Effect of radius mismatch on performance of segmented telescopic systems

There exist great interests in using segmented mirrors instead of monoliphic primary mirror to build large aperture telescopes. The use of segmented mirrors reduces the difficulties in fabrication, transportation and replication as well as decreases the impact of gravity. In the meanwhile, one of the grand challenges in this approach lies in matching the individual mirrors to yield the form of a continuous surface. The erroneous differences between the global radii of curvature (GROC) of the segmented mirrors have significant influence on image quality. In this paper, we present a model of segmented systems and an analysis technique which reveals the effect of these errors on the image quality. Our analytical results show that the GROC differences have great influence on image quality and the impact remains high despite of using active optics to compensate these errors. The local radii of curvature of individual mirror segment should be used to correct these errors. We propose a new approach to generate compensators that controls the local radius of curvature of each segment efficiently. Finally, through simulation results, we demonstrate that the new compensators can dramatically reduce the effect of radius mismatch.