Exploring the impact of PSF reconstruction errors on the reduction of astronomical adaptive optics based data

Astronomical adaptive optics (AO) data analysis requires the knowledge of the PSF associated to the AO run. With new AO modes soon to become available (LTAO, GLAO) there is a request from the AO users community for the development of new PSF reconstruction algorithms. Question is: what is the required accuracy on the quality of the reconstruction ? Guide-lines are needed in order to check the validity/usefulness of a given PSF reconstruction approach. LTAO/GLAO PSF reconstruction algorithms are being studied but are not available yet, so we propose to analyze this issue by simulating AO data with an AO modeling tool, and doing the data reduction using modeled AO PSF with an increased level of difference with the initial AO PSF, for parameters that have potentially a large impact on the PSF structure: the seeing angle, the C2N vertical distribution, the residual tip-tilt, LGS altitude fluctuations, and off-axis PSF variation (anisoplanatic effects). Results are given in the context of data analysis of an LTAO mode mimicking the planned VLT/GALACSI system. We do not take into account any instrument mode, and the telescope is assumed without aberrations. The current study is focused on the most critical type of data reduction: deconvolution. Algorithms are reviewed, and it is shown that for most classical deconvolution methods, the main impact of PSF reconstruction errors can already be described using either the so-called residual filter (ratio of exact OTF over reconstructed OTF) or more simply the difference between the exact and the reconstructed PSF. Using these two metrics, we explore the consequences of uncertainties on the five parameters introduced above. It is found that (1) in general, the impact of PSF reconstruction errors, while noticeable, appears to be surprisingly low, relaxing apparently the need for highly sophisticated PSF reconstruction algorithms; (2) in the case of Winer-like deconvolution, tip-tilt uncertainty is the most critical parameter, and has a noticeable impact on the residual PSF wings - which can be a problem when looking for faints objects in the vicinity of a bright star; (3) in the case of source extraction (CLEAN-like algorithms), seeing error clearly dominates, and the other errors have basically the same impact; (4) the impact of numerical effects during PSF deconvolution or extraction (sub-pixel PSF positioning error) is of the same order of magnitude than the effect of AO PSF parameters uncertainties