Criterion of phasing in the presence of segment aberrations

In order to achieve a spatial resolution comparable to a monolithic telescope of the same diameter, the segmented mirror surface must be phased with an accuracy about V20 wavefront rms , which is comparable with the accuracy of the segment figure. During the phasing procedure, piston, tip-tilt are controlled to achieve the best image quality of the telescope. The residual rms wavefront error of whole aperture taken as the merit function reaches minimum analytically when the least-square-fit plane of tested segment meets together with that of reference mirror, which means that "phasing" is a statistical mood of the whole aperture, not to match some small areas of the segments. The impact of segment aberration on the whole aperture residual rms wavefront error is simulated using the whole segment aperture sensing and edge sensing respectively. By the analytical and numerical simulation, it is demonstrated that the whole segment aperture phase sensing can make a better image quality than the edge sensing.