A method for high-precision measuring differential transformer asymmetry.

The differential transformer is an important component in the front-end electronics of high-precision capacitive position sensing circuits, which are widely employed in space inertial sensors and electrostatic accelerometers. The position sensing offset, one of the space inertial sensors' most critical error sources in the performance range, is dominated by the differential transformer asymmetry and requires a high-precision evaluation. This paper proposes a method to assess differential transformers' asymmetry and realize a prototype circuit to test a transformer sample. The results show that the asymmetry measurement precision can achieve 0.6 ppm for the transformer with an asymmetry level of about -278.2 ppm.

High-precision laser beam lateral displacement measurement based on differential wavefront sensing.

Accurately lateral displacement measurement is essential for a vast of non-contact sensing technologies. Here, we introduce a high-precision lateral displacement measurement method based on differential wavefront sensing (DWS). Compared to the conventional differential power sensing (DPS) method, the DWS method based on phase readout has the potential to achieve a higher resolution. The beam lateral displacement can be obtained by the curvature distribution of the wavefront on the surface of the detector. According to the theoretical model of the DWS method, the sensitivity of the lateral displacement can be greatly improved by increasing the wavefront curvature of the measured laser beam by means of lenses. An optical system for measuring the lateral displacement of the laser beam is built and calibrated by a high-precision hexapod. The experimental results show that the DWS-based lateral displacement measurement achieves a resolution of 40 pm/Hz1/2 (at 1-10 Hz) with a linear range of about 40 µm, which is consistent with the theoretical model. This technique can be applied to high-precision multi-degree-of-freedom interferometers.

Identification and compensation of quadratic terms of a space electrostatic accelerometer.

The ultra-sensitive space electrostatic accelerometers have been successfully employed in the Earth's gravity field recovery missions and the space gravitational experiments. Since the accelerometer output in the measurement bandwidth can be influenced by the orbital high-frequency disturbances due to the second-order nonlinearity effects, the relevant quadratic term must be accurately compensated to guarantee the accuracy of the electrostatic accelerometer. In this paper, three sources of the quadratic term are studied and formulated. They are the offset of the test mass in the housing due to the bias of the capacitive position transducer, the asymmetry of the electrode area, and the asymmetry of the actuation electronics. Two feasible compensation methods and an identification means are proposed. Compensation is achieved by adjusting the test mass actual working position or the asymmetry factor of the feedback actuation voltage. Identification is conducted by applying a periodic high frequency signal on the electrodes. Finally, the proposed methods are demonstrated, in view of future space applications, by suspending the accelerometer test mass on a torsion pendulum.

Measurements of the gravitational constant using two independent methods.

The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way to resolve this issue is to measure G using a number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10-11 and 6.674484 × 10-11 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

Self-calibration method of the bias of a space electrostatic accelerometer.

The high precision space electrostatic accelerometer is an instrument to measure the non-gravitational forces acting on a spacecraft. It is one of the key payloads for satellite gravity measurements and space fundamental physics experiments. The measurement error of the accelerometer directly affects the precision of gravity field recovery for the earth. This paper analyzes the sources of the bias according to the operating principle and structural constitution of the space electrostatic accelerometer. Models of bias due to the asymmetry of the displacement sensing system, including the mechanical sensor head and the capacitance sensing circuit, and the asymmetry of the feedback control actuator circuit are described separately. According to the two models, a method of bias self-calibration by using only the accelerometer data is proposed, based on the feedback voltage data of the accelerometer before and after modulating the DC biasing voltage (Vb) applied on its test mass. Two types of accelerometer biases are evaluated separately using in-orbit measurement data of a space electrostatic accelerometer. Based on the preliminary analysis, the bias of the accelerometer onboard of an experiment satellite is evaluated to be around 10-4 m/s2, about 4 orders of magnitude greater than the noise limit. Finally, considering the two asymmetries, a comprehensive bias model is analyzed. A modified method to directly calibrate the accelerometer comprehensive bias is proposed.

Low frequency noise elimination technique for 24-bit Σ-Δ data acquisition systems.

Low frequency 1/f noise is one of the key limiting factors of high precision measurement instruments. In this paper, digital correlated double sampling is implemented to reduce the offset and low frequency 1/f noise of a data acquisition system with 24-bit sigma delta (Σ-Δ) analog to digital converter (ADC). The input voltage is modulated by cross-coupled switches, which are synchronized to the sampling clock, and converted into digital signal by ADC. By using a proper switch frequency, the unwanted parasitic signal frequencies generated by the switches are avoided. The noise elimination processing is made through the principle of digital correlated double sampling, which is equivalent to a time shifted subtraction for the sampled voltage. The low frequency 1/f noise spectrum density of the data acquisition system is reduced to be flat down to the measurement frequency lower limit, which is about 0.0001 Hz in this paper. The noise spectrum density is eliminated by more than 60 dB at 0.0001 Hz, with a residual noise floor of (9 ± 2) nV/Hz(1/2) which is limited by the intrinsic white noise floor of the ADC above its corner frequency.