Even though Adaptive Optics (AO) correction is used in modern instru-
ments of ground based telescopes, the quality of astronomical images still is
degraded due to the time delay stemming from the wavefront sensor (WFS)
integration time and adjustment of the deformable mirror(s) (DM). This re-
sults in a blur which can be mathematically described by a convolution of
the original image with the point spread function (PSF) of the instrument,
telescope and residual atmospheric perturbations. The PSF of an astronom-
ical image varies with the position in the observed field, which is a crucial
aspect in observations on Extremely Large Telescopes (ELT).

We present an algorithm to reconstruct the PSF in any position in the field
of view using AO telemetry data and knowledge on the atmospheric profile.
Our algorithm can easily be adapted to Single Conjugate AO (SCAO) and
Multi Conjugate AO (MCAO) systems. In particular, we adapt an approach
for atmospheric tomography to be used with a time series of AO telemetry
data in SCAO mode. As input our algorithm requires knowledge of the
strength of the different turbulent atmospheric layers, their wind speeds and
directions in order to perform the tomography step. To obtain the respective
contribution to the PSF, we project the reconstructed layers in the direction
of interest.

Our results are obtained for a simulated ELT setting in OCTOPUS, the
ESO end-to-end simulation tool, and in Compass, the simulation tool de-
veloped by LESIA, as well as for on-sky data from LBT. For a variety of
atmosphere and system parameters, they suggest a good qualitative perfor-
mance along with reasonable computational effort.