Development of the Warm Astrometric Mask for MICADO astrometry calibration

The achievement of $\mu$arcsec relative astrometry with ground-based, near infrared, extremely large telescopes requires a significant endeavour of calibration strategies. In this paper we address the removal of instrument optical distortions coming from the ELT first light instrument MICADO and its adaptive optics system MAORY by means of an astrometric calibration mask. The results of the test campaign on a prototype mask (scale 1:2) has probed the manufacturing precision down to $\sim$ 50nm/1mm scale, leading to a relative precision $\delta\sigma \sim 5e-5$. The assessed manufacturing precision indicates that an astrometric relative precision of $\delta\sigma \sim 5e-5 = \frac{50\mu as}{1 arcsec}$ is in principle achievable, disclosing $\mu$arcsec near infrared astrometry behind an extremely large telescope. The impact of $\sim$ 10-100 nm error residuals on the mask pinholes position is tolerable at a calibration level as confirmed by ray tracing simulations of realistic MICADO distortion patterns affected by mid spatial frequencies residuals. We demonstrated that the MICADO astrometric precision of 50 $\mu$as is achievable also in presence of a mid spatial frequencies pattern and manufacturing errors of the WAM by fitting the distorted WAM pattern seen through the instrument with a 10$^{th}$ order Legendre polynomial.