Phase tracking with differential dispersion

Differential chromatic dispersion in single-mode optical fibres leads to a loss of contrast of the white light fringe. For the GRAVITY instrument, this aspect is critical since it limits the fringe tracking performance. We present a real-time algorithm that compensates for differential dispersion due to varying fibre lengths using prior calibration of the optical fibres. This correction is limited by the accuracy to which the fibres stretch is known. We show how this affects the SNR on the white light fringe for different scenarios and we estimate how this phenomenon might eventually impact the astrometric accuracy of GRAVITY observations.