System Estimates Radius of Curvature of a Segmented Mirror

A system that estimates the global radius of curvature (GRoC) of a segmented telescope mirror has been developed for use as one of the subsystems of a larger system that exerts precise control over the displacements of the mirror segments. This GRoC-estimating system, when integrated into the overall control system along with a mirror-segment- actuation subsystem and edge sensors (sensors that measure displacements at selected points on the edges of the segments), makes it possible to control the GROC mirror-deformation mode, to which mode contemporary edge sensors are insufficiently sensitive. This system thus makes it possible to control the GRoC of the mirror with sufficient precision to obtain the best possible image quality and/or to impose a required wavefront correction on incoming or outgoing light. In its mathematical aspect, the system utilizes all the information available from the edge-sensor subsystem in a unique manner that yields estimates of all the states of the segmented mirror. The system does this by exploiting a special set of mirror boundary conditions and mirror influence functions in such a way as to sense displacements in degrees of freedom that would otherwise be unobservable by means of an edge-sensor subsystem, all without need to augment the edge-sensor system with additional metrological hardware. Moreover, the accuracy of the estimates increases with the number of mirror segments.