Phasing piston error in segmented telescopes

To achieve a diffraction-limited imaging, the piston errors between the segments of the segmented primary mirror telescope should be reduced to λ/40 RMS. We propose a method to detect the piston error by analyzing the intensity distribution on the image plane according to the Fourier optics principle, which can capture segments with the piston errors as large as the coherence length of the input light and reduce these to 0.026λ RMS (λ = 633nm). This method is adaptable to any segmented and deployable primary mirror telescope. Experiments have been carried out to validate the feasibility of the method.