Phase-shifting fringe tracking method for sparse aperture interferometer arrays

Because they will comprise more and more collecting telescopes, modern interferometric facilities such as the Very Large Telescope Interferometer, the Center for High Angular Resolution Astronomy or the future Magdalena Ridge Observatory should provide new and astounding visible and IR high angular resolution images in the near future. In this perspective, such interferometer arrays should be equipped with new generation fringe trackers, being able to combine all the beams originating from an increasing number of telescopes and to sense differential piston errors varying between them. Here is described a new method suitable for co-phasing many interferometer sub-apertures at the same time, by means of a multi-axial integrated optics beam combiner associated with a phase-shifting technique originally intended for wavefront sensing. We present the principle of the method and its achievable performance in the cases of four, six and eight telescope arrays as function of the magnitude of the guide star in presence of various noise sources. Numerical simulations are carried out assuming typical VLTI parameters for what concerns geometry and radiometry. The main results are discussed in the concluding sections, showing an increasing advantage in favour of the phase-shifting technique when more and more collecting telescopes are operating together.