Approaching Free Fall on Two Degrees of Freedom: Simultaneous Measurement of Residual Force and Torque on a Double Torsion Pendulum

A torsion pendulum with 2 soft degrees of freedom (DOFs), realized by off-axis cascading two torsion fibers, has been built and operated. This instrument helps characterize the geodesic motion of a test mass for LISA Pathfinder or any other free-fall space mission, providing information on cross talk and other effects that cannot be detected when monitoring a single DOF. We show that it is possible to simultaneously measure both the residual force and the residual torque acting on a quasifree test mass. As an example of the investigations that a double pendulum allows, we report the measurement of the force-to-torque cross talk, i.e., the amount of actuation signal, produced by applying a force on the suspended test mass, that leaks into the rotational DOF, detected by measuring the corresponding (unwanted) torque.

Figure 1

A sketch of the PETER pendulum. A diagram of the GRS electrodes, surrounding the TM, is also shown: the gray electrodes feed ac bias while the black ones are for sensing and actuation. Labels 1 and 2 indicate two of the four electrodes sensing $x$ and $\phi$ DOFs: each one is paired in a bridge with an identical electrode on the opposite side.

Figure 2

Amplitude spectral density of the translational ($x$, black) and rotational ($\phi$, blue) DOFs of the double pendulum. The useful “free-fall” band extends above the resonances (1.3 and 2.0 mHz) till 30 mHz, where read-out noise becomes dominant in both spectra. The peak near 25 mHz results from the beats of a swinging doublet mode (see Ref. [14]).

Figure 3

Spectra of residual force (left panel) and torque (right panel) acting on the test mass. Read-out noise is shown in red.

Figure 4

Cross talk measurement (the black line) vs offset mean position (center of oscillation) inside the GRS. Data of a typical run are compared with the model predictions (the red line).