  Point spread function (PSF) reconstruction (PSF-R) is a well established
technique to determine reliably and accurately the PSF from Adaptive Optics
(AO) control loop data. We have successfully applied this technique to improve
the precision on photometry and astrometry to observation of NGC6121 obtained
with SPHERE/ZIMPOL as it will be presented in a forthcoming letter. Firstly, we
present the methodology we followed to reconstruct the PSF combining
pupil-plane and focal-plane measurements using using our PSF-R method PRIME
(Beltramo-Martin et al. 2019), with upgrade of both the model and best-fitting
steps compared to previous papers. Secondly, we highlight that PRIME allows to
maintain the PSF fitting residual below 0.2% over 2 hours of observation and
using only 30 s of AO telemetry, which may have important consequences for
telemetry storage for PSF-R purpose on future 30-40 m class telescopes.
Finally, we deploy PRIME in a more realistic regime using faint stars so as to
identify the precision needed on the initial guess parameters to ensure the
convergence towards the optimal solution.
