(ed.). Gravitational waves (IOP, 2001)(422s).

Description of the LISA mission 125the antenna is 40 nm/rtHz. With only shot noise considered, the correspondingvalue would be 22 nm/rtHz, and with beam pointing jitter included also, thevalue becomes 30 nm/rtHz. Other error sources considered explicitly are asfollows: residual laser phase noise after the correction procedure discussed earlieris applied; noise in the ultra-stable oscillators after a similar correction procedure;noise in the laser phase measurements and phase locks; and scattered light effects.The 40 nm/rtHz total error allocation for the difference in round-trip paths for twoarms corresponds to 20 nm/rtHz for determining the difference in lengths for thetwo arms.10.1.4 Free mass sensorsHistorically, the first free mass sensor was developed jointly by the Johns HopkinsUniversity Applied Physics Laboratory and by Stanford University, and was flownon the TRIAD satellite in 1972 [16]. A spherical test mass was contained in aspherical cavity with three opposing pairs of capacitive electrodes on the insideof the housing for sensing the relative position of the test mass. Whenever theatmospheric drag caused the housing to move a few millimetres with respect tothe test mass, pulsed thrusters on the satellite fired to keep it centred on averageon the test mass. Care was taken to keep forces on the test mass other than thosedue to external gravitational fields as small as possible. Thus, the orbit of thesatellite was nearly drag-free, and was much more predictable than normal. Thetheory of such drag-free systems had been given earlier in 1964 by Lange [17].There is a close connection between free mass sensors and the highperformanceforce-rebalance accelerometers developed over the last three decadesby the Office National d’Etudes et de Recherches Aerospatiales (ONERA) in Parisfor flight on various missions. The basic approach in the accelerometers is tomeasure the position of a free or nearly free test mass inside a housing by meansof capacitive electrodes on the inside of the housing. Forces are then applied tothe test mass by means of voltages on the electrodes to keep the test mass centredin the housing. The required voltages are measures of the accelerations along thethree perpendicular axes.The first such accelerometer designed and built by ONERA was flown from1975 to 1979 on the French CASTOR-D5B satellite. It had a spherical test mass.However, later ONERA-designed accelerometers have used test masses in theform of rectangular parallelepipeds. The first such design, called the GRADIOaccelerometer, was for possible use in a proposed gravity gradiometer mission(ARISTOTLES) to map the Earth’s gravity field, and has been the basis for anumber of later designs.The test mass for the GRADIO accelerometer is 4 cm by 4 cm by 1 cm indimensions. The material used for the test mass is a Pt–Rh alloy with a densityof about 20 g cm −3 . The housing is made of ultra-low expansion glass (ULE),with a gold coating on the inside that is carefully patterned to form the capacitiveplate electrodes. The gaps between the plates are recessed and kept very small