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

Abstract

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.

Development of the primary mirror for CAS500-1 (Compact Advanced Satellite 500-1)

“…We use Eq. ( 1), which is the 2-clocking method [23], to obtain the gravity-free figure error S, where P 0° and P 180° are the 0° and 180° surface errors respectively, and R 180° is the 180° rotation operator.…”

Review on thermal and mechanical challenges in the development of deployable space optics

“…One of the mitigation strategies is using simulations with different mounting boundary conditions, and extracting the zero-gravity sag from the deflections resulting from pointing the mirror upward and downward. 17…”

Adjustable bipod flexures for mounting mirrors in a space telescope

“…The mirror and the optical interferometer are aligned parallel to the ground or perpendicular to the gravity direction. Extracting or calibrating nongravity surface figure errors is possible by rotating the mirror with respect to the optic axis (clocking) and combining the results thereof [8]. However, if there is a system requirement regarding modulation transfer function combined with a detector, image degrade due to gravity can hardly be compensated.…”

“…Figure 7 show the plots of the Z5 term with respect to the shim thickness obtained from experiments using an optical interferometer and computer simulations using FEA. We used the 2-clocking method to obtain systematic errors due to 1 g gravity [8]. We combined five measurements from 0°position, named P 0 , and five measurements from 180°position, named P 180 , resulting in 25 combinations of system error P s in the following equation:…”