Extracting the zero-gravity surface figure of a mirror through multiple clockings in a flightlike hexapod mount

An elegant and accurate way to determine the zero-gravity surface figure of an optic from ground-based interferometric metrology is to average the figures found in two or more configurations that are rotated with respect to the direction of gravity, so gravity forces in the frame of the optic cancel in the average. In a recent elucidation of this technique, we emphasized that care must be taken to ensure that mount forces at each attachment point similarly cancel, and we presented some specific mounting schemes that gave accurate zero-gravity surface determinations during fabrication and acceptance testing of the Space Interferometry Mission PT-M1 mirror. Here we show that multiconfiguration averaging techniques work well for the most important special case of a mirror in a flightlike hexapod mount clocked into either two or three symmetrically placed positions. We explicitly compute mount forces (axial forces in the six struts of the hexapod) and show that at any attachment point their average over multiple clocked configurations vanishes in the frame of the optic, ensuring the success of zero-gravity surface figure extraction.