ELT/MICADO astrometric calibration: I. Stability under sky de-rotation

Abstract

MICADO will be a first-light instrument at the Extremely Large Telescope (ELT), with the capability of diffraction-limited relative astrometry down to the 50 μas level. High-precision relative astrometry with MICADO on the ELT requires accurate characterization and calibration of geometric distortion across the full instrument optical path. Due to the altitude-azimuth mounting of the ELT, the system has inevitable rotation-dependent distortions. We describe in detail various distortion contributors, including the warm relay optics, the optional SCAO dichroic, and the cryostat optics of the MICADO instrument itself, which de-rotates. We conclude that a 10th order Legendre polynomial is sufficient to keep the astrometric calibration precision better than 10 μas. The quantification of the differential distortion variation over a full 360 deg de-rotator cycle using high-resolution distortion maps shows that a minimal calibration discretization strategy requires a calibration every ∼20 deg. With our suitable spline interpolation method, we can use these coarsely distributed calibration points to reconstruct the full rotation-dependent distortion, reducing calibration effort without loss of astrometric precision. This is critical, as a rotation mismatch of only 32 arcsec between science and calibration data can already violate the goal of a relative calibration precision of <10 μas . In addition, we investigate the SCAO dichroic contributions. Although this dichroic is removable, it introduces an additional rotating geometric distortion component. These contributions do not need to be calibrated regularly, which effectively halves the required calibration time once the dichroic has been fully characterized. Finally, we provide calibration precisions achievable for MICADO using its Warm Astrometric Mask (WAM) for various calibration schemes. Although only the full distortion characterization of the instrument can preserve a <10 μas astrometric precision, a simple interpolated WAM calibration scheme proposed in this work still allows for milli-arcsecond precision sufficient for stacking data in regular imaging modes.