Christian Rothleitner

The European Comparison of Absolute Gravimeters 2011 (ECAG-2011) in Walferdange, Luxembourg: results and recommendations

We present the results of the third European Comparison of Absolute Gravimeters held in Walferdange, Grand Duchy of Luxembourg, in November 2011. Twenty-two gravimeters from both metrological and non-metrological institutes are compared. For the first time, corrections for the laser beam diffraction and the self-attraction of the gravimeters are implemented. The gravity observations are also corrected for geophysical gravity changes that occurred during the comparison using the observations of a superconducting gravimeter. We show that these corrections improve the degree of equivalence between the gravimeters. We present the results for two different combinations of data. In the first one, we use only the observations from the metrological institutes. In the second solution, we include all the data from both metrological and non-metrological institutes. Those solutions are then compared with the official result of the comparison published previously and based on the observations of the metrological institutes and the gravity differences at the different sites as measured by non-metrological institutes. Overall, the absolute gravity meters agree with one another with a standard deviation of 3.1 µGal. Finally, the results of this comparison are linked to previous ones. We conclude with some important recommendations for future comparisons.

Development of new free-fall absolute gravimeters

The design and first results of two free-fall absolute gravimeters are reported: a stationary gravimeter is designed and can be used as a reference system and a portable gravimeter is aimed at field measurements.The determination of the acceleration due to gravity is done interferometrically in both instruments. The whole fringe signal is digitized by a high-speed analogue-to-digital converter, which is locked to a rubidium frequency standard. This fringe recording and processing is novel as compared with commercial free-fall gravimeters, which use an electronic zero-crossing discrimination. Advantages such as the application of a zero-phase-shifting digital filter to the digitized data are depicted. The portable gravimeters mechanics deviate from the conventional type. Springs are used to accelerate and decelerate the carriage supporting the falling object.A detailed uncertainty budget is given for both gravimeters. The combined standard uncertainty for the portable and for the stationary gravimeter is estimated at 38.8 µGal and 16.6 µGal, respectively. The corresponding statistical uncertainties are 1.6 µGal (over one day of measurement) and 0.6 µGal (over one month of measurement).The different designs and dimensions of the new free-fall gravimeters can help to reveal unknown or so far underestimated systematic effects. The assessments of the uncertainties due to seismic noise and shock vibrations, and electronic phase shifts give validity to this assumption.

Results of the European Comparison of Absolute Gravimeters in Walferdange (Luxembourg) of November 2007

The second international comparison of absolute gravimeters was held in Walferdange, Grand Duchy of Luxembourg, in November 2007, in which twenty absolute gravimeters took part. A short description of the data processing and adjustments will be presented here and will be followed by the presentation of the results. Two different methods were applied to estimate the relative offsets between the gravimeters. We show that the results are equivalent as the uncertainties of both adjustments overlap. The absolute gravity meters agree with one another with a standard deviation of 2 μgal (1 gal = 1 cm/s2).

On the influence of the rotation of a corner cube reflector in absolute gravimetry

Test masses of absolute gravimeters contain prism or hollow retroreflectors. A rotation of such a retroreflector during free-fall can cause a bias in the measured g-value. In particular, prism retroreflectors produce phase shifts, which cannot be eliminated. Such an error is small if the rotation occurs about the optical centre of the retroreflector; however, under certain initial conditions the error can reach the microgal level. The contribution from these rotation-induced accelerations is calculated.

Second-order Doppler-shift corrections in free-fall absolute gravimeters

In a free-fall absolute gravimeter usually a Michelson type interferometer is employed to track the trajectory of a freely falling retroreflector. The accelerated motion of the retroreflector produces a Doppler-shift in the laser wavelength. From the interference signal (beat signal) of the Doppler-shifted and the reference electromagnetic waves the relative motion of the freely falling retroreflector with respect to an inertial reference retroreflector is reconstructed. Considerations of second-order Doppler-shift terms lead to a correction in the acceleration due to gravity of several microgals (1??Gal = 10?nm?s?2). This correction is commonly called speed of light correction. To date different correction formulae have been proposed, which differ by several microgals.In this paper we review several previous publications and show the reasons for the different results.

A method for adjusting the centre of mass of a freely falling body in absolute gravimetry

In absolute gravimeters, rotation of the falling body causes a systematic error. This error can be minimized by coinciding the centre of mass (COM) of the body with its optical centre (OC). A method to measure the distance between these centres in 3D space is described. The method is based on a mechanical balancing technique. Using this method, the COM of a hollow corner cube mirror assembly is adjusted to the OC to within (43 ? 16)??m. An uncertainty budget is given.

On the gravimetric contribution to watt balance experiments

It has been recommended that the relative standard uncertainty of the numerical value of the Planck constant required for the redefinition of the kilogram should not exceed 2???10?8. To reach this goal using experiments based on a watt balance, the free-fall acceleration (g) traceable to the SI, at a given point and a given time, needs to be known with a sufficiently small uncertainty well below 2???10?8. Reducing the uncertainty in g allows the other uncertainties related to the watt balance to be increased. Instead of a simultaneous operation of an absolute gravimeter with a watt balance, we propose an alternative approach and demonstrate that a standard uncertainty below 5??Gal (relative uncertainty of 5???10?9) is reachable under the conditions at BIPM. Further decreasing the uncertainty could significantly increase commitments in terms of personnel and equipment and would not significantly improve the uncertainty targeted for the BIPM watt balance experiment. A 5??Gal uncertainty might also satisfy the needs of other watt balance experiments underway or planned. In our approach we combine the following information: (1) the Key Comparison Reference Values obtained from the CCM.G-K1, a key comparison carried out in the frame of the International Comparison of Absolute Gravimeters in 2009 (ICAG2009); (2) the accurate gravity network established using the qualified absolute and relative gravimeters; (3) temporal gravity variations based on observed Earth-tide parameters and modelled effects of polar motion and atmospheric mass redistribution; (4) uncertainty estimates that account for non-modelled effects; (5) the option to carry out absolute gravity measurements once every one or two years with two or more gravimeters for monitoring the stability of the gravity field at the BIPM.

Improvements of the MPG-2 transportable absolute ballistic gravimeter

The MPG-2 (Max-Planck-Gravimeter) is a transportable absolute gravimeter built on a classical free-fall scheme to measure the local gravity value. With significant improvements and further investigations in recent years, the standard deviation of the mean for a typical measurement over 12 h to 24 h is 1.0 µGal to 3.0 µGal (1 µGal = 10−8 m s−2), and the combined standard uncertainty is estimated to be less than 10 µGal. The major improvements include the new interferometer design and alignment, longer drop length, reduced recoil effects and demagnetization of the falling body. The revised uncertainty budget and new measurement results of MPG-2 are reported. The results of observations at the reference gravity station Bad Homburg confirmed the revised uncertainty budget.

Comparison of three digital fringe signal processing methods in a ballistic free-fall absolute gravimeter

This paper reports results of comparison of three digital fringe signal processing methods implemented in the same free-fall absolute gravimeter. A two-sample zero-crossing method, a windowed second-difference method and a method of non-linear least-squares adjustment on the undersampled fringe signal are compared in numerical simulations, hardware tests and actual measurements with the MPG-2 absolute gravimeter, developed at the Max Planck Institute for the Science of Light, Germany. The two-sample zero-crossing method realizes data location schemes that are both equally spaced in distance and equally spaced in time (EST) along the free-fall trajectory. The windowed second-difference method and the method of non-linear least-squares adjustment with complex heterodyne demodulation operate with the EST data. Results of the comparison verify an agreement of the three methods within one part in 109 of the measured gravity value, provided a common data location scheme is considered.

Accuracy assessment of the two-sample zero-crossing detection in a sinusoidal signal

The accuracy of a two-sample zero-crossing detection method is assessed by analytical uncertainty propagation and is verified in numerical simulations. Approximated expressions are given to evaluate uncertainty components due to linear interpolation, quantization, white noise and time jitter. The combined standard uncertainty of a detected zero phase is expressed as a function of the signal frequency, power of external noise and parameters of the digitizer used. The evaluation of the uncertainty of the measurand, derived from several detected zero-crossings, is illustrated with applications in frequency, displacement and free-fall acceleration measurements. The reported results can be used for uncertainty analysis and parameter optimization of a measurement system or a procedure, involving processing of sinusoidal signals.