Mitigation of third order spherical, coma, and astigmatism using segmented mirrors

Constructing telescope pupil mirrors, most traditionally the primary mirror, from a series of hexagonal segments enables the construction of larger telescopes and offers a degree of aberration mitigation beyond what is feasible with traditional monolithic mirror design. The degree of correction possible varies as a function of the number of segments used to construct the mirror, the nature of the mirror surface, and the degrees of freedom available to adjust each segment. This presentation discusses the degree of aberration mitigation possible as the number of segments used increases from 6 to 60 for a constant aperture system. It includes considerations for powered or flat segmented mirrors for the cases where segmentation at other pupil positions besides the primary might be considered. It also includes the effects of 3 levels of segment adjustability: (a) piston and tilt only, (b) 6 degree of freedom, and (c) 6DOF plus radius of curvature adjustment.