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The measurements of gravity have been widely applied to earthquake monitoring, resource exploration and identification of natural voids. Traditional gravimeters, restricted by the exorbitant price and bulk, are hardly to be utilized in newly developed applications such as AUV-borne gravimetry and the multi-pixels gravimetry. Fortunately, this is changing with the development of portable MEMS gravimeters.Here, we have already developed a relative MEMS gravimeter with a quasi-zero stiffness spring-mass system and an arrayed area-changed capacitor for displacement transducing and actuating. This quasi-zero stiffness spring-mass system transfers the acceleration variation to the displacement of the proof-mass with high sensitivity. The displacement is then detected by the arrayed area-changed capacitor. The spring-mass system was installed inside a vacuum chamber for reducing the thermal noise and environmental disturbances. However, the response time of the gravimeter was enlarged when operating in open-loop mode dues to the decreased air damping. Therefore, a force-balance system is utilized in a MEMS gravimeter to improve the response time and the measurement range. This paper proposes an area-changed capacitors for transducing the displacement and balancing the inertial force on the proof-mass. As no additional structures are required on the MEMS chip, the design of the force-balance system is beneficial to simplifying the fabricating process and avoiding additional noise sources.We calibrated our MEMS gravimeter statically in our cave lab. After linear correction of the drift, the output of the MEMS agrees well with the theoretical earth tide with a coefficient of association of 0.92. The self-noise is evaluated to be 1 μGal/√Hz, which is one of the most sensitive MEMS-based gravimeter reported. In addition, the response time of the MEMS gravimeter was calibrated to be 0.2 s in close-loop mode, which is 2000 times faster than that in open-loop mode. This will promote improved accessibility of mobile gravity measurements at an affordable cost.

This paper reports a miniaturized resonant Lorentz-force magnetometer that exploits blue-sideband actuation to attain a better sensitivity and resolution. The resonant magnetometer consists of a double-ended tuning fork (DETF) resonator with cavity slots to optimize thermoelastic dissipation, as well as a Lorentz-force generator structure to transduce the magnetic force to the axial of the resonator. The proposed device demonstrates a Lorentz-force sensitivity of 5.5 mV/nN, a noise floor of 1.25 μV/ √ Hz, and a resolution of 0.23 pN/ √ Hz. In comparison with a conventional drive scheme, the blue- sideband actuation achieves approximately two orders of magnitude improvement regarding sensitivity and resolution than that of the amplitude modulation (AM) readout and 3.6-fold enhancement than that of the frequency modulation (FM) readout. The results affirm the merit of the novel excitation method and provide solid evidence of its effectiveness in practical applications.

Simultaneously and independently measuring two-dimensional (2D) displacement, one-dimensional (1D) for out-of-plane measurement and 1D for in-plane measurement, is important for practical applications. Although extrinsic fiber Fabry-Perot interferometers (EFPIs) have been reported for highly precise out-of-plane displacement measurements for many years, simultaneous measurement of 2D displacement with submicron accuracy has not been realized by a monolithic EFPI as far as we know. In this paper, a monolithic dual-cavity EFPI to realize 2D displacement measurement of a target is reported. By quantitatively analyzing and experimentally calibrating the linear dependences of the in-plane displacement sensitivity and interception on the cavity length, the effect of out-of-plane displacement on the in-plane displacement measurement is removed, which is the basis of the 2D displacement detection. 2D random movement detection and the repeatability of the system are investigated experimentally. Within the range of 10m for in-plane displacement, and 352m-358m for cavity length, demodulation errors better than 96nm are achieved. The 2D displacement measurement system based on the dual-cavity EFPI with the advantages of noncontact, high accuracy and compact size is promising to be applied in the 2D acceleration measurement, 2D rotor vibration measurement, 2D precise positioning in semiconductor manufacture, thermal expansion coefficient measurement, and so on.

Magnetometers are ubiquitous in applications covering many aspects of modern life, such as navigation, smart devices, biomedical systems, geological surveying and aerospace. This work reports a resonant Lorentz-force magnetometer featuring structural topology, in which cavity slots are incorporated in the device structure to improve the thermoelastic dissipation. Such a device is capable of sensing a small Lorentz-force and can be used as a sensitive magnetic field sensor. The most prominent property of this subject is implementing sensing tasks under a large bias magnetic field. The proposed magnetometer achieves a quality factor of 43000 in a vacuum of 4 mPa, a Lorentz-force sensitivity of 0.2 Hz/nN, and a magnetic field change sensitivity of 3375 Hz/T. The topology of the double-ended tuning fork (DETF) using cavity slots in the tine beams resulted in a 5.9-fold enhancement of the Q-factor compared to a common DETF resonator with the same geometry. Experimental characterization of the proposed magnetometer confirms its feasibility and functionality. Experiments about an application scenario with a large pre-existing bias magnetic field were carried out. The prototype device demonstrated a magnetic field change sensitivity of 2585 Hz/T and a noise-limited resolution of 210 nT/√ Hz, under a bias magnetic field of 0.13 T. [2021-0162]

ispartof: PETROLEUM SCIENCE vol:19 issue:6 pages:2631-2648 status: published

In this paper, the air buoyancy effect on Micro-Electro-MechanicalSystem (MEMS)-based gravity sensors for high-resolution gravity measurements is investigated. The MEMS gravimeter is operated in an atmospheric environment without any vacuum chamber; thus significantly simplifying the design, implementation and maintenance, and reducing the cost of the instrument. It is experimentally observed that the measured acceleration signal shows a clear correlation with the air buoyancy, and consequently the air pressure. A detailed theoretical model of the air buoyant force acting on the MEMS gravity sensor is proposed, giving a gravity-air pressure coefficient of 501.5 $\mu$ Gal/hPa for the silicon springmass system. After removing the error introduced by the air buoyant force, the MEMS gravity sensor exhibits an ultra-low self-noise floor of 1 $\mu {\mathrm {Gal}}/\sqrt{\rm Hz}$ @1 Hz, as well as an excellent stability, with an Allan deviation of 3 $\mu$ Gal (40 s integration time). The sensor is capable of measuring the Earth tides in a 16-day span. This discovery identified one major error source in high-resolution MEMS gravity sensors operating in atmosphere, which could potentially be useful for the development of future MEMS-based gravimeters.

The reduction of temperature effect is vitally important for high precision sensors. This paper introduces the theoretical analysis and experimental verification of an in-situ compensation method on the temperature coefficient of the scale factor for a single-axis electromagnetic force-balance feedback MEMS accelerometer. A micro thermistor, fabricated together with the MEMS accelerometer, is integrated to in-situ sense the temperature variation of the accelerometer. The thermistor is connected to the voltage-to-current resistance in series, which compensates the variation of the scale factor of the accelerometer that is influenced by temperature variation. The experimental results reveal that the temperature coefficient of the scale factor of the compensated accelerometer is within 6 ppm/°C for the temperature range from 25°C to 50°C, which is reduced by 68 times compared with the uncompensated accelerometer. Benefiting from the compatible fabrication process and the in-situ compensation, the proposed method is promising to be low-cost and high-efficiency.

In this paper, a new approach for enhancing the temperature sensitivity of a resonant MEMS thermometer, based on parametric modulation, is proposed. By periodically modulating the effective stiffness of a standard clamped-clamped beam (C-C beam), which is used as a proof-of-concept resonant MEMS thermometer, it is possible to create a virtual energy coupling between two fundamental modes of vibration. Through this energy transfer link, one particular mode (ideally high sensitivity) can be transferred to the vicinity of another mode (ideally low noise), thus creating an operating region where both increased sensitivity and low noise can be achieved. As a starting point, a sensitivity enhancement of up to 126% can be achieved in this particular study, while not deteriorating the readout noise floor. A noise floor of 19.7 $\mu $ K/Hz 1/2 has been achieved. Potentially, this approach could be extended to other structures, or be used to decrease sensitivity to temperature fluctuations as well. [2021-0050]

The assumption of implementing a Bender-type mission with two pairs of inline satellites by two institutions, one in the inclined satellite formation (ISF) and the other in the polar satellite formation (PSF), has been proven as an optimal selection for the next-generation gravimetric mission (NGGM). The prerequisite of this assumption is to ensure the combination as well as the independency of the missions in the PSF scenario as well as in the ISF scenario. To promote NGGM, we implement a close-loop simulation study to evaluate the performance of the stand-alone ISF mission. In the spectral domain, the ISF estimations show extremely poor quality for zonal and near-zonal coefficients due to the absence of observations over the polar regions, while the sectorial and near-sectorial coefficient estimations show approximately 71 ~ 77% noise reductions when compared with the PSF estimations. In the spectral domain, the ISF mission presents its superior capability in detecting the Earth’s mass variations within its observational areas than the PSF mission. The improvements of ISF are also obtained over the transition zones (50°N ~ 70°N and 50°S ~ 70°S) with 41% noise reductions. In addition, the general better performance of gravity estimations via ISF may promote the potential geoscience applications over the small river basins, the coastal ice sheet and the earthquake areas with better accuracy and finer resolution. The simulation results demonstrate the feasibility of implementing a stand-alone mission in the inclined orbits, and the further possibility of promoting a Bender-type mission via a profound cooperation by two institutions.

Mounting requirements of a rotating accelerometer gravity gradiometer (RAGG) beyond the art of manufacture, the RAGG is susceptible to the motion of itself. Motion error is a main source of error in airborne gravity gradiometry data. This study presented a posterror compensation method, which consists of postmotion error compensation and post-self-gradient compensation. The motion error and self-gradients are compensated before that the combined output of the four accelerometers is quadrature amplitude demodulated. The motion error compensation is based on the RAGG analytical model; motion response of the RAGG (namely, motion error) is related well to the motion of the RAGG, independent of the gravitational gradient response; recording the motion status of the RAGG, with least squares regression method and the RAGG analytical model, the motion response of the RAGG are separated and removed. RAGG numerical simulation experiment results show that the postmotion error compensation method is feasible, and its limit accuracy could reach 0.5 E/ $\surd $ Hz.

Nano- $g$ accelerometers are widely used in space exploration and measurement of the earth’s gravitational field. It is essential to precisely evaluate error effects at high orders such as cross-coupling for applications in a dynamic environment. Nevertheless, it remains challenging to meet the precision requirements using conventional calibration measures. In this article, we propose a method to separate the cross-coupling coefficients of a linear single-axis accelerometer by mounting it on a steadily rotating rate table that is tilted at a fixed deviation angle with respect to the horizontal plane. The gravity component is periodically modulated along the input axis per revolution. Simultaneously, a series of centripetal acceleration is applied along the cross axis in sequence while adjusting the rotation frequency of the rate table by steps. Thus, the cross-coupling coefficient can be separated by its dependence both on the modulated gravity acceleration and the centripetal acceleration. In comparison to the static multipoint angular rotation test on a tilted dividing head, the proposed dynamic modulation method demonstrates improved robustness against corruption from bias drift, with an improved uncertainty. This method to separate the cross-coupling coefficient is suitable for testing high-resolution accelerometers, without requiring high bias stability or sensitive response sustaining at ultralow frequency.

High-precision microelectromechanical inertial sensors based on spring-mass structures are of great interests for a wide range of applications, including inertial navigation, disaster warning and resource exploration. Lowering the resonant frequency is essential to further improve the sensitivity of the sensors. However, conventional approaches are facing insurmountable difficulties from size reduction to machining precision. This paper proposed a novel quasi-zero-stiffness mechanism that is compatible with MEMS technologies together with a micromaching approach for adjusting the stiffness precisely. By improving the compliance of a typical spring with a negative-stiffness compensation mechanism induced by axial force, the resonant frequency of the micro spring-mass structure is lowered to 0.7 Hz, which is at least 3 times lower than current state-of-the-art micro structures. Based on this ultra-sensitive micro structure base on the quasi-zero-stiffness mechanism, the micro inertial sensor, with a chip size of a postage stamp, has shown a low self-noise of 0.6 nrad/ $\surd $ Hz at 0.04 Hz and a high long-term stability that are comparable to traditional pendulum inertial sensors. It is the first micro device, to our knowledge, that can successfully measure the tidal tilt signal. [2020-0048]

The large-scale fabrication of high-performance on-chip micro-supercapacitors (MSCs) is the footstone for the development of next-generation miniaturized electronic devices. In practical applications, however, MSCs may suffer from a low areal energy density as well as a complicated fabrication strategy that is incompatible with semiconductor processing technology. Herein, we propose a scalable fabrication strategy for the realization of a silicon-based three-dimensional (3D) all-solid-state MSC via the combination of semiconductor-based electrode processing, chemical vapor deposition, and hydrothermal growth. The individual Si/C/MnO2 electrode shows a maximum specific capacitance of 223.74 mF cm-2, while the symmetric electrodes present a maximum areal energy density of 5.01 μWh cm-2 at the scan rate of 1 mV s-1. The full 3D Si/C/MnO2 MSC delivers a high energy density of 2.62 μWh cm-2, at a power density of 117.82 μW cm-2, as well as a long cycle life with capacitance retention >92% after 4000 cycles. Our proposed method enables the fabrication of 3D MSCs based on a thick silicon interdigitated electrode array, holding a great promise for the development of 3D on-chip microscale energy storage devices.

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.

An in-plane displacement sensor based on an asymmetric extrinsic fiber Fabry–Perot interferometer (EFPI) is proposed and demonstrated. The asymmetric EFPI composed of a step-shaped external reflector and a cleaved fiber end face can be equivalent to two parallel FPIs with slightly different cavity lengths. By calculating the peak intensity difference of the two FPIs, the in-plane displacement can be demodulated with enhanced sensitivity and suppressed common mode noise. Both theoretical analyses and experimental results show that the sensitivity and the linear range of the in-plane displacement sensor are dependent on the cavity length. A displacement resolution of 5 nm and a linear range of ± 7 µ m under the cavity length of 250 µm are achieved in the experiment. The proposed in-plane displacement sensor with a nanometric resolution and compact size can be widely used in the fields of metrology, accelerometers, and semiconductor manufacture.

Electromagnetic wave absorbers are essential devices in imaging, wireless communication and energy harvesting systems. In this paper, we propose and experimentally demonstrate a flexible and ultra-broadband terahertz (THz) wave absorber based on graphene–vertically aligned carbon nanotube (G-VACNT) hybrids. The THz wave absorber consists of Cu/PDMS/graphene/VACNT functional layers on a PET substrate. The measured results show a 100% qualified operating bandwidth (i.e., absorptance >0.9) and an average power absorptance of 0.986 within the 0.2–3.0 THz range. The absorber also exhibits good absorption performances for a wide range of incident angles up to 60°, and can function normally in different bending states due to its excellent flexibility. The incoming energy of THz waves absorbed by the G-VACNT hybrids results in a temperature increase whose spatial distribution is corresponding to the profile of the incident THz beam, providing an efficient and low cost approach for THz beam profiling, collimation and focusing. This work paves the way for the development of large-scale and broadband THz wave absorbers.

Materials with high and broadband absorption characteristics in the terahertz (THz) range are desirable for many applications. In this paper, we propose, fabricate and experimentally demonstrated a wafer-scale vertically aligned carbon nanotube (VACNT) array for broadband THz wave absorption. The effects of VACNT parameters on the absorption performance are investigated within the THz and infrared spectra using the Maxwell-Garnett theory, revealing that the absorption in the THz range can be greatly enhanced by suitable selections of the length, volume fraction and vertical alignment factor of CNTs. A VACNT array with an average CNT length of ∼600 μm is fabricated on a 4-inch silicon substrate. Experimental results measured by a THz time-domain spectroscopic system show an average power absorptance of ∼98% from 0.3 to 2.5 THz, and agree well with the numerical modelling. This device can be used as a cost-effective near-perfect absorber across the THz and infrared regions for thermal emission and imaging, electromagnetic interference shielding, stealth and energy harvesting applications. This work was partially supported by the National Key R&D Program of China (Grant No. 2018YFC0603301), the National Natural Science Foundation of China (Grant No. 61801185), and HUST Key Innovation Team Foundation for Interdisciplinary Promotion (Grant No. 2016JCTD102). We thank Kejia Wang and Yue Song at the Wuhan National Laboratory for Optoelectronics at HUST for their assistance in THz-TDS measurements.

Ultra-wideband absorbers have been extensively used in wireless communications, energy harvesting, and stealth applications. Herein, with the combination of experimental and theoretical analyses, we develop a flexible ultra-wideband terahertz absorber based on vertically aligned carbon nanotubes (VACNTs). Measured results show that the proposed absorber is able to work efficiently within the entire THz region (e.g., 0.1–3.0 THz), with an average power absorptance of >98% at normal incidence. The absorption performance remains at a similar level over a wide range of incident angle up to 60°. More importantly, our devices can function normally, even after being bent up to 90° or after 300 bending cycles. The total thickness of the device is about 360 μm, which is only 1/8 of the wavelength for the lowest evaluated frequency of 0.1 THz. The new insight into the VACNT materials paves the way for applications such as radar cross-section reduction, electromagnetic interference shielding, and flexible sensing because of the simplicity, flexibility, ultra-wideband operation, and large-scale fabrication of the device. Accepted version This work was partially supported by the National Key R&D Program of China (grant no. 2018YFC0603301), and the National Natural Science Foundation of China (grant nos. 61801185, 51902112).

MEMS magnetometers have been applied in numerous fields, such as navigation, biomedical, geological exploration and aerospace. This work reports a resonant Lorentz-force magnetometer with a quality factor of 43000 in vacuum and a sensitivity of 3.3 Hz/nN under a 2 mT bias magnetic field. A differential pair of two magnetometers based on double-ended tuning fork (DETF) resonator is implemented to enhance the system signal to noise ratio (SNR). The topology of the DETF with cavity slots can improve the quality factor (Q-factor) effectively, resulting in an enhancement of 5.9-fold compared to a DETF resonator without slots. Theoretical computations are in good agreement with the simulation model and the actual experimental measurements confirm the feasibility of the proposed magnetometer. Future effort of this work will constitute an important step towards a magnetometer that can measure small variations of the magnetic field in tens of $\mu \mathrm{T}$ range with a resolution of $\text{nT}/\surd\text{Hz}$ level, even under a strong bias magnetic field.

This paper presents a high-sensitivity microelectromechanical system (MEMS) gravimeter that can operate without a vacuum chamber for long-term earth tide observations. The proposed MEMS gravimeter system can be greatly simplified, including a spring-mass acceleration unit and a controlled temperature environment. To operate without the vacuum chamber, the effect of air buoyancy on the output signal is investigated and corrected in the time domain. A strong correlation between the corrected output of the gravimeter and the theoretical tidal signal is observed. The MEMS gravimeter shows an ultra-low noise floor of ~2 µGal/√Hz at 1 Hz and superior stability, indicating the potential for the mass production of MEMS gravimeters that can operate without any vacuum unit.

This paper describes a hybrid mass sensing system comprising a QCM (quartz crystal microbalance) mass sensor operating under atmospheric pressure and a 3-DOF mode localized coupled resonator operating in vacuum. Nanoparticles as consecutive mass perturbations are added onto the QCM, the output signals with respect to the amount of mass change are then being manipulated to generate electrostatic forces. Subsequently, the electrostatic forces act on the 3-DOF mode localized coupled resonator as external stiffness perturbations. The output metrics of the hybrid system were defined as: the resonant frequency shifts, vibration amplitude changes, and the changes in resonance amplitude ratio. Measured data was analyzed for these metrics and compared. This work demonstrated that the proposed hybrid mass sensing system attained a ${2.5\times }10^{\text 6}{N}{(\text{m}\bullet \text{kg})}^{-1}$ mass to stiffness transduction factor, and has the potential to be employed as a direct liquid contact biochemical transducer.

The TianQin Project is aiming at gravitational wave (GW) detection in space. TianQin GW observatory comprises three satellites orbiting on 1 × 105 km Earth orbits to form an equilateral-triangle constellation. In order to minimize the variations in arm lengths and breathing angles, the satellites must be launched and adjusted precisely into an optimized orbit. Therefore, satellite laser ranging must be used to enhance the precision of satellite orbit determination. To develop the capability of satellite laser ranging for TianQin’s orbit, the TianQin Laser Ranging Station has been designed and constructed to perform high-precision laser ranging for TianQin satellites and lunar laser ranging as well. Applying a 1064 nm Nd: YAG laser with 100 Hz repetition frequency, 80 pico-second pulse duration, and 2 × 2 array of superconducting nanowire single-photon detectors, we have obtained the laser echo signals from the five lunar retro-reflector arrays, and the measurement data have been packaged into 234 normal points (NPs), including a few data measured during the full-moon lunar phase. Each NP is calculated from continuous measurement for about ten minutes and the statistical error of the NPs is about 7 mm (1σ).

In this work, a new scheme to enhance or decrease the sensitivity of a MEMS resonator is proposed. The proposed approach utilizes a periodic modulation on the stiffness of a standard clamped-clamped (C-C) beam, i.e. parametric modulation, to couple two intrinsic fundamental modes of vibration. Through this coupling, it is possible to transfer the sensitivity of one fundamental mode to the other, thereby creating regions where the sensitivity of the MEMS resonator can be enhanced or reduced. Finally, the effect of this approach on the noise performance is also investigated. And it is found that this approach does not deteriorate the noise performance. Potentially, this approach can be extended to other resonator structures, and could be applied to resonant MEMS sensors or timing references.

Compared with airborne gravimetry, a technique frequently used to infer the seafloor topography at places inaccessible to ship soundings due to the presence of ice shelf or ice mélange, airborne gravity gradiometry inherently could achieve higher spatial resolution, thus it is promising for improved inference of seafloor topography. However, its estimation capability has not been demonstrated by real projects. Theoretical analysis through admittance shows that compared with gravity disturbance, gravity gradient is more sensitive to the short-wavelength seafloor topography but diminishes faster with the increase of the distance between the seafloor and airplane, indicating its superiority is recovering short-wavelength topographic features over shallow waters. We present the first numerical experiment that estimates seafloor topography from a 0.4-km resolution, real airborne gravity gradients. It is shown that airborne gravity gradiometry can recover smaller topographic features than typical airborne gravimetry, but the estimation accuracy is only ±17 m due to the presence of subsurface density variations. The long-wavelength effect of the subsurface density variations can be removed with the aid of constraining bathymetry inside the study area, whereas the short wavelengths cannot. This study expands the applications of airborne gravity gradiometry, and helps glaciologists understand its performance in seafloor topography estimation.

High-sensitivity micro-electromechanical systems (MEMS) accelerometers have been widely used in many applications. Although the optical MEMS accelerometers have the advantage of insensitive to electromagnetic interferences, there are still difficulties of integration and fabrication. Therefore, capacitive MEMS accelerometers are more commonly used. This paper introduces a high-sensitivity optical MEMS accelerometer based on silicon-on-insulator (SOI) double-side micromachining technology which can overcome the difficulties of both optical component integration and low-frequency suspension system micromachining. The proposed sensor is a silicon flexure accelerometer whose spring-mass structure consists of the compliant spring beams, the proof mass and the sensor frame. When acceleration applies, the in-plane motion of the proof mass can be transduced by an optical interferometer with the Fabry-Perot (F-P) cavity formed between the fiber end-face and the proof mass sidewall. The sensitivity of the micro-machined optical accelerometer is measured as 100 ng/√Hz@1 Hz which is better than most of the reported optical MEMS accelerometers.

TianQin is a planned space-based gravitational wave (GW) observatory consisting of three earth orbiting satellites with an orbital radius of about $10^5~{\rm km}$. The satellites will form a equilateral triangle constellation the plane of which is nearly perpendicular to the ecliptic plane. TianQin aims to detect GWs between $10^{-4}~{\rm Hz}$ and $1~{\rm Hz}$ that can be generated by a wide variety of important astrophysical and cosmological sources, including the inspiral of Galactic ultra-compact binaries, the inspiral of stellar-mass black hole binaries, extreme mass ratio inspirals, the merger of massive black hole binaries, and possibly the energetic processes in the very early universe or exotic sources such as cosmic strings. In order to start science operations around 2035, a roadmap called the 0123 plan is being used to bring the key technologies of TianQin to maturity, supported by the construction of a series of research facilities on the ground. Two major projects of the 0123 plan are being carried out. In this process, the team has created a new generation $17~{\rm cm}$ single-body hollow corner-cube retro-reflector which has been launched with the QueQiao satellite on 21 May 2018; a new laser ranging station equipped with a $1.2~{\rm m}$ telescope has been constructed and the station has successfully ranged to all the five retro-reflectors on the Moon; and the TianQin-1 experimental satellite has been launched on 20 December 2019 and the first round result shows that the satellite has exceeded all of its mission requirements., 16 pages, 1 figure, invited article to a special section in PTEP

Capacitive displacement transducers (CDTs) have been widely used in many physical sensors, attributing to high-resolution, simple electricity and easy manufacturing process. Gap-variation CDTs generally have higher displacement resolution due to small electrode gaps but suffer from the pull-in effect, the nonlinear effect and squeeze-film damping; whereas area-variation CDTs have intrinsically good linearity and much smaller slide-film damping. However, the parallel-plate-based area-variation CDTs have the electrode width much larger than the electrode gap with negligible fringe effect; therefore, the sensitivity is limited by periodic electrode numbers. In this paper, we introduce a novel fringe-effect dominated area-variation CDT with a much higher sensitivity within a certain electrode-deployable area. Both theoretical and numerical analysis are applied to investigate the working principle of the CDT design. The proposed fringe-effect-based CDT benefits from a much larger capacitance-to-displacement sensitivity than the traditional periodic array parallel-plate-based CDT, due to the more displacement-sensitive fringe field and more deployable electrode periods. A set of experiments are designed, and the proposed area-variation CDTs are evaluated. Experimental results suggested that the proposed CDT design, which had equal electrode width, separation and gap, could universally be applied to sensors with different featured dimensions either in macroscale or microscale. Angular misalignments with both out-of-plane tilts and in-plane rotations, which affect the output offset and sensitivity, should be minimized or alleviated. The proposed fringe-effect-based CDT are successfully applied to a single-axis in-plane sensing micro-electromechanical systems (MEMS) accelerometer, showing a noise floor as low as 0.25 ng/Hz1/2@1 Hz. The corresponding displacement noise of the proposed CDT is 0.1 pm/Hz1/2.

This paper reports a newly developed chip-level micro-electromechanical system (MEMS) accelerometer for tilt sensing based on differential array area-change capacitive displacement transducer and through-silicon-wafer etching process. The proposed MEMS accelerometer consists of a silicon-based acceleration-sensitive spring-mass structure, a upper glass cover plate and an universal capacitive readout application specific integrated circuit (ASIC) die, which is used to apply differential driving signals and pickup capacitance change due to area-variation under in-plane motion. The MEMS accelerometer has a linear measurement range of ±30° with a scale factor of 33.6 mV/°. The tilt measurement resolution of the MEMS accelerometer is evaluated by the modified Allan deviation with the results showing that an angle resolution of 0.003° at an integral time of 3 seconds. Compared with the commercial MEMS tilt sensors, the proposed MEMS accelerometer in this work has a larger full measurement range and a larger bandwidth but a little bit poor linearity. Hence, it is believed that the proposed chip-level MEMS accelerometer is promising to be a high-resolution tilt sensor with a lower power consumption and smaller volume.

MEMS Accelerometers are one of the core inertial measurement components in inertial navigation systems. This paper reports a high-precision force balance accelerometer based on MEMS technology. Utilizing a springmass structure with a low resonant frequency of 8 Hz and a periodic capacitive displacement transducer, the accelerometer has an extremely low self-noise of 1 ng/Hz1/2, which is one of the most sensitive MEMS-based accelerometers reported to date.

Capacitive transducers are widely used in fundamental physics experiments, seismology, Earth or planetary observations, and space scientific and technical applications because of their high precision, simple structure, and compatibility with various measurements. However, in real applications, there is a trade-off between their resolution and dynamic range. Therefore, this paper is aimed at enlarging the dynamic range while ensuring high resolution. In this paper, a noise analysis of a capacitive transducer is presented, which shows that the amplitude noise of the carrier wave is the main limiting factor. Hence, a new method of generating a carrier wave with lower-amplitude noise is proposed in the paper. Based on the experimental verification, it is found that the carrier wave produced through the new method performed significantly better than the typical digital carrier wave when they were compared in the same sensing circuit. With the carrier wave produced through the new method, the dynamic range of the capacitive transducer can reach 120.7 dB, which is 18.3 dB greater than for the typical direct digital synthesis (DDS) method. In addition, the resolution of the carrier wave is mainly limited by the voltage reference components.

High-precision seismic sensors are key components in geophysical applications. Traditional seismic sensors apply levelling systems to avoid overload by the gravity projection, introducing additional volume, weight and cost. In this paper, we design, fabricate and experimentally demonstrate a levelling-free single-axis in-plane seismic sensor based on MEMS technology. Three kinds of capacitive sensors are integrated into one chip. Two encoder-like area-varying capacitive displacement sensors work alternatively to avoid the inflection points, enabling the seismic sensor to work linearly in arbitrary attitudes with a high sensitivity and an angle sensor selects the working array from the two arrays and measures the angle between the sensitive direction and gravity direction at the same time. In order to calibrate the scale factor, a gap-varying capacitive displacement sensor is integrated to measure the spacing. By the combination of these capacitive sensors, the micromachined seismic sensor is able to work in arbitrary attitudes with a resolution of better than 50 ng/√Hz at 1 atmosphere. Assembling three seismic sensors along axes orthogonal to each other, a three-axis seismic measurement system can be constructed. This system has successfully detected a MS7.0 earthquake at 2017-08-08 (UTC time), which happened in Sichuan Province (1000 km away), and another MS6.6 earthquake happened about 10 h later in Xinjiang Province (2700 km away). Being low cost and low power, this nano-g MEMS seismic sensor provides an alternative solution for geophysical applications.

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.

In this paper, we present a suppression method for the thermal drift of an ultra-stable laser interferometer. The detailed analysis on the Michelson interferometer indicates that the change in optical path length induced by temperature variation can be effectively reduced by choosing proper thickness and/or incident angle of a compensator. Taking the optical bench of the Laser Interferometer Space Antenna Pathfinder as an example, we analyze the optical bench model with a compensator and show that the temperature coefficient of this laser interferometer can be reduced down to 1 pm/K with an incident angle of 0.267828 rad. The method presented in this paper can be used in the design of ultra-stable laser interferometers, especially for space-based gravitational waves detection.

TianQin-1 is a mission in the TianQin project, which uses a single satellite to demonstrate the maturity of the key technology for the space-based gravitational wave detection. The spaceborne laser in the TianQin-1 mission consists of a self-developed DBR one and a commercial RIO one. The DBR laser is also developed as a pumping source for the main NPRO laser in the final solution of TianQin. The two lasers were mutual backups and both passed the environment performance verification. The on ground results showed that the self-developed DBR laser could provide a stable output of 18 mW with a drift of 0.6 mW/h. Meanwhile, the internal temperature was controlled at the mK level. The results of in-orbit experiments show that the DBR laser works well as a direct source of the laser interferometer. The overall displacement resolution and the noise floor of the interferometer was approximately 25 pm and 30 pm/√Hz at 0.1 Hz, respectively, better than the goals of the TianQin-1 mission.

Capacitive MEMS accelerometers with area‐variable periodic‐electrode displacementtransducers found wide applications in disaster monitoring, resource exploration and inertialnavigation. The bonding‐induced warpage, due to the difference in the coefficients of thermalexpansion of the bonded slices, has a negative influence on the precise control of the interelectrodespacing that is essential to the sensitivity of accelerometers. In this work, we propose the theory,simulation and experiment of a method that can alleviate both the stress and the warpage byapplying different bonding temperature on the bonded slices. A quasi‐zero warpage is achievedexperimentally, proving the feasibility of the method. As a benefit of the flat surface, the spacing ofthe capacitive displacement transducer can be precisely controlled, improving the self‐noise of theaccelerometer to 6 ng/&radic, Hz @0.07 Hz, which is about two times lower than that of the accelerometerusing a uniform‐temperature bonding process.

We improve the test of the gravitational inverse-square law at the submillimeter range by suppressing the vibration of the electrostatic shielding membrane to reduce the disturbance coupled from the residual surface potential. The result shows that, at a 95% confidence level, the gravitational inverse-square law holds ($|\ensuremath{\alpha}|\ensuremath{\le}1$) down to a length scale $\ensuremath{\lambda}=48\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. This work establishes the strongest bound on the magnitude $\ensuremath{\alpha}$ of the Yukawa violation in the range of $40--350\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, and improves the previous bounds by up to a factor of 3 at the length scale $\ensuremath{\lambda}\ensuremath{\approx}70\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for $k=4$ and 5.

The TianQin-1 satellite (TQ-1), which is the first technology demonstration satellite for the TianQin project, was launched on 20 December 2019. The first round of experiment had been carried out from 21 December 2019 until 1 April 2020. The residual acceleration of the satellite is found to be about $1\times10^{-10}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$ and about $5\times10^{-11}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.05~{\rm Hz}\,$, measured by an inertial sensor with a sensitivity of $5\times10^{-12}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The micro-Newton thrusters has demonstrated a thrust resolution of $0.1~\mu{\rm N}$ and a thrust noise of $0.3~\mu{\rm N}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}$. The residual noise of the satellite with drag-free control is $3\times10^{-9}~{\rm m}/{\rm s}^{2}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The noise level of the optical readout system is about $30~{\rm pm}/{\rm Hz}^{1/2}$ at $0.1~{\rm Hz}\,$. The temperature stability at temperature monitoring position is controlled to be about $\pm3~{\rm mK}$ per orbit, and the mismatch between the center-of-mass of the satellite and that of the test mass is measured with a precision of better than $0.1~{\rm mm}$., Comment: 17 pages, 11 figures

Precise measurement of variations in the local gravitational acceleration is valuable for natural hazard forecasting, prospecting, and geophysical studies. Common issues of the present gravimetry technologies include their high cost, high mass, and large volume, which can potentially be solved by micro-electromechanical-system (MEMS) technology. However, the reported MEMS gravimeter does not have a high sensitivity and a large dynamic range comparable with those of the present commercial gravimeters, lowering its practicability and ruling out worldwide deployment. In this paper, we introduce a more practical MEMS gravimeter that has a higher sensitivity of 8 μGal/√Hz and a larger dynamic range of 8000 mGal by using an advanced suspension design and a customized optical displacement transducer. The proposed MEMS gravimeter has performed the co-site earth tides measurement with a commercial superconducting gravimeter GWR iGrav with the results showing a correlation coefficient of 0.91., Sensors: A MEMS gravimeter combines high precision with portability Researchers in China have developed a small, portable gravimeter based on micro-electromechanical-system (MEMS) technology with a sensitivity and dynamic range comparable with larger, commercially available gravimeters. The new device was created by a team led by Liangcheng Tu at Huazhong University of Science and Technology. The MEMS mechanism consists of a spring-mass system designed around a combination of curved and folded beams. Together, these ensure that the system is stiff under low loads but flexible at loads around 1 g. An optical component measures the displacement of the proof mass to measure gravitational acceleration. The team tested their design alongside a commercial gravimeter and found a 90% correlation in the measurements of Earth tides, demonstrating its utility for applications from oil and gas exploration to hazard detection.

The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10−11 m3 kg−1 s−2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.

This paper presents a micromachined micro-g capacitive accelerometer with a silicon-based spring-mass sensing element. The displacement changes of the proof mass are sensed by an area-variation-based capacitive displacement transducer that is formed by the matching electrodes on both the movable proof mass die and the glass cover plate through the flip-chip packaging. In order to implement a high-performance accelerometer, several technologies are applied: the through-silicon-wafer-etching process is used to increase the weight of proof mass for lower thermal noise, connection beams are used to reduce the cross-sensitivity, and the periodic array area-variation capacitive displacement transducer is applied to increase the displacement-to-capacitance gain. The accelerometer prototype is fabricated and characterized, demonstrating a scale factor of 510 mV/g, a noise floor of 2 &micro, g/Hz1/2 at 100 Hz, and a bias instability of 4 &micro, g at an averaging time of 1 s. Experimental results suggest that the proposed MEMS capacitive accelerometer is promising to be used for inertial navigation, structural health monitoring, and tilt measurement applications.

This paper introduces a prototype of a diamagnetic levitation based inertial sensor which includes the diamagnetic levitation system and the optical displacement transducer. The proof mass is a floating magnet which is lifted by a fixed magnet above and sandwiched by two pyrolytic graphite sheets for stable levitation. A high precision optical displacement transducer has been developed with a noise floor of 1 nm/√Hz@1 Hz at atmosphere and room temperature. The fundamental frequency of the levitation system was measured as 0.65 Hz, giving an acceleration noise floor of 20 ng/√Hz@0.5 Hz. Benefitting on the excellent sensitivity and low-frequency responses, earth tremors at 0.2~0.3 Hz and 2~3 Hz have been observed using this inertial sensor.

This paper presents a MEMS gravimeter that is sensitive and stable enough to observe earth tides. A novel quasi-zero stiffness suspension, which includes a curved beam and two folded beams, is used to achieve an ultra-low resonant frequency of 3.0 Hz. The measured acceleration noise floor of the MEMS gravimeter is 20 μGal/√Hz at 1 Hz. The MEMS gravimeter shows a good agreement with the theoretical model for earth tides measurements. The results indicate that the proposed MEMS gravimeter is qualified for earth tides measurement and is promising to be a very low-cost gravimeter.

Capacitive sensing is a key technique to measure the test mass movement with a high resolution for space-borne gravitational wave detectors, such as Laser Interferometer Space Antenna (LISA) and TianQin. The capacitance resolution requirement of TianQin is higher than that of LISA, as the arm length of TianQin is about 15 times shorter. In this paper, the transfer function and capacitance measurement noise of the circuit are modeled and analyzed. Figure-of-merits, including the product of the inductance L and the quality factor Q of the transformer, are proposed to optimize the transformer and the capacitance measurement resolution of the circuit. The LQ product improvement and the resonant frequency augmentation are the key factors to enhance the capacitance measurement resolution. We fabricated a transformer with a high LQ product over a wide frequency band. The evaluation showed that the transformer can generate a capacitance resolution of 0.11 aF/Hz1/2 at a resonant frequency of 200 kHz, and the amplitude of the injection wave would be 0.6 V. This result supports the potential application of the proposed transformer in space-borne gravitational wave detection and demonstrates that it could relieve the stringent requirements for other parameters in the TianQin mission.

Electroplating is a popular method to produce solders in micromechanical systems (MEMS) encapsulation and interconnection applications. In this work, a fabrication process is introduced for generation of three-dimensional (3D) Sn solder microstructures. Based on the proposed method, the Sn solders with different heights can be easily obtained after reflow. Metal-armoring provided by the solder-solder contact can be used at the extremes of the suspension travel, greatly increasing the capability of shock resistance. The helium leak rates of the packaged samples are lower than the reject limit based on MIL-STD-883E standard. The bonding strength of samples is measured by die shear strength tests with an average value of 7.4 MPa. In addition, the ohmic behavior of the Sn solder bonding is verified as well. These excellent results show an outstanding packaging quality in MEMS encapsulation applications.

Improving the precision of current tests of the equivalence principle with a rotating torsion pendulum requires a more complete analysis of systematic effects. Here, we discuss in detail one of the important systematic effects, the influence from the tilt error motion of the rotation axis of a rotary stage, namely, wandering of the instantaneous rotation axis around its average direction. Its influence on the rotating torsion pendulum is modeled phenomenologically, and the parameters in the model are calibrated. It is shown that the influence can contribute a correction of η ≈ 5 × 10−13 to the equivalence-principle violating parameter for a rotary stage whose tilt error motion of interest is about 31 nrad in magnitude. We also show that such an influence can be reduced to the level of η ≈ 1 × 10−14 by means of active compensation of the tilt error motion using a set of piezoelectric actuators placed under the stage stator.

Tilt sensors have been widely used in many applications, such as instrumentation leveling, oil drilling and structural health monitoring. With the rapid development of the micro-electromechanical system (MEMS) technology, MEMS accelerometer-based high-performance tilt sensors are capable of replacing conventional tilt sensors in most of application fields. High-sensitivity MEMS resonant accelerometers (MRAs) are fully qualified for tilt sensing. However, MRA chips have to be vacuum packaged and require complex circuits; therefore, they are difficult to be miniaturized and commercialized. In this case, this paper introduces a commercial-oriented capacitive MEMS accelerometer for tilt sensing with both high-resolution and compact size. The proposed MEMS sensor utilizes simplified fabrication processes, the area-change-based capacitive displacement transducer and the capacitance-to-voltage conversion application specific integrated circuit (ASIC) for low-cost, high-sensitivity, low power consumption and miniaturization. The developed MEMS sensor has a package dimension of 14 mm × 14 mm × 3.6 mm with a single +5 V power supply and analog voltage output. Several evaluation experiments have been conducted with the results showing that the developed MEMS tilt sensor has a full measurement range of ±180°, a linear measurement range of ±30° with a nonlinearity of ±2.8%, a sensitivity of 33.6 mV/°, a noise floor of 2 × 10−4°/√Hz, a bandwidth of 100 Hz and an angle resolution of 7 × 10−4° with an integral time of 0.5 s. Compared with other commercial MEMS tilt sensors, the proposed sensor has a better resolution, a lower noise floor, a larger bandwidth, a lower power consumption and a smaller package. The simplified fabrication process and high performance suggest the developed MEMS tilt sensor is promising to be competitive in the market.