MAVIS: the impact of the mid-spatial frequency figure errors of optics on the astrometric error

Mid-spatial frequency figure errors (MSFEs) occurring on optical surfaces are an unavoidable issue that may influence the performance of an optical system. In this paper, we present the results of an analysis dedicated to the impact of MSFE of the optical surfaces on the relative astrometric error. The method involves an almost end-to-end simulation, encompassing the calibration of the optical distortions. Although the analysis described here is primarily focused on the specific case of the MCAO-Assisted Visible Imager and Spectrograph (MAVIS) instrument, it is worth noting that the same methodology can be applied to other instruments as well. To provide context, MAVIS, short for multi-conjugate adaptive optics-assisted visible imager and spectrograph, represents the next-generation instrument designed for the Very Large Telescope. The distortions considered in the analysis stem from the optical components of the adaptive optics module of MAVIS. The results take into account both field rotation and wavelength dependencies. Relative astrometric errors are computed across different separations between sources. Furthermore, we analyze distortions introduced by the atmospheric dispersion corrector, factoring in the zenith angle dependence. A similar in-depth analysis is conducted for the imager components. This approach offers a comprehensive understanding of the intricate interplay between MSFE of optical components and astrometric precision.