Sensitivity of a "dispersed-speckles" piston sensor for multi-aperture interferometers and hypertelescopes

In multi-aperture interferometers and hypertelescopes, the piston errors can be determined from multi-spectral images of the speckle pattern using a 3-dimensional Fourier transform. We study the limiting magnitude of the method in the case of non-redundant apertures using analytical derivations and numerical simulations. We show specifically for the case of sub-r(0) apertures that a few photons per aperture within the full spectral bandwidth will suffice to measure piston errors. The method's sensitivity is thus comparable to that of the Shack-Hartmann and other methods used with monolithic apertures.