Effect of vibration noise with fixed phase on absolute gravimetry applying vibration isolator

Abstract

Absolute gravimeter, an instrument which is applied to laser interferometry or atom interferometry for measuring the gravitational acceleration <i>g</i> (approximately 9.8 m/s<sup>2</sup>), plays an important role in metrology, geophysics, geological exploration, etc. To achieve a high accuracy of several microGals (μGal, 1μGal = 1 × 10<sup>–8</sup> m/s<sup>2</sup>), a vertical vibration isolator is widely employed in the absolute gravimeter to protect the reference object (a retro-reflector or a mirror) from being disturbed by ground vibration noises. However, the reference object in vibration isolator may still move due to isolator’s response to the impulse caused by the self-vibration effect in laser-interferometry gravimeter, or the forced vibration of the ferromagnetic component in the isolator under the varying magnetic field of magneto-optical traps (MOTs) in atom-interferometry gravimeter. This vibration of the reference object has a fixed phase relative to the detection of the free-fall of a falling object or atoms, leading an additional systematic error to be introduced into measured <i>g</i> value. In this paper, the physical models of four typical vertical vibration isolators used in the current absolute gravimeters are introduced, i.e. a passive Minus K isolator, a passive Lacoste isolator, a one-stage active isolator, and a double-stage active isolator. The simulation models of these isolators are also created with specific resonance periods. Taking a laser-interferometry gravimeter for example, the responses of these isolators under impulse input are analyzed, proving that the real vibration of the reference object, namely the output of each isolator, has a fixed phase relative to the detection of the fringe signal, which indicates the trajectory of the free-falling object, hence resulting in an additional systematic error. To provide a detailed evaluation, firstly the vibration of the reference object under an impulse, a seismic noise, and a random noise, which represent typical ground vibrations, are obtained by running the simulation. Then the corresponding errors in the calculation of <i>g</i> value are presented. Besides, the experimental results of T-1 laser-interferometry gravimeter at a noisy site in Tsinghua University, with either a Minus K isolator or a Superspring isolator used, are compared with the simulated results. According to the above simulations and experiments, the systematic error introduced by the vibration of resonance object in a Minus K isolator or a one-stage active isolator under impulse can respectively exceed 600 μGal or 10 μGal, while the error with the object in a Lacoste isolator or a double-stage active isolator can be neglected. Therefore, it is better to use a double-stage active vibration isolator in absolute gravimeter to avoid this systematic error and achieve higher measurement accuracy. With more information about the forced vibration in the isolators under varying magnetic fields of MOT, the systematic error introduced by the vibration of reference object can also be specifically evaluated in the future.