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.

Study on TPD Phasemeter to Suppress Low-Frequency Amplitude Fluctuation and Improve Fast-Acquiring Range for GW Detection.

A phasemeter as a readout system for the inter-satellite laser interferometer in a space-borne gravitational wave detector requires not only high accuracy but also insensitivity to amplitude fluctuations and a large fast-acquiring range. The traditional sinusoidal characteristic phase detector (SPD) phasemeter has the advantages of a simple structure and easy realization. However, the output of an SPD is coupled to the amplitude of the input signal and has only a limited phase-detection range due to the boundedness of the sinusoidal function. This leads to the performance deterioration of amplitude noise suppression, fast-acquiring range, and loop stability. To overcome the above shortcomings, we propose a phasemeter based on a tangent phase detector (TPD). The characteristics of the SPD and TPD phasemeters are theoretically analyzed, and a fixed-point simulation is further carried out for verification. The simulation results show that the TPD phasemeter tracks the phase information well and, at the same time, suppresses the amplitude fluctuation to the noise floor of 1 µrad/Hz1/2, which meets the requirements of GW detection. In addition, the maximum lockable step frequency of the TPD phasemeter is almost three times larger than the SPD phasemeter, indicating a greater fast-acquiring range.

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.

Highly precise in-plane displacement sensor based on an asymmetric fiber Fabry-Perot interferometer.

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 ±7µm 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.

Improvement for Testing the Gravitational Inverse-Square Law at the Submillimeter Range.

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 (|α|≤1) down to a length scale λ=48 µm. This work establishes the strongest bound on the magnitude α of the Yukawa violation in the range of 40-350 µm, and improves the previous bounds by up to a factor of 3 at the length scale λ≈70 µm. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for k=4 and 5.

Temperature Gradient Method for Alleviating Bonding-Induced Warpage in a High-Precision Capacitive MEMS Accelerometer.

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/√Hz @0.07 Hz, which is about two times lower than that of the accelerometerusing a uniform-temperature bonding process.

An Integrated Gold-Film Temperature Sensor for In Situ Temperature Measurement of a High-Precision MEMS Accelerometer.

Temperature sensors are one of the most important types of sensors, and are employed in many applications, including consumer electronics, automobiles and environmental monitoring. Due to the need to simultaneously measure temperature and other physical quantities, it is often desirable to integrate temperature sensors with other physical sensors, including accelerometers. In this study, we introduce an integrated gold-film resistor-type temperature sensor for in situ temperature measurement of a high-precision MEMS accelerometer. Gold was chosen as the material of the temperature sensor, for both its great resistance to oxidation and its better compatibility with our in-house capacitive accelerometer micro-fabrication process. The proposed temperature sensor was first calibrated and then evaluated. Experimental results showed the temperature measurement accuracy to be 0.08 °C; the discrepancies among the sensors were within 0.02 °C; the repeatability within seven days was 0.03 °C; the noise floor was 1 mK/√Hz@0.01 Hz and 100 µK/√Hz@0.5 Hz. The integration test with a MEMS accelerometer showed that by subtracting the temperature effect, the bias stability within 46 h for the accelerometer could be improved from 2.15 µg to 640 ng. This demonstrates the capability of measuring temperature in situ with the potential to eliminate the temperature effects of the MEMS accelerometer through system-level compensation.

Design of a Carrier Wave for Capacitive Transducer with Large Dynamic Range.

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.

Test of the Equivalence Principle with Chiral Masses Using a Rotating Torsion Pendulum.

Here we present a new test of the equivalence principle designed to search for the possible violation of gravitational parity using test bodies with different chiralities. The test bodies are a pair of left- and right-handed quartz crystals, whose gravitational acceleration difference is measured by a rotating torsion pendulum. The result shows that the acceleration difference towards Earth Δa_{left-right}=[-1.7±4.1(stat)±4.4(syst)]×10^{-15} m s^{-2} (1-σ statistical uncertainty), correspondingly the Eötvös parameter η=[-1.2±2.8(stat)±3.0(syst)]×10^{-13}. This is the first reported experimental test of the equivalence principle for chiral masses and opens a new way to the search for the possible parity-violating gravitation.

Scale Factor Calibration for a Rotating Accelerometer Gravity Gradiometer.

Rotating Accelerometer Gravity Gradiometers (RAGGs) play a significant role in applications such as resource exploration and gravity aided navigation. Scale factor calibration is an essential procedure for RAGG instruments before being used. In this paper, we propose a calibration system for a gravity gradiometer to obtain the scale factor effectively, even when there are mass disturbance surroundings. In this system, four metal spring-based accelerometers with a good consistency are orthogonally assembled onto a rotary table to measure the spatial variation of the gravity gradient. By changing the approaching pattern of the reference gravity gradient excitation object, the calibration results are generated. Experimental results show that the proposed method can efficiently and repetitively detect a gravity gradient excitation mass weighing 260 kg within a range of 1.6 m and the scale factor of RAGG can be obtained as (5.4 ± 0.2) E/µV, which is consistent with the theoretical simulation. Error analyses reveal that the performance of the proposed calibration scheme is mainly limited by positioning error of the excitation and can be improved by applying higher accuracy position rails. Furthermore, the RAGG is expected to perform more efficiently and reliably in field tests in the future.

Study on Misalignment Angle Compensation during Scale Factor Matching for Two Pairs of Accelerometers in a Gravity Gradient Instrument.

A method for automatic compensation of misalignment angles during matching the scale factors of two pairs of the accelerometers in developing the rotating accelerometer gravity gradient instrument (GGI) is proposed and demonstrated in this paper. The purpose of automatic scale factor matching of the four accelerometers in GGI is to suppress the common mode acceleration of the moving-based platforms. However, taking the full model equation of the accelerometer into consideration, the other two orthogonal axes which is the pendulous axis and the output axis, will also sense the common mode acceleration and reduce the suppression performance. The coefficients from the two axes to the output are δO and δP respectively, called the misalignment angles. The angle δO, coupling with the acceleration along the pendulous axis perpendicular to the rotational plane, will not be modulated by the rotation and gives little contribution to the scale factors matching. On the other hand, because of coupling with the acceleration along the centripetal direction in the rotating plane, the angle δP would produce a component with 90 degrees phase delay relative to the scale factor component. Hence, the δP component coincides exactly with the sensitive direction of the orthogonal accelerometers. To improve the common mode acceleration rejection, the misalignment angle δP is compensated by injecting a trimming current, which is proportional to the output of an orthogonal accelerometer, into the torque coil of the accelerometer during the scale factor matching. The experimental results show that the common linear acceleration suppression achieved three orders after the scale factors balance and five orders after the misalignment angles compensation, which is almost down to the noise level of the used accelerometers of 1~2 × 10−7 g/√Hz (1 g ≈ 9.8 m/s²).

A Subnano-g Electrostatic Force-Rebalanced Flexure Accelerometer for Gravity Gradient Instruments.

A subnano-g electrostatic force-rebalanced flexure accelerometer is designed for the rotating accelerometer gravity gradient instrument. This accelerometer has a large proof mass, which is supported inversely by two pairs of parallel leaf springs and is centered between two fixed capacitor plates. This novel design enables the proof mass to move exactly along the sensitive direction and exhibits a high rejection ratio at its cross-axis directions. Benefiting from large proof mass, high vacuum packaging, and air-tight sealing, the thermal Brownian noise of the accelerometer is lowered down to less than 0.2 ng / Hz with a quality factor of 15 and a natural resonant frequency of about 7.4 Hz . The accelerometer's designed measurement range is about ±1 mg. Based on the correlation analysis between a commercial triaxial seismometer and our accelerometer, the demonstrated self-noise of our accelerometers is reduced to lower than 0.3 ng / Hz over the frequency ranging from 0.2 to 2 Hz, which meets the requirement of the rotating accelerometer gravity gradiometer.

High-Sensitivity Encoder-Like Micro Area-Changed Capacitive Transducer for a Nano-g Micro Accelerometer.

Encoder-like micro area-changed capacitive transducers are advantageous in terms of their better linearity and larger dynamic range compared to gap-changed capacitive transducers. Such transducers have been widely applied in rectilinear and rotational position sensors, lab-on-a-chip applications and bio-sensors. However, a complete model accounting for both the parasitic capacitance and fringe effect in area-changed capacitive transducers has not yet been developed. This paper presents a complete model for this type of transducer applied to a high-resolution micro accelerometer that was verified by both simulations and experiments. A novel optimization method involving the insertion of photosensitive polyimide was used to reduce the parasitic capacitance, and the capacitor spacing was decreased to overcome the fringe effect. The sensitivity of the optimized transducer was approximately 46 pF/mm, which was nearly 40 times higher than that of our previous transducer. The displacement detection resolution was measured as 50 pm/√Hz at 0.1 Hz using a precise capacitance detection circuit. Then, the transducer was applied to a sandwich in-plane micro accelerometer, and the measured level of the accelerometer was approximately 30 ng/√Hz at 1Hz. The earthquake that occurred in Taiwan was also detected during a continuous gravity measurement.

A New Scale Factor Adjustment Method for Magnetic Force Feedback Accelerometer.

A new and simple method to adjust the scale factor of a magnetic force feedback accelerometer is presented, which could be used in developing a rotating accelerometer gravity gradient instrument (GGI). Adjusting and matching the acceleration-to-current transfer function of the four accelerometers automatically is one of the basic and necessary technologies for rejecting the common mode accelerations in the development of GGI. In order to adjust the scale factor of the magnetic force rebalance accelerometer, an external current is injected and combined with the normal feedback current; they are then applied together to the torque coil of the magnetic actuator. The injected current could be varied proportionally according to the external adjustment needs, and the change in the acceleration-to-current transfer function then realized dynamically. The new adjustment method has the advantages of no extra assembly and ease of operation. Changes in the scale factors range from 33% smaller to 100% larger are verified experimentally by adjusting the different external coefficients. The static noise of the used accelerometer is compared under conditions with and without the injecting current, and the experimental results find no change at the current noise level, which further confirms the validity of the presented method.

New Test of the Gravitational Inverse-Square Law at the Submillimeter Range with Dual Modulation and Compensation.

By using a torsion pendulum and a rotating eightfold symmetric attractor with dual modulation of both the interested signal and the gravitational calibration signal, a new test of the gravitational inverse-square law at separations down to 295 µm is presented. A dual-compensation design by adding masses on both the pendulum and the attractor was adopted to realize a null experiment. The experimental result shows that, at a 95% confidence level, the gravitational inverse-square law holds (|α|≤1) down to a length scale λ=59 µm. This work establishes the strongest bound on the magnitude α of Yukawa-type deviations from Newtonian gravity in the range of 70-300 µm, and improves the previous bounds by up to a factor of 2 at the length scale λ≈160 µm.

Boosting the electron beam transmittance of field emission cathode using a self-charging gate.

The gate-type carbon nanotubes cathodes exhibit advantages in long-term stable emission owing to the uniformity of electrical field on the carbon nanotubes, but the gate inevitably reduces the transmittance of electron beam, posing challenges for system stabilities. In this work, we introduce electron beam focusing technique using the self-charging SiNx/Au/Si gate. The potential of SiNx is measured to be approximately -60 V quickly after the cathode turning on, the negative potential can be maintained as the emission goes on. The charged surface generates rebounding electrostatic forces on the following electrons, significantly focusing the electron beam on the center of gate hole and allowing them to pass through gate with minimal interceptions. An average transmittance of 96.17% is observed during 550 hours prototype test, the transmittance above 95% is recorded for the cathode current from 2.14 µA to 3.25 mA with the current density up to 17.54 mA cm-2.

Analysis of the Frequency-Dependent Vibration Rectification Error in Area-Variation-Based Capacitive MEMS Accelerometers.

The presence of strong ambient vibrations could have a negative impact on applications such as high precision inertial navigation and tilt measurement due to the vibration rectification error (VRE) of the accelerometer. In this paper, we investigate the origins of the VRE using a self-developed MEMS accelerometer equipped with an area-variation-based capacitive displacement transducer. Our findings indicate that the second-order nonlinearity coefficient is dependent on the frequency but the VRE remains constant when the displacement amplitude of the excitation is maintained at a constant level. This frequency dependence of nonlinearity is a result of several factors coupling with each other during signal conversion from acceleration to electrical output signal. These factors include the amplification of the proof mass's amplitude as the excitation frequency approaches resonance, the nonlinearity in capacitance-displacement conversion at larger displacements caused by the fringing effect, and the offset of the mechanical suspension's equilibrium point from the null position of the differential capacitance electrodes. Through displacement transducer and damping optimization, the second-order nonlinearity coefficient is greatly reduced from mg/g2 to µg/g2.

Test of the gravitational inverse square law at millimeter ranges.

We report a new test of the gravitational inverse square law at millimeter ranges by using a dual-modulation torsion pendulum. An I-shaped symmetric pendulum and I-shaped symmetric attractors were adopted to realize a null experimental design. The non-Newtonian force between two macroscopic tungsten plates is measured at separations ranging down to 0.4 mm, and the validity of the null experimental design was checked by non-null Newtonian gravity measurements. We find no deviations from the Newtonian inverse square law with 95% confidence level, and this work establishes the most stringent constraints on non-Newtonian interaction in the ranges from 0.7 to 5.0 mm, and a factor of 8 improvement is achieved at the length scale of several millimeters.

Comparison study of high-sensitivity area-changed capacitive displacement transducers with low-impedance and high-impedance readout circuits.

Area-changed capacitive displacement transducers (CDTs) are widely used in the high-precision displacement measurement due to their high accuracy and large dynamic range. The preamplifier circuit is used to convert the capacitance variation signal into voltage, which requires low noise and is significant for the high-sensitivity area-changed CDTs. Current CDT preamplifiers are mainly categorized as the low-impedance preamplifier and the high-impedance preamplifier; however, their characteristics and application scopes have not been systematically compared. This paper builds comprehensive models of the low-impedance and the high-impedance preamplifiers. Then, three-electrode configurations with different electrode separations and gaps are designed to carry out displacement variation experiments with low-impedance and high-impedance readout circuits, respectively. The results show that the sensitivity decrease caused by the gap change with the high-impedance preamplifier is 70%, while the counterpart of the low-impedance preamplifier is 85%. When the gap is 0.1 mm and the width-to-separation ratio varies from 1:1 to 5:1, the sensitivity of the CDT based on the low-impedance preamplifier is increased by 64%, while the counterpart with the high-impedance preamplifier is increased by 22%. Hence, this paper gives the universal guiding rules of preamplification circuit selections for different CDT electrode configurations and application requirements. For a capacitive sensor design with large and unavoidable parasitic capacitance, the low-impedance preamplifier and a CDT with a large electrode width-to-separation ratio match best. For a capacitive sensor design requiring both a large sensitivity and good robustness to out-of-plane interferences, the high-impedance preamplifier and a CDT with a small electrode width-to-separation ratio match best.

Multi-Grid Capacitive Transducers for Measuring the Surface Profile of Silicon Wafers.

The measurements of wafers' surface profile are crucial for safeguarding the fabrication quality of integrated circuits and MEMS devices. The current techniques measure the profile mainly by moving a capacitive or optical spacing sensing probe along multiple lines, which is high-cost and inefficient. This paper presents the calculation, simulation and experiment of a method for measuring the surface profile with arrayed capacitive spacing transducers. The calculation agreed well with the simulation and experiment. Finally, the proposed method was utilized for measuring the profile of a silicon wafer. The result is consistent with that measured by a commercial instrument. As a movement system is not required, the proposed method is promising for industry applications with superior cost and efficiency to the existing technology.