In preparation of future Multi-Object Spectrographs ( MOS ) whose one of the major role is to provide an extensive statistical studies of high redshifted galaxies surveyed , the demonstrator Canary has been designed to tackle technical challenges related to open-loop Adaptive-Optics ( AO ) control with jointed Natural Guide Star ( NGS ) and Laser Guide Star ( LGS ) tomography .

We have developed a Point Spread Function ( PSF ) -Reconstruction algorithm dedicated to MOAO systems using system telemetry to estimate the PSF potentially anywhere in the observed field , a prerequisite to post-process AO-corrected observations in Integral Field Spectroscopy ( IFS ) .

In this paper we show how to handle off-axis data to estimate the PSF using atmospheric tomography and compare it to a classical approach that uses on-axis residual phase from a truth sensor observing a natural bright source .

We have reconstructed over 450 on-sky Canary PSFs and we get bias/1- \sigma standard-deviation ( std ) of 1.3/4.8 on the H-band Strehl ratio ( SR ) with 92.3 % of correlation between reconstructed and sky SR. On the Full Width at Half Maximum ( FWHM ) , we get respectively 2.94 mas , 19.9 mas and 88.3 % for the bias , std and correlation .
The reference method achieves 0.4/3.5/95 % on the SR and 2.71 mas/14.9 mas/92.5 % on the FWHM for the bias/std/correlation .