Reaching micro-arcsecond astrometry with long baseline optical interferometry: Application to the GRAVITY instrument

A basic principle of long baseline interferometry is that an optical path difference (OPD) directly translates into an astrometric measurement. In the simplest case, the OPD is equal to the scalar product between the vector that links the two telescopes and the normalized vector pointing toward the star. However, in some circumstances, too simple an interpretation of this scalar product leads to seemingly conflicting results, called here "the baseline paradox". For micro-arcsecond accuracy astrometry, we have to model the metrology measurement in full. It involves a complex system subject to many optical effects: from pure baseline errors to static, quasi-static, and high-order optical aberrations. The goal of this paper is to present the strategy used by the "General Relativity Analysis via VLT InTerferometrY" instrument (GRAVITY) to minimize the biases introduced by these defects. The result of this work is an error budget of the biases caused by the multiple optical imperfections, including optical dispersion.