  Adaptive optics (AO) allows one to derive the point spread function (PSF)
simultaneously to the science image, which is a major advantage in
post-processing tasks such as astrometry/photometry or deconvolution. Based on
the algorithm of \citet{veran97}, PSF reconstruction has been developed for
four different AO systems so far: PUEO, ALFA, Lick-AO and Altair. A similar
effort is undertaken for NAOS/VLT in a collaboration between the group PHASE
(Onera and Observatoire de Paris/LESIA) and ESO. In this paper, we first
introduce two new algorithms that prevent the use of the so-called "$U\_{ij}$
functions" to: (1) avoid the storage of a large amount of data (for both new
algorithms), (2) shorten the PSF reconstruction computation time (for one of
the two) and (3) provide an estimation of the PSF variability (for the other
one). We then identify and explain issues in the exploitation of real-time
Shack-Hartmann (SH) data for PSF reconstruction, emphasising the large impact
of thresholding in the accuracy of the phase residual estimation. Finally, we
present the data provided by the NAOS real-time computer (RTC) to reconstruct
PSF ({\em (1)} the data presently available, {\em (2)} two NAOS software
modifications that would provide new data to increase the accuracy of the PSF
reconstruction and {\em (3)} the tests of these modifications) and the PSF
reconstruction algorithms we are developing for NAOS on that basis.
