Rotational disturbance in laser-interferometric gravity gradiometry

Laser interferometers have been used for precise measurements of gravity and related effects. These include experiments to search for a fifth force and absolute ballistic gravimeters, which use a Michelson-type laser interferometer to measure the acceleration of a free-falling test mass. In these methods of instrumentation, the motion of free-falling test masses is measured using corner-cube laser interferometers, in which at least one retroreflector is embedded in each test mass. However carefully each of such test masses is released into free fall, a small amount of rotation is unavoidable which changes the optical path length and causes acceleration disturbance. This rotational disturbance could ultimately limit the measurement sensitivity of the laser interferometers. Various experimental and theoretical studies have been conducted to minimise the rotational disturbance in absolute ballistic gravimeters. This paper focuses on the rotational disturbance in laser-interferometric gravity gradiometers (LIGGs) that measure differential acceleration between two test masses freely falling at different heights in a vacuum. LIGGs can be configured to measure not only vertical gravity gradients, but also horizontal gradients, or gradients in both horizontal and vertical directions. However, only those to measure vertical gravity gradients have been constructed so far. Hence, in this paper, the term LIGGs specifically indicates the gravity gradiometers that measure vertical gravity gradients. Unlike absolute ballistic gravimeters, the LIGGs are, in principle, insensitive to ground vibrations; they can potentially detect some effects that are buried in seismic noise in absolute gravity data. To fully leverage this advantage of the LIGGs, it is crucial to keep the rotational disturbance to a minimum. Expressions for the rotational disturbance are derived and its magnitude is estimated based on available experimental data. The results show that the magnitude would not be more than 0.1 mu Gal /m in the measurement of vertical gravity gradients in a compact LIGG. Alternative designs and requirements for increasing the sensitivity of the LIGGs are also discussed.