  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.
