Adaptive-optics correction of a stellar interferometer with a single pyramid wave-front sensor

We investigate the pyramid wave-front sensor's capability to reconstruct in a closed loop, with only one sensor, the wave fronts on both apertures of a stellar interferometer, including the differential piston: The method consists of placing the principal element of this sensor, namely, a refractive-square-based pyramid, in a combined focal plane of the interferometer instead of using two sensors, one for each individual telescope. We show that the sensor signals allow one to measure the wave-front aberrations on both apertures and the differential piston at the same time. The performance of an adaptive-optics loop is computed numerically for the Large Binocular Telescope in terms of differential-piston rejection under several conditions. The results show that atmospheric correction including differential-piston compensation is possible as long as the corrected Strehl ratio at the wave-front sensing wavelength is greater than 20%.