The GRAVITY metrology system: modeling a metrology in optical fibers

GRAVITY is the second generation VLT Interferometer (VLTI) instrument for high-precision narrow-angle astrometryand phase-referenced interferometric imaging. The laser metrologysystem of GRAVITY is at the heart of its astrometric mode, which must measure the distance of 2 stars with a precision of 10 micro-arcseconds. This means the metrologyhas to measure the optical path difference between the two beam combiners of GRAVITY to a level of 5 nm. The metrologydesign presents some non-common paths that have consequently to be stable at a level of 1 nm. Otherwise they would impact the performance of GRAVITY. The various tests we made in the past on the prototype give us hints on the components responsible for this error, and on their respective contribution to the total error. It is however difficult to assess their exact origin from only OPD measurements, and therefore, to propose a solution to this problem. In this paper, we present the results of a semi-empirical modeling of the fibered metrologysystem, relying on theoretical basis, as well as on characterisations of key components. The modeling of the metrologysystem regarding various effects, e.g., temperature, waveguide heating or mechanical stress, will help us to understand how the metrologybehave. The goals of this modeling are to 1) model the test set-ups and reproduce the measurements (as a validation of the modeling), 2) determine the origin of the non-common path errors, and 3) propose modifications to the current metrologydesign to reach the required 1nm stability.