Performance and limitations of using ELT and MCAO for 50 µas astrometry

MCAO is essential to perform astrometry with the Extremely Large Telescope (ELT). Differently from the 8m class telescopes, the ELT will be a fully adaptive telescope, and a significant portion of the Adaptive Optics (AO) dynamic range will be absorbed by the correction and stabilization of the telescope aberrations and instabilities. Of particular interest for the ground-based astrometry is the use of Multi-Conjugated AO systems that allow to stabilize the low order field distortions against the transient plate scale instabilities of different origin occurring at the telescope and in the instrument. The instruments have several optical elements relatively far away from the pupil that can potentially challenge the astrometric precision of the observations with their residual mid-spatial frequencies errors. Using a combined simulation of ray tracing and AO numerical codes we assess the impact of these systematic errors at different field of view scales and fitting scenarios. The distortions have been assessed at different sky Position Angles (PA) and indicate that over large field of views only small PA ranges (±1^◦-3^◦) are accessible with astrometric residuals ≤ 50 µas. A full compliance, at any PA is achievable for 2 arcsec² FoV patches already with a 3^rd order polynomial. The natural partition of the optical system in three segments, ELT-MAORY-MICADO, respectively telescope, MCAO module and instrument, resembles also a splitting of the astrometric problem in the three subsystems that are characterized by different distortion amplitudes and calibration strategies. The result is a family portrait of the different optical segments with their prescription, dynamic motions, conjugation height and AO correctability, leading to trace their role in the bigger puzzle of the 50 µas astrometric endeavor.