Study of the impact of E-ELT and MICADO distortion and wavefront errors residuals on the MICADO astrometric observations

The paper describes the developments towards an end-to-end optical model based on a commercial ray tracing software for studying the effects of the telescope and instrumental instabilities on the Multi-AO Imaging Camera for Deep Observations (MICADO). The primary goal and observing mode of MICADO is imaging, with a focus on relative astrometry with an accuracy of about 50 μas. To achieve this ambitious goal a careful examination of the possible random and systematic effects that can influence the astrometric accuracy is required. Here we concentrate on the perturbations coming from the different telescope and instrumental instabilities, mainly related to the static and dynamical perturbations of the European-Extremely Large Telescope (E-ELT) optics, the cold optics tolerances of the instrument and the intrinsic geometric distortions of both the systems. ESO developed an extended dataset of the E-ELT perturbations that are integrated inside the optical model of the telescope and the instrument relay optics for gathering the aberrated wavefronts. The wavefront error residuals are then propagated inside the system to check the distortions and their effects on the astrometric measurement at the instrument focal plane. From our analysis the dominating instrumental errors are: (i) the telescope induced distortions, in the order of => 100μas, that originate from the optics misalignments and presumably vary over <= 1hr time-scales, and must be calibrated against sky measurements; (ii) the instrument optics induced distortions that can reach ∼ 1 arcsec levels, but are more stable than the telescope perturbations. They will be calibrated with the use of an astrometric calibration mask. We derived the order of magnitude of the astrometric distortions of E-ELT and MICADO. The results of our study will help to define an efficient instrumental calibration strategy against the astrometric error of the instrument.