Active supports and force optimization for a 3.5-m honeycomb sandwich mirror

We describe the active support system and optimization of support forces for a 3.5-m honeycomb sandwich mirror. The optimization was based on interferometric figure measurements made in a vibration-isolated test tower. We obtained actuator influence functions by measurement and by finite-element analysis. The two sets of influence functions are similar in shape, but the computed figure changes are 25% smaller in magnitude than the measured figure changes. We achieved a figure accuracy of 25 nm rms surface error with the computed influence functions and only slightly worse with the measured influence functions, but were unable to reproduce the 21-nm rms surface error obtained on the passive polishing support. This implies that subtle differences between the polishing support and operational support caused small, uncorrectable figure changes. The optimization was performed by singular-value decomposition of the influence functions into normal modes. The best results were obtained using 20 - 30 out of a possible 37 modes.