Tip-tilt anisoplanatism in multiconjugate adaptive optics systems and its impact on astrometric observations with next-generation telescopes

The new class of 25-40 m extremely large telescopes will provide unprecedented resolutions to astronomical observations from the ground. The use of adaptive optics (AO) is mandatory to overcome the effects of atmospheric turbulence on the images and to fully exploit the capabilities of these telescopes by restoring their diffraction limit. In particular, the use of multiconjugate adaptive optics (MCAO) is foreseen for near-infrared observations at the Extremely Large Telescope (ELT) with the Multiconjugate adaptive Optics Relay For ELT Observations (MORFEO) and at the Thirty Meter Telescope with the Narrow Field InfraRed Adaptive Optics System (NFIRAOS). MCAO will also assist observations in the visible at the Very Large Telescope with the MCAO Assisted Visible Imager and Spectrograph (MAVIS). The high angular resolution, the uniformity of the correction over wide areas, the large number of reference sources with high image quality provided and the control of the field distortions through the DMs conjugated in altitude are characteristics that make MCAO a good candidate for astrometric observations. High-precision differential astrometry is, indeed, among the main science drivers of the future instruments equipped with MCAO. Among them, the near-infrared Multi-AO Imaging CamerA for Deep Observations (MICADO) assisted by MORFEO is required to achieve 50 μas (goal of 10 μas) of precision on the differential astrometry. Such challenging requirements ask for accurate analyses of the astrometric error budget, that must include an estimation of the impact of the MCAO control on astrometric measurements as well. In this context, the aim of the present PhD project is to investigate the contribution to the astrometric error of the residuals of atmospheric tip-tilt from an MCAO loop and to include the results in the framework of the MORFEO project. The work is divided in different steps that are below described. First, an analytical formulation has been derived to estimate temporal cross power spectral densities (CPSDs) of the turbulent phase: considering a general framework with two different apertures each looking at a different object, the spatiotemporal correlation between the two observed wavefronts has been computed. Analytical expressions have been derived either considering the whole (piston-filtered) phase, either assuming the phase as decomposed into Zernike modes. The general framework allows to study different aspects of actual and future AO systems. For our case study in particular, the configuration with one aperture and two sources can help analyze the spatiotemporal statistics between the multiple beams involved in MCAO-assisted observations. Temporal CPSDs have then been used for the estimation of the residual phase from an AO loop. The calculations have been performed first for the simpler SCAO case: the residual phase in the direction of a scientific target on axis considering an off-axis guide star has been derived and the AO control has been included. From the residual phase, estimated in the temporal domain, the temporal PSD, as well as the variance of the residuals, have been extracted. The formulation takes into account temporal and noise errors, as well as the effect of anisoplanatism on the residuals. The work on SCAO residuals has then been extended to the MCAO case: an analytical formulation to estimate the residual phase from an MCAO loop in any direction of the scientific field of view has been carried out. In this context, temporal transfer functions to describe the MCAO control have been derived. The formulas are general and allows to analyze specific frameworks depending on the telescope aperture, the turbulence profile, the guide stars constellation, the number and conjugation heights of the deformable mirrors and the modes of distortion, both sensed and corrected. Results have been provided also considering different tomographic reconstruction algorithms. The analytical derivation for the MCAO case has represented a basis for the analysis of tip-tilt anisoplanatism in MCAO observations. Different aspects of MCAO tip-tilt residuals have been analyzed: the dependence on the asterism of guide stars, on the position of the target with respect to the asterism, as well as on the integration time of the scientific exposure. Thus, the impact of tip-tilt residuals on MCAO-assisted astrometric observations has been investigated: analytical expressions for the computation of differential tilt jitter in MCAO observations has been derived and an estimation of the centroiding error due to tip-tilt residuals has been provided. The results have been applied to the MORFEO case, to estimate the contribution of tip-tilt residuals within the astrometric error budget of the system. The analysis has been carried out for MAVIS as well. All the analytical derivations have been implemented into Python codes, that have been included in the libraries of the AO group of INAF - Arcetri Astrophysical Observatory (https://github.com/ArcetriAdaptiveOptics/arte) and that are going to be available for the MORFEO project. Finally, a proposal of observation of Jupiter’s light bending by means of differential astrometry with the Single conjugated adaptive Optics Upgrade for LBT (SOUL) at the Large Binocular Telescope has been submitted; the aim is to test the astrometric capabilities of actual AO systems for a better comprehension of potential issues with future facilities like MORFEO.