High-precision ground simulator for laser tracking of gravity satellite.

Inter-satellite laser ranging is a key technology to improve the measurement precision of gravity satellites in future missions. However, it requires a stable laser link between satellites, which would be affected by external disturbances in space and internal couplings of satellite components. This paper presents a dynamic model to describe the tracking error and proposes a high-precision satellite simulator for the validation of inter-satellite laser tracking. Then, the noises of the sensors and actuators are tested to give the theoretical tracking performance of the simulator. Finally, the laser tracking performance is validated through two experiments: fixed-position tracking and motion tracking. The experimental results show that the measured tracking error of the satellite platform is better than 10 mrad/Hz in the fixed-position tracking and 50 mrad/Hz in the motion tracking. Furthermore, the optical platform can reduce the measured tracking error to 80 µrad/Hz in both two experiments. This work provides a theoretical foundation for optimizing laser tracking performance in space missions, and the proposed simulator has demonstrated a potential for mission simulation with laser tracking.

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.

Ground testing of release impulse for the aluminum cubic test mass with a compound pendulum for the TianQin project.

In the space-borne gravitational wave detection TianQin project, the locking and releasing of test mass is one of the key technologies. The test mass will be locked during the spacecraft launch and then released to free fall for the science phase. The residual release impulse is required to be on the order of magnitude of 10-5 kg m/s, which allows us to capture the test mass by the force authority of the capacity control. In this paper, the release impulse of the aluminum test mass is measured with a compound pendulum for the TianQin project. The test mass is locked by two tips from opposite positions, and the release impulse is obtained from the oscillation of the pendulum. When the aluminum test mass is locked and released by the stainless steel and aluminum tips, the release impulses and their uncertainties are on the order of magnitude of 10-5and 10-7 kg m/s, respectively. This provides a feasible measurement scheme for the impulse testing in the TianQin project.

A construction method of the quasi-monolithic compact interferometer based on UV-adhesive bonding.

Quasi-monolithic interferometers play a crucial role in high-precision measurement experiments, including gravitational wave detection, inertial sensing, vibrometry, and seismology. Achieving high stability and accuracy in such interferometers requires a method for bonding the optical components to a baseplate. While optical contact bonding and silicate bonding are common methods, UV adhesives offer advantages such as controlled curing and low geometrical requirements for optical components and baseplates. This paper presents a detailed construction method for a quasi-monolithic compact interferometer based on UV-adhesive bonding. We built two types of interferometers using this method: a 100 × 100 × 20 mm3 Mach-Zender homodyne interferometer with unequal arm lengths of about 100 mm for laser frequency noise monitoring and a heterodyne interferometer as a displacement sensing head, sizing 20 × 30 × 20 mm3. Our Mach-Zender interferometer achieved a phase noise level of 2µradHz at 1 Hz and an equivalent laser frequency noise monitoring sensitivity of about 1kHz/Hz at 1 Hz. The compact heterodyne interferometer sensing head showed a sensitivity level of 1pm/Hz in translation and 0.2nrad/Hz in two tilts above 0.4 Hz. Our tests demonstrate that quasi-monolithic compact interferometers based on UV-adhesive bonding can achieve high sensitivity levels at the pico-meter and nano-radian scales.

A method and its validation for measuring the absolute time-delay of the read-out system of a space electrostatic accelerometer.

High-precision accelerometers play an important role in satellite gravity field missions to measure the non-conservative forces acting on the satellites. To map the Earth's gravity field, the accelerometer data must be time-tagged using the on-board global navigation satellite system time reference. For example, in the Gravity Recovery and Climate Experiment mission, the time-tag error of the accelerometers must be within 0.1 ms with respect to the satellite clock. To realize this requirement, the time delay between the actual measurement time and the nominal time of the accelerometer should be considered and corrected. This paper presents the techniques for measuring the absolute time delay of an electrostatic accelerometer on the ground, where this delay is mainly introduced by the low-noise scientific data read-out system, which is based on a Σ-Δ (sigma-delta) analog-to-digital converter (ADC). First, the time-delay sources of the system are theoretically analyzed. Then, a time-delay measurement method is proposed, and its principle and system error are presented. Finally, a prototype is built to demonstrate and investigate the feasibility of the method. Experimental results show that the absolute time delay of the read-out system is 150.80 ± 0.04 ms. This important value is the basis for the final time-tag error correction of the scientific accelerometer data. Meanwhile, the time-delay measurement method described in this paper is also useful for other data acquisition systems.

A high precision surface potential imaging torsion pendulum facility to investigate physical mechanism of patch effect.

The physical mechanism of the patch effect is still an open question. Thus, a high-precision surface potential mapping facility based on a specially designed electrostatically-controlled torsion pendulum is proposed in this paper. The facility not only features high sensitivity and a two-dimensional mapping function but also adapts to various measurement requirements for centimeter-sized samples. The sensitivity of the torsion pendulum reaches about 2.0 × 10-14 N m/Hz1/2 in a frequency range of 1-8 mHz. The temporal variation of the surface potential can be detected at a level of 30 µV/Hz1/2 with a probe whose surface area is 7 mm2. The potential spatial distribution resolution comes to 0.1 mm2 at a level of 40 µV with 1 h integration time.

Bias Stability Investigation of a Triaxial Navigation-Compatible Accelerometer with an Electrostatic Spring.

The bias stability performance of accelerometers is essential for an inertial navigation system. The traditional pendulous accelerometer usually has a flexible connection structure, which could limit the long-term bias stability. Here, based on the main technologies employed in previous space missions of our group, we developed a terrestrial triaxial navigation-compatible accelerometer. Because there is no mechanical connection between the inertial test mass and the frame, the bias performance relies on the stability of the equivalent electrostatic spring, where further sources are analyzed to get the optimal electrostatic force scheme. To investigate the bias stability under different ranges, the vertical and horizontal measurement ranges are designed at 5 g and ±10 mg, respectively. A low-noise high-voltage levitation scheme is adopted to extend the vertical measurement range from sub-mg to more than earth's 1-g gravity. Finally, the experimental validation results show that the 24-h bias stability of vertical and two horizontal directions come to 13.8 µg, 0.84 µg, and 0.77 µg, respectively.

Precision improvement of patch potential measurement in a scanning probe equipped torsion pendulum.

Patch effect is important for ultra-sensitive experiments involving closely spaced conducting surfaces. A scanning probe equipped torsion pendulum is an experimental apparatus for measuring spatial resolved patch potential on conductive surfaces. An effective approach to improve its measurement precision is by the optimization on the amplitude and frequency of the injected signal in the probe. In this paper, a method based on single- and double-frequency signal injection modes is proposed. The analysis results demonstrate that the potential resolution could achieve the level of 2-4 µV/Hz1/2. In the same integration time, the surface potential precision in the double-frequency mode is twice better than that in the single-frequency mode. In addition, when achieving the same measurement precision, the double-frequency mode takes less time than the single-frequency mode, which improves the measuring efficiency.

2.4 ng/√Hz low-noise fiber-optic MEMS seismic accelerometer.

This paper introduces a fiber-optic microelectromechanical system (MEMS) seismic-grade accelerometer that is fabricated by bulk silicon processing using photoresist/silicon dioxide composite masking technology. The proposed sensor is a silicon flexure accelerometer whose displacement transduction system employs a light intensity detection method based on Fabry-Perot interference (FPI). The FPI cavity is formed between the end surface of the cleaved optical fiber and the gold-surfaced sidewall of the proof mass. The proposed MEMS accelerometer is fabricated by one-step silicon deep reactive ion etching with different depths using the composite mask, among which photoresist is used as the etching-defining mask for patterning the etching area while silicon dioxide is used as the depth-defining mask. Noise evaluation experiment results reveal that the overall noise floor of the fiber-optic MEMS accelerometer is 2.4 ng/H z at 10 Hz with a sensitivity of 3165 V/g, which is lower than that of most reported micromachined optical accelerometers, and the displacement noise floor of the optical displacement transduction system is 208 fm/H z at 10 Hz. Therefore, the proposed MEMS accelerometer is promising for use in high-performance seismic exploration applications.

Noise investigation of an electrostatic accelerometer by a high-voltage levitation method combined with a translation-tilt compensation pendulum bench.

A high precision electrostatic accelerometer has widely been employed to measure gravity gradients and detect gravitational waves in space. The high-voltage levitation method is one of the solutions for testing electrostatic accelerometers on the ground, which aims at simultaneously detecting all six-degree-of-freedom movements of the electrostatic accelerometers engineering and flight prototypes. However, the noise performance in the high-voltage levitation test is mainly limited by seismic noise. The combined test of the accelerometer and vibration isolation platform is adopted to improve the detection precision of the high-voltage levitation method. In this paper, a high precision electrostatic accelerometer prototype is developed after designed appropriate mechanical parameters with a test mass weighing 300 g and with an estimated resolution of 2 × 10-12 m/s2/Hz1/2 from 0.01 to 0.4 Hz. Such a prototype is tested by the high-voltage levitation method, its measurement noise on the ground is mainly limited by the seismic noise, which is about 5 × 10-7 m/s2/Hz1/2 around 0.2 Hz and about 4 × 10-8 m/s2/Hz1/2 around 0.1 Hz. A vibration isolation pendulum bench based on the translation-tilt compensation principle is adopted for accelerometer prototype combined tests to suppress the seismic noise, which has a large bench area and the ability to adjust the tilt angle precisely. The measured accelerometer noise of the combined test with the translation-tilt compensation pendulum has reached 3 × 10-9 m/s2/Hz1/2 around 0.2 Hz, and it is about two orders of magnitude lower than the measurement noise on the ground. The combined test method provides technical guidance for further improving the noise level of ground test in the future.

The earth's gravity field recovery using the third invariant of the gravity gradient tensor from GOCE.

Due to the independence of the gradiometer instrument's orientation in space, the second invariant [Formula: see text] of gravity gradients in combination with individual gravity gradients are demonstrated to be valid for gravity field determination. In this contribution, we develop a novel gravity field model named I3GG, which is built mainly based on three novel elements: (1) proposing to utilize the third invariant [Formula: see text] of the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient tensor, instead of using the [Formula: see text], similar to the previous studies; (2) applying an alternative two-dimensional fast fourier transform (2D FFT) method; (3) showing the advantages of [Formula: see text] over [Formula: see text] in the effect of measurement noise from the theoretical and practical computations. For the purpose of implementing the linearization of the third invariant, this study employs the theory of boundary value problems with sphere approximation at an accuracy level of [Formula: see text]. In order to efficiently solve the boundary value problems, we proposed an alternative method of 2D FFT, which uses the coherent sampling theory to obtain the relationship between the 2D FFT and the third invariant measurements and uses the pseudo-inverse via QR factorization to transform the 2D Fourier coefficients to spherical harmonic ones. Based on the GOCE gravity gradient data of the nominal mission phase, a novel global gravity field model (I3GG) is derived up to maximum degree/order 240, corresponding to a spatial resolution of 83 km at the equator. Moreover, in order to investigate the differences of gravity field determination between [Formula: see text] with [Formula: see text], we applied the same processing strategy on the second invariant measurements of the GOCE mission and we obtained another gravity field model (I2GG) with a maximum degree of 220, which is 20 degrees lower than that of I3GG. The root-mean-square (RMS) values of geoid differences indicates that the effects of measurement noise of I3GG is about 20% lower than that on I2GG when compared to the gravity field model EGM2008 (Earth Gravitational Model 2008) or EIGEN-5C (EIGEN: European Improved Gravity model of the Earth by New techniques). Then the accuracy of I3GG is evaluated independently by comparison the RMS differences between Global Navigation Satellite System (GNSS)/leveling data and the model-derived geoid heights. Meanwhile, the re-calibrated GOCE data released in 2018 is also dealt with and the corresponding result also shows the similar characteristics.

A charge control method for space-mission inertial sensor using differential UV LED emission.

Various space missions and applications require the charge on isolated test masses to be strictly controlled because any unwanted disturbances will introduce acceleration through the Coulomb interaction between the test masses and their surrounding conducting surfaces. In many space missions, charge control has been realized using ultraviolet (UV) photoemission to generate photoelectrons from metal surfaces. The efficiency of photoelectron emission strongly depends on multiple physical parameters of gold-coated surfaces, such as the work function, reflectivity, and quantum yield. Therefore, to achieve satisfactory charge control performance, these parameters need to be measured accurately. This paper describes a charge control method that achieves self-adaptive charge neutralization while removing the need to measure the above-mentioned physical parameters. First, to explain the principle, a differential illumination model is constructed based on the typical structure of an inertial sensor. A charge management system based on a torsion pendulum system is then introduced along with an UV light emitting diode coupling system. Finally, experimental results are obtained in a vacuum chamber system with a pressure of 10-7 mbar, showing that precise calibration allows the test mass potential to be automatically controlled below 10 mV without considering the physical parameters or measuring the potential of the test mass before or after the control process.

Investigation on Stray-Capacitance Influences of Coaxial Cables in Capacitive Transducers for a Space Inertial Sensor.

Ultra-sensitive inertial sensors are one of the key components in satellite Earth's gravity field recovery missions and space gravitational wave detection missions. Low-noise capacitive position transducers are crucial to these missions to achieve the scientific goal. However, in actual engineering applications, the sensor head and electronics unit usually place separately in the satellite platform where a connecting cable is needed. In this paper, we focus on the stray-capacitance influences of coaxial cables which are used to connect the mechanical core and the electronics. Specially, for the capacitive transducer with a differential transformer bridge structure usually used in high-precision space inertial sensors, a connecting method of a coaxial cable between the transformer's secondary winding and front-end circuit's preamplifier is proposed to transmit the AC modulated analog voltage signal. The measurement and noise models including the stray-capacitance of the coaxial cable under this configuration is analyzed. A prototype system is set up to investigate the influences of the cables experimentally. Three different types and lengths of coaxial cables are chosen in our experiments to compare their performances. The analysis shows that the stray-capacitance will alter the circuit's resonant frequency which could be adjusted by additional tuning capacitance, then under the optimal resonant condition, the output voltage noises of the preamplifier are measured and the sensitivity coefficients are also calibrated. Meanwhile, the stray-capacitance of the cables is estimated. Finally, the experimental results show that the noise level of this circuit with the selected cables could all achieve 1-2 × 10-7 pF/Hz1/2 at 0.1 Hz.

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.

Research and Development of Electrostatic Accelerometers for Space Science Missions at HUST.

High-precision electrostatic accelerometers have achieved remarkable success in satellite Earth gravity field recovery missions. Ultralow-noise inertial sensors play important roles in space gravitational wave detection missions such as the Laser Interferometer Space Antenna (LISA) mission, and key technologies have been verified in the LISA Pathfinder mission. Meanwhile, at Huazhong University of Science and Technology (HUST, China), a space accelerometer and inertial sensor based on capacitive sensors and the electrostatic control technique have also been studied and developed independently for more than 16 years. In this paper, we review the operational principle, application, and requirements of the electrostatic accelerometer and inertial sensor in different space missions. The development and progress of a space electrostatic accelerometer at HUST, including ground investigation and space verification are presented.

A Novel Controller Design for the Next Generation Space Electrostatic Accelerometer Based on Disturbance Observation and Rejection.

The state-of-the-art accelerometer technology has been widely applied in space missions. The performance of the next generation accelerometer in future geodesic satellites is pushed to 8 × 10 - 13 m / s 2 / H z 1 / 2 , which is close to the hardware fundamental limit. According to the instrument noise budget, the geodesic test mass must be kept in the center of the accelerometer within the bounds of 56 pm / Hz 1 / 2 by the feedback controller. The unprecedented control requirements and necessity for the integration of calibration functions calls for a new type of control scheme with more flexibility and robustness. A novel digital controller design for the next generation electrostatic accelerometers based on disturbance observation and rejection with the well-studied Embedded Model Control (EMC) methodology is presented. The parameters are optimized automatically using a non-smooth optimization toolbox and setting a weighted H-infinity norm as the target. The precise frequency performance requirement of the accelerometer is well met during the batch auto-tuning, and a series of controllers for multiple working modes is generated. Simulation results show that the novel controller could obtain not only better disturbance rejection performance than the traditional Proportional Integral Derivative (PID) controllers, but also new instrument functions, including: easier tuning procedure, separation of measurement and control bandwidth and smooth control parameter switching.

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.