Limitations on the control of hexagonal mirror segment figures by means of edge measurements

摘要

Giant segmented telescopes in general require in situ control of the figures of their hexagonal segments. The necessary inputs may be either direct, through surface measurements, or indirect, through measurements of the intersegment edge heights. We investigate the limitations on the indirect (edge height) control that follow from the geometrical properties of hexagonal surfaces and find that these may be substantial. In particular, there are many unmeasurable modes, which we construct and count systematically, and whose potential effect on the segment figure problem we discuss.