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.

Influence of the tilt error motion of the rotation axis on the test of the equivalence principle with a rotating torsion pendulum.

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.

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.

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.

Precision measurement of the Newtonian gravitational constant.

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.

A MEMS Micro-g Capacitive Accelerometer Based on Through-Silicon-Wafer-Etching Process.

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 µg/Hz1/2 at 100 Hz, and a bias instability of 4 µg 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.

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.

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.

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.

Novel Capacitive Sensing System Design of a Microelectromechanical Systems Accelerometer for Gravity Measurement Applications.

This paper presents an in-plane sandwich nano-g microelectromechanical systems (MEMS) accelerometer. The proof-mass fabrication is based on silicon etching through technology using inductive coupled plasma (ICP) etching. The capacitive detection system, which employs the area-changing sensing method, combines elementary capacitive pickup electrodes with periodic-sensing-array transducers. In order to achieve a large dynamic range with an ultrahigh resolution, the capacitive detection system employs two periodic-sensing-array transducers. Each of them can provide numbers for the signal period in the entire operating range. The suspended proof-mass is encapsulated between two glass caps, which results in a three dimensional structure. The measured resonant frequency and quality factor (Q) are 13.2 Hz and 47, respectively. The calibration response of a ±0.7 g input acceleration is presented, and the accelerometer system presents a sensitivity of 122 V/g and a noise floor of 30 ng/√Hz (at 1 Hz, and 1 atm). The bias stability for a period of 10 h is 30 µg. The device has endured a shock up to ±2.6 g, and the full scale output appears to be approximately ±1.4 g presently. This work presents a new opportunity for highly sensitive MEMS fabrication to enable future high-precision measurement applications, such as for gravity measurements.

Preliminary determination of Newtonian gravitational constant with angular acceleration feedback method.

This paper describes the preliminary measurement of the Newtonian gravitational constant G with the angular acceleration feedback method at HUST. The apparatus has been built, and preliminary measurement performed, to test all aspects of the experimental design, particularly the feedback function, which was recently discussed in detail by Quan et al. The experimental results show that the residual twist angle of the torsion pendulum at the signal frequency introduces 0.4 ppm to the value of G. The relative uncertainty of the angular acceleration of the turntable is approximately 100 ppm, which is mainly limited by the stability of the apparatus. Therefore, the experiment has been modified with three features: (i) the height of the apparatus is reduced almost by half, (ii) the aluminium shelves were replaced with shelves made from ultra-low expansion material and (iii) a perfect compensation of the laboratory-fixed gravitational background will be carried out. With these improvements, the angular acceleration is expected to be determined with an uncertainty of better than 10 ppm, and a reliable value of G with 20 ppm or below will be obtained in the near future.

G measurements with time-of-swing method at HUST.

We review the G measurements with time-of-swing method at HUST. Two independent experiments have been completed and an improved experiment is in progress. The first G value was determined as 6.6699(7)×10-11 m3 kg-1 s-2 with a relative standard uncertainty (ur) of 105 ppm by using a long period torsion pendulum and two cylindrical source masses. Later, this result was corrected to be 6.6723(9)×10-11 m3 kg-1 s-2 with ur=130 ppm after considering the density distribution of the cylinders and the air buoyancy, which was 360 ppm larger than the previous value. In 2009, a new experiment by using a simple block pendulum and spherical source masses with more homogeneous density was carried out. A series of improvements were performed, and the G value was determined to be 6.67349(18)×10-11 m3 kg-1 s-2 with ur=26 ppm. To reduce the anelasticity of the torsion fibre, fused silica fibres with Q's of approximately 5×104 are used to measure G in the ongoing experiment. These fibres are coated with thin layers of germanium and bismuth in turn to reduce the electrostatic effect. Some other improvements include the gravity compensation, reduction of the coating layer effect, etc. The prospective uncertainty of the next G value is 20 ppm or lower.

Feedback control of torsion balance in measurement of gravitational constant G with angular acceleration method.

The performance of the feedback control system is of central importance in the measurement of the Newton's gravitational constant G with angular acceleration method. In this paper, a PID (Proportion-Integration-Differentiation) feedback loop is discussed in detail. Experimental results show that, with the feedback control activated, the twist angle of the torsion balance is limited to [Formula: see text] at the signal frequency of 2 mHz, which contributes a [Formula: see text] uncertainty to the G value.

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.

A torsion balance for impulse and thrust measurements of micro-Newton thrusters.

This paper reports the performance of a torsion-type thrust stand suitable for studies of micro-Newton thrusters, which is developed for ground testing the micro-Newton thruster in Chinese Test of the Equivalence Principle with Optical readout space mission. By virtue of specially suspending design and precise assembly of torsion balance configuration, the thrust stand with load capacity up to several kilograms is able to measure the impulse bit up to 1350 µNs with a resolution of 0.47 µNs, and the average thrust up to 264 µN with a resolution of 0.09 µN in both open and close loop operation. A pulsed plasma thruster, the preliminary prototype developed for Chinese TEPO space mission, is tested by the thrust stand, and the results reveal that the average impulse bit per pulse is measured to be 58.4 µNs with a repeatability of about 5%.

Determination of the Newtonian gravitational constant G with time-of-swing method.

We present a new value of the Newtonian gravitational constant G by using the time-of-swing method. Several improvements greatly reduce the uncertainties: (1) measuring the anelasticity of the fiber directly; (2) using spherical source masses minimizes the effects of density inhomogeneity and eccentricities; (3) using a quartz block pendulum simplifies its vibration modes and minimizes the uncertainty of inertial moment; (4) setting the pendulum and source masses both in a vacuum chamber reduces the error of measuring the relative positions. By two individual experiments, we obtain G = 6.673 49(18) x 10;{-11} m;{3} kg;{-1} s;{-2} with a standard uncertainty of about 2.6 parts in 10;{5}.

Null test of Newtonian inverse-square law at submillimeter range with a dual-modulation torsion pendulum.

A null experimental test of the Newtonian inverse-square law at submillimeter range using a torsion pendulum was presented. Under the dual modulations of both the expected signal and the gravitational torque for calibration, our data concluded with 95% confidence that no new forces were observed and any gravitational-strength Yukawa forces (|alpha|>or=1) must have a length scale lambda<66 microm, agreeing well with the latest result of the Eöt-wash group. Our result sets a unification energy scale of M*>or=2.8 TeV/c2 for the two compactified extra space dimensions with the same size R*<47 microm.

New experimental limit on the photon rest mass with a rotating torsion balance.

A rotating torsion balance method is used to detect the product of the photon mass squared and the ambient cosmic vector potential A(e). The signal is modulated by rotating the torsion balance to ensure the effectiveness of detection for all possible orientations of the vector potential. The influences of sidereal disturbances of environment are also removed by virtue of this modulation method. The experimental result shows micro (2)(gamma)A(e)<1.1 x 10(-11) T m/m(2), with micro (-1)(gamma) as the characteristic length associated with photon mass. If the ambient cosmic vector potential A(e) is 10(12) T m due to cluster level fields, we obtain a new upper limit on photon mass of 1.2 x 10(-51) g.