High precision six-degree-of-freedom interferometer for test mass readout

High precision six-degree-of-freedom sensing plays an important role in future gravitational space missions. In gravitational or geodesy missions, measurements of all six degrees of freedom of freely floating test mass are required for reducing the cross-coupling noise, which is frequently an important limiting factor in the performance. Interferometry and capacitive sensing have been successfully combined in LISA pathfinder to achieve six degrees of freedom measurements. In this paper, we report a six-degree-of-freedom interferometer system based on multiplex differential wavefront sensing and longitudinal pathlength sensing. Compared to conventional capacitive sensing or optical levers, it has a higher measurement accuracy. The results of our table-top experiment show motion in all six degrees of freedom of a cubic test mass are simultaneously measured with a translational and tilt sensitivity of 100 pm/Hz(1/2) and 10 nrad Hz(-1/2) above 1 Hz, respectively. The translational dynamic range is greater than +/- 10 mm with nonlinear residuals less than 6 mu m, and the tilt dynamic range is approximately +/- 500 mu rad with nonlinear residuals less than 60 mu rad. The coupling errors between multiple degrees of freedom are dominated by tilt-to-translation and tilt-to-tilt coupling, which are roughly 2-4 mu m and 15-25 mu rad, respectively, within a range of [-500 mu rad, +500 mu rad].