VLTI extensions and limiting sensitivity: how to win on both counts

There is a general belief that increasing the number of apertures in an interferometer comes at a cost in terms of fringe tracking sensitivity. We have developed, tested on an optical bench and fully simulated a fringe tracking concept which has the remarkable property of having a sensitivity independent of the number of apertures. The limiting sensitivity of this hierarchical fringe tracking (HFT) concept is this of a two telescopes fringe tracker using all the flux of a pair of telescopes, whatever the total number of apertures. Within that sensitivity, the tracking accuracy globally increases with the number of apertures, particularly on the longest baselines. Compared with the "pairwise" and "all-in-one" concepts, the HFT offers a gain in sensitivity for a NT apertures interferometer of at least NT-1. This sets new parameters for an extension of the number of VLTI apertures. This presentation will discuss the sensitivity limits and some science benefits of several VLTI extensions, with more UTs, more ATs or combinations of UTs and AT