The VLTI instrument GRAVITY will provide very powerful astrometry by combining the light from four telescopes for two objects simultaneously. It will measure the angular separation between the two astronomical objects to a precision of 10 microarcseconds. This corresponds to a differential optical path difference (dOPD) between the targets of few nanometers and the paths within the interferometer have to be maintained stable to that level. For this purpose, the novel metrology system of GRAVITY will monitor the internal dOPDs by means of phase-shifting interferometry. We present the four-step phase-shifting concept of the metrology with emphasis on the method used for calibrating the phase shifts. The latter is based on a phase-step insensitive algorithm which unambiguously extracts phases in contrast to other methods that are strongly limited by non-linearities of the phase-shifting device. The main constraint of this algorithm is to introduce a robust ellipse fitting routine. Via this approach we are able to measure phase shifts in the laboratory with a typical accuracy of lambda/2000 or 1 nanometer of the metrology wavelength.
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