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.
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