets. The pivotal addition in SAXO+ is a second-stage adaptive
optics system featuring a dedicated near-infrared pyramid wavefront sensor and
a second deformable mirror. This secondary stage is strategically integrated to
address any residual wavefront errors persisting after the initial correction
performed by the current primary AO loop, SAXO. However, several recent studies
clearly showed that in good conditions, even in the current system SAXO,
non-common path aberrations (NCPAs) are the limiting factor of the final
normalized intensity in focal plane, which is the final metric for ground-based
high-contrast instruments. This is likely to be even more so the case with the
new AO system, with which the AO residuals will be minimized. Several
techniques have already been extensively tested on SPHERE in internal source
and/or on-sky and will be presented in this paper. However, the use of a new
type of sensor for the second stage, a pyramid wavefront sensor, will likely
complicate the correction of these aberrations. Using an end-to-end AO
simulation tool, we conducted simulations to gauge the effect of measured
SPHERE NCPAs in the coronagraphic image on the second loop system and their
correction using focal plane wavefront sensing systems. We finally analyzed how
the chosen position of SAXO+ in the beam will impact the evolution of the NCPAs
in the new instrument.
