Capacitive sensing of test mass motion with nanometer precision over millimeter-wide sensing gaps for space-borne gravitational reference sensors

We report on the performance of the capacitive gap-sensing system of the Gravitational Reference Sensor on board the LISA Pathfinder spacecraft. From in-flight measurements, the system has demonstrated a performance, down to 1 mHz, that is ranging between 0.7 and \ud 1.8\ud \ud \ud aF\ud \ud Hz\ud −\ud 1\ud /\ud 2\ud . That translates into a sensing noise of the test mass motion within 1.2 and \ud 2.4\ud \ud nm\ud \ud Hz\ud −\ud 1\ud /\ud 2\ud in displacement and within 83 and \ud 170\ud \ud nrad\ud \ud Hz\ud −\ud 1\ud /\ud 2\ud in rotation. This matches the performance goals for LISA Pathfinder, and it allows the successful implementation of the gravitational waves observatory LISA. A \ud 1\ud /\ud f\ud tail has been observed for frequencies below 1 mHz, the tail has been investigated in detail with dedicated in-flight measurements, and a model is presented in the paper. A projection of such noise to frequencies below 0.1 mHz shows that an improvement of performance at those frequencies is desirable for the next generation of gravitational reference sensors for space-borne gravitational waves observation.