Improved GRAVITY astrometric accuracy from modeling optical aberrations

The GRAVITY instrument on the ESO VLTI pioneers field of high-precision near-infrared interferometry by providing astrometry at $10 - 100\,\mu$as level. Measurements such high precision crucially depend control systematic effects. Here, we investigate how aberrations introduced small optical imperfections along path from telescope to detector affect astrometry. We develop an analytical model that describes impact measurement complex visibilities. Our formalism accounts for pupil-plane and focal-plane aberrations, as well interplay between static turbulent successfully reproduces calibration measurements a binary star. Galactic Center observations with in 2017 2018, when both Sgr A* star S2 were targeted single fiber pointing, are affected these level less than 0.5 mas. Removal effects brings harmony dual beam 2019 2020, which not aberrations. This also resolves discrepancies derived distance $R_0$ reported previously.