Joint estimation of atmospheric and instrumental defects using a parsimonious point spread function model: On-sky validation using state of the art worldwide adaptive-optics assisted instruments

Context. Modeling the optical point spread function (PSF) is particularly challenging for adaptive optics (AO)-assisted observations owing to the its complex shape and spatial variations.Aims. We aim to (i) exhaustively demonstrate the accuracy of a recent analytical model from comparison with a large sample of imaged PSFs, (ii) assess the conditions for which the model is optimal, and (iii) unleash the strength of this framework to enable the joint estimation of atmospheric parameters, AO performance and static aberrations.Methods. We gathered 4812 on-sky PSFs obtained from seven AO systems and used the same fitting algorithm to test the model on various AO PSFs and diagnose AO performance from the model outputs. Finally, we highlight how this framework enables the characterization of the so-called low wind effect on the Spectro-Polarimetic High contrast imager for Exoplanets REsearch (LWE; SPHERE) instrument and piston cophasing errors on the Keck II telescope.Results. Over 4812 PSFs, the model reaches down to 4% of error on both the Strehl-ratio (SR) and full width at half maximum (FWHM). We particularly illustrate that the estimation of the Fried's parameter, which is one of the model parameters, is consistent with known seeing statistics and follows expected trends in wavelength using the Multi Unit Spectroscopic Explorer instrument (lambda (6/5)) and field (no variations) from Gemini South Adaptive Optics Imager images with a standard deviation of 0.4 cm. Finally, we show that we can retrieve a combination of differential piston, tip, and tilt modes introduced by the LWE that compares to ZELDA measurements, as well as segment piston errors from the Keck II telescope and particularly the stair mode that has already been revealed from previous studies.Conclusions. This model matches all types of AO PSFs at the level of 4% error and can be used for AO diagnosis, post-processing, and wavefront sensing purposes.