<title>Co-phasing of segmented mirror telescopes with curvature sensing</title>

The applicability of the curvature method for co-phasing of segmented mirrors is investigated by means of simulations for the case of strongly defocused images. The simulations are performed for both the monochromatic and the white light as well. A simple wavefront reconstruction from curvature signal was made. The reconstruction quality of the piston modes and the aberrations up to the fourth order is analyzed. The dependence of the Central Intensity Ratio for a segmented mirror as a function of the rms segment's aberrations is presented. The effect of turbulence-induced distortions on the quality of mirror co-phasing is analyzed. It is shown that the local pistons and the local tip-tilts can be measured directly from the curvature signal without any phase recovering procedure. The results obtained show that, even in the presence of the atmospheric turbulence, the curvature method is sensitive enough to detect the errors of segmented mirrors.