Actuation crosstalk in free-falling systems: Torsion pendulum results for the engineering model of the LISA pathfinder gravitational reference sensor

In this paper we report on measurements on actuation crosstalk, relevant to the gravitational reference sensors for LISA Pathfinder and LISA. In these sensors, a Test Mass (TM) falls freely within a system of electrodes used for readout and control. These measurements were carried out on ground with a double torsion pendulum that allowed us to estimate both the torque injected into the sensor when a control force is applied and, conversely, the force leaking into the translational degree of freedom due to the applied torque. The values measured on our apparatus (the engineering model of the LISA Pathfinder sensor) agree to within 0.2% (over a maximum measured crosstalk of 1%) with predictions of a mathematical model when measuring force to torque crosstalk, while it is somewhat larger than expected (up to 3.5%) when measur- ing torque to force crosstalk. However, the values in the relevant range, i.e. when the TM is well centered ( ±10 μm) in the sensor, remain smaller than 0.2%, satisfying the LISA Pathfinder requirements.