Interferometry for the space mission LISA Pathfinder

In 1916 Albert Einstein published the Theory of General Relativity (GRT). One of its predictions is the existence of gravitational waves, that is accelerated matter could emit energy in the form of gravitational waves, similar to the emission of electromagnetic waves by an accelerated charge. However, compared with electromagnetic waves, where the lowest order is a dipole, in the case of gravitational waves the lowest order is a quadrupole, because mass does not exhibit the positive/negative signs like electric charge. General Relativity Theory says that gravitational waves should propagate with the speed of light [6]. The first indirect proof of the existence of gravitational waves was provided by Russell Hulse and Joseph Taylor [7] [8]. They tracked a double star system over several years and detected a decrease of the revolution time of the Pulsar PSR 1913+16 arround its neighbour star. The energy emission corresponding to this agrees within 0.5 % with the GRT prediction for the energy lost through gravitational waves. For this observation Hulse and Taylor were awarded the Nobel prize for physics in 1993. A gravitational wave would stretch and compress space perpendicular to its direction of propagation. However, the elongations occurring would be so tiny that a direct measurement has not yet been done. It is conceivable though, that in the near future it should be possible to measure gravitational waves caused by violent astronomic events such as the explosion of a supernova or the inspiral of a double star system. The advanced detectors on ground and in space will open a new field of astronomy. Since the early 1960s there are huge efforts dedicated to detecting gravitational waves. There are different experimental setups. On the one hand, there are resonant detectors with a resonance frequency range of a few 100 Hz up to a few kHz, which can be excited by a gravitational wave. However those detectors only cover a small range of frequencies. On the other hand, there are experiments to measure gravitational waves with laser interferometry between separated masses. In total there are at this time six interferometrical gravitational earth-based detectors [9], working in a world wide collaboration: TAMA300 (Japan) [10], GEO600 (Germany) [11], VIRGO (Italy/France) [12] and LIGO [13], three detectors, (USA). All these detectors are based on Michelson interferometry [14] and are limited in sensitivity below 10 Hz due to the natural seismic and gravity gradient noise. A new experiment, LISA, a NASA and ESA joint mission, is planned as an interferometric detector in space. Laser Interferometer Space Antenna (LISA) is an ensemble of three identical satellites moving in a heliocentric orbit. In doing so they would form an equilateral triangle with a five million km side length and with an offset of 20○ behind the Earth’s orbit. This structure rotates around itself once per year. The triangular plane is tilted by 60o with respect to the ecliptic. The mission is planned to be launched in 2018. LISA Pathfinder (LPF) is planned as a test mission of LISA consisting of only one satellite and expected to launch in 2011. The aim of LPF is not to detect gravitational waves, but rather to prove and test key components for LISA. There will be two experiments on board, the American Disturbance Reduction System (DRS) [15] and the European LISA Technology Package (LTP). One of the key tasks of LTP is to measure the relative displacement between two drag-free falling test masses with a noise level of 10 pm/ √ Hz in the frequency range of 3 – 30 mHz [16]. Figure 2 shows the engineering model of the optical bench for LTP.