Photon-noise limits to the detection of the closure phase in optical interferometry

Michelson stellar interferometers with long baselines have been proposed as a means for obtaining high-resolution images of space objects. The fringes measured in such interferometers move randomly owing to atmospheric turbulence effects. For overcoming turbulence effects the fringe phase at any instant is summed around groups of three or more aperture pairs to create the so-called closure phase. The closure phase is insensitive to atmospheric turbulence effects; however, it is corrupted by photon-noise effects. The probability-density function of the error in the closure-phase estimate that is due to photon noise is derived as a function of the fringe visibility and is evaluated. It is shown that, for dim objects and low fringe visibility, several hundred to several thousand independent realizations of the closure phase must be averaged to obtain acceptable closure-phase variance.