Cophasing the Planet Formation Imager
  The Planet Formation Imager (PFI) is a project for a very large optical interferometer intended to obtain images of the planet formation process at scales as small as the Hill sphere of giant exoplanets. Its main science instruments will work in the thermal infrared but it will be cophased in the near infrared, where it requires also some capacity for scientific imaging. PFI imaging and resolution specifications imply an array of 12 to 20 apertures and baselines up to a few kilometers cophased at near infrared coherent magnitudes as large as 10. This paper discusses various cophasing architectures and the corresponding minimum diameter of individual apertures, which is the dominant element of PFI cost estimates. From a global analysis of the possible combinations of pairwise fringe sensors, we show that conventional approaches used in current interferometers imply the use of prohibitively large telescopes and we indicate the innovative strategies that would allow building PFI with affordable apertures smaller than 2 m in diameter. The approach with the best potential appears to be Hierarchical Fringe Tracking based on "two beams spatial filters" that cophase pairs of neighboring telescopes with all the efficiency of a two telescopes fringe tracker and transmit most of the flux as if it was produced by an unique single mode aperture to cophase pairs of pairs and then pairs of groups of apertures. We consider also the adaptation to PFI of more conventional approaches such as a combination of GRAVITY like fringe trackers or single or multiple chains of 2T fringe trackers. 
Romain G. Petrov, Abdelkarim Boskri, Thami Elhalkouj, John Monnier,   Michael Ireland, Stefan Kraus
astro-ph.IM