Investigation of the Charge Accumulation Based on Stiffness Variation of the Micro-Shell Resonator Gyroscope.

In capacitive microelectromechanical system (MEMS) devices, the application of dielectric materials causes long-term charging problems in the dielectric layers or substrates, which especially affect the repeatability and stability of high-performance devices. Due to the difficulties of observation and characterization of charge accumulation, an accurate characterization method is needed to study the effect of charge and propose suppression methods. In this paper, we analyze the influence of charge accumulation on the MSRG and propose a characterization method for charge accumulation based on stiffness variation. Experiments are carried out to characterize the charge accumulation in MSRG, and the effect of temperature on the process is also investigated. In the experiment, the charge accumulation is characterized accurately by the variation of the frequency split and stiffness axes. Furthermore, the acceleration of the charge accumulation is observed at high temperatures, as is the higher additional voltage from the charge accumulation.

Simulations and Experiments on the Vibrational Characteristics of Cylindrical Resonators with First Three Harmonic Errors.

A cylindrical resonator gyroscope is a kind of Coriolis gyroscope, which measures angular velocity or angle via processing of the standing wave. The symmetry of a cylindrical resonator is destroyed by different degrees of geometric nonuniformity and structural damage in the machining process. The uneven mass distribution caused by the asymmetry of the resonator can be expressed in the form of a Fourier series. The first three harmonics will reduce the anti-interference ability of the resonator to the external vibration, as well as increase the angular random walk and zero-bias drift of the gyroscope. In this paper, the frequency split of different modes caused by the first three harmonic errors and the displacement of the center of the cylindrical resonator bottom plate are obtained by simulation, and the relationship between them is explored. The experimental results on five fused silica cylindrical resonators are consistent with the simulation, confirming the linear relationship between the n = 1 frequency split and second harmonic error. A method for evaluating the first three harmonic errors of fused silica cylindrical resonators is provided.

A High-Precision Method of Stiffness Axes Identification for Axisymmetric Resonator Gyroscopes.

Axisymmetric resonators are key elements of Coriolis vibratory gyroscopes (CVGs). The performance of a CVG is closely related to the stiffness and damping symmetry of its resonator. The stiffness symmetry of a resonator can be effectively improved by electrostatic tuning or mechanical trimming, both of which need an accurate knowledge of the azimuth angles of the two stiffness axes of the resonator. Considering that the motion of a non-ideal axisymmetric resonator can be decomposed as two principal oscillations with two different natural frequencies along two orthogonal stiffness axes, this paper introduces a novel high-precision method of stiffness axes identification. The method is based on measurements of the phase difference between the signals detected at two orthogonal sensing electrodes when an axisymmetric resonator is released from all the control forces of the force-to-rebalance mode and from different initial pattern angles. Except for simplicity, our method works with the eight-electrodes configuration, in no need of additional electrodes or detectors. Furthermore, the method is insensitive to the variation of natural frequencies and operates properly in the cases of either large or small frequency splits. The introduced method is tested on a resonator gyroscope, and two stiffness axes azimuth angles are obtained with a resolution better than 0.1°. A comparison of the experimental results and theoretical model simulations confirmed the validity of our method.

A Novel Mechanical Frequency Tuning Method Based on Mass-Stiffness Decoupling for MEMS Gyroscopes.

MEMS gyroscopes play an important role in inertial navigation measurements, which mainly works in n = 2 mode. However, mode matching is the basis for high-precision detection, which can improve the sensitivity, resolution, and signal-to-noise ratio of the gyroscopes. An initial frequency split is inevitably generated during the manufacturing process. There are two methods to eliminate the frequency split and to achieve mode matching for the gyroscopes, which are electrostatic tuning and mechanical trimming, respectively. In this paper, we report a novel ring MEMS resonator and a novel method of mechanical frequency tuning. The most prominent characteristic of the resonator is that 16 raised mass blocks are increased in the circumferential positions of the ring uniformly. This structural design can achieve mass-stiffness decoupling, which means that punching holes on the mass blocks only affects the mass distribution but the stiffness is almost unchanged for the resonator. We verify the mass-stiffness decoupling by way of comparing the simulation with the conventional resonator. In addition, we put up an online tuning platform based on a femtosecond laser and reduce a resonator's frequency split from 23.3 Hz to 0.4 Hz, which reveals that the frequency split is linearly related to the removed mass. These findings will have a referential significance for other transducers.

Effects of Structural Dimension Variation on the Vibration of MEMS Ring-Based Gyroscopes.

This study investigated the effects of structural dimension variation arising from fabrication imperfections or active structural design on the vibration characteristics of a (100) single crystal silicon (SCS) ring-based Coriolis vibratory gyroscope. A mathematical model considering the geometrical irregularities and the anisotropy of Young's modulus was developed via Lagrange's equations for simulating the dynamical behavior of an imperfect ring-based gyroscope. The dynamical analyses are focused on the effects on the frequency split between two vibration modes of interest as well as the rotation of the principal axis of the 2θ mode pair, leading to modal coupling and the degradation of gyroscopic sensitivity. While both anisotropic Young's modulus and nonideal deep trench verticality affect the frequency difference between two vibration modes, they have little contribution to deflecting the principal axis of the 2θ mode pair. However, the 4θ variations in the width of both the ring and the supporting beams cause modal coupling to occur and the degenerate 2θ mode pair to split in frequency. To aid the optimal design of MEMS ring-based gyroscopic sensors that has relatively high robustness to fabrication tolerance, a geometrical compensation based on the developed model is demonstrated to identify the geometries of the ring and the suspension.

Frequency Disentanglement Distillation Image Deblurring Network.

Due to the blur information and content information entanglement in the blind deblurring task, it is very challenging to directly recover the sharp latent image from the blurred image. Considering that in the high-dimensional feature map, blur information mainly exists in the low-frequency region, and content information exists in the high-frequency region. In this paper, we propose a encoder-decoder model to realize disentanglement from the perspective of frequency, and we named it as frequency disentanglement distillation image deblurring network (FDDN). First, we modified the traditional distillation block by embedding the frequency split block (FSB) in the distillation block to separate the low-frequency and high-frequency region. Second, the modified distillation block, we named frequency distillation block (FDB), can recursively distill the low-frequency feature to disentangle the blurry information from the content information, so as to improve the restored image quality. Furthermore, to reduce the complexity of the network and ensure the high-dimension of the feature map, the frequency distillation block (FDB) is placed on the end of encoder to edit the feature map on the latent space. Quantitative and qualitative experimental evaluations indicate that the FDDN can remove the blur effect and improve the image quality of actual and simulated images.

A Novel Method for Estimating and Balancing the Second Harmonic Error of Cylindrical Fused Silica Resonators.

The cylindrical resonator gyroscope (CRG) is a type of Coriolis vibratory gyroscope which measures the angular velocity or angle through the precession of the elastic wave of the cylindrical resonator. The cylindrical fused silica resonator is an essential component of the CRG, the symmetry of which determines the bias drift and vibration stability of the gyroscope. The manufacturing errors breaking the symmetry of the resonator are usually described by Fourier series, and most studies are only focusing on analyzing and reducing the fourth harmonic error, the main error source of bias drift. The second harmonic error also is one of the obstacles for CRG towards high precision. Therefore, this paper provides a chemical method to evaluate and balance the second harmonic error of cylindrical fused silica resonators. The relation between the frequency split of the n = 1 mode and the second harmonic error of the resonator is obtained. Simulations are performed to analyze the effects of the first three harmonic errors on the frequency splits. The relation between the location of the low-frequency axis of n = 1 mode and the heavy axis of the second harmonic error is also analyzed by simulation. Chemical balancing experiments on two fused silica resonators demonstrate the feasibility of this balancing procedure, and show good consistency with theoretical and simulation analysis. The second harmonic error of the two resonators is reduced by 86.6% and 79.8%, respectively.

Automatic Mode-Matching Method for MEMS Disk Resonator Gyroscopes Based on Virtual Coriolis Force.

An automatic mode-matching method for MEMS (Micro-electromechanical Systems) disk resonator gyroscopes (DRGs) based on virtual Coriolis force is presented in this paper. For this mode-matching method, the additional tuning electrodes are not required to be designed, which simplifies the structure design. By using the quadratic relationship between the driving voltage and the electrostatic force, the virtual Coriolis force is obtained by applying an AC voltage whose frequency is half of the driving mode resonant frequency to the sense electrode. The phase difference between the virtual Coriolis force and the sense output signal is used for mode-matching. The structural characteristics and electrode distribution of the DRG are briefly introduced. Moreover, the mode-matching theories of the DRG are studied in detail. The scheme of the mode-matching control system is proposed. Simultaneously, the feasibility and effectiveness of the mode-matching method are verified by system simulation. The experimental results show that under the control of mode-matching at room temperature, the bias instability is reduced from 30.7575 ° /h to 2.8331 ° /h, and the Angle Random Walk (ARW) decreases from 1.0208 ° / h to 0.0524 ° / h . Compared with the mode mismatch condition, the ARW is improved by 19.48 times.

Trimming of Imperfect Cylindrical Fused Silica Resonators by Chemical Etching.

The cylindrical resonator gyroscope (CRG) is a kind of solid-state gyroscope with a wide application market. The cylindrical resonator is the key component of CRG, whose quality factor and symmetry will directly affect the performance of the gyroscope. Due to the material properties and fabrication limitations, the actual resonator always has some defects. Therefore, frequency trimming, i.e., altering the local mass or stiffness distribution by certain methods, is needed to improve the overall symmetry of the resonator. In this paper, we made further derivation based on the chemical trimming theory proposed by Basarab et al. We built up the relation between the frequency split and the balanced mass to determine the mass to be removed. Chemical trimming experiments were conducted on three cylindrical fused silica resonators. The frequency splits of the three resonators were around 0.05 Hz after chemical trimming. The relation between frequency split and balanced mass established from experimental data was consistent with the theoretical calculation. Therefore, frequency split can be reduced to lower than 0.05 Hz under rigorous theoretical calculation and optimized chemical trimming parameters.

Optical and Electrical Method Characterizing the Dynamic Behavior of the Fused Silica Cylindrical Resonator.

Fused silica cylindrical resonant gyroscope (CRG) is a novel high-precision solid-wave gyroscope, whose performance is primarily determined by the cylindrical resonator's frequency split and quality factor (Q factor). The laser Doppler vibrometer (LDV) is extensively used to measure the dynamic behavior of fused silica cylindrical resonators. An electrical method was proposed to characterize the dynamic behavior of the cylindrical resonator to enhance the measurement efficiency and decrease the equipment cost. With the data acquisition system and the designed signal analysis program based on LabVIEW software, the dynamic behavior of the fused silica cylindrical resonator can be analyzed automatically and quickly. We compared all the electrical measurement results with the optical detection by LDV, demonstrating that the fast Fourier transform (FFT) result of the resonant frequency measured by the electrical method was 0.12 Hz higher than that with the optical method. Thus, the frequency split measured by the electrical and optical methods was the same in 0.18 Hz, and the measurement of the Q factor was basically the same in 730,000. We conducted all measurements under the same operation condition, and the optical method was used as a reference, demonstrating that the electrical method could characterize the dynamic behavior of the fused silica cylindrical resonator and enhance the measurement efficiency.

The Effect of the Anisotropy of Single Crystal Silicon on the Frequency Split of Vibrating Ring Gyroscopes.

This paper analyzes the effect of the anisotropy of single crystal silicon on the frequency split of the vibrating ring gyroscope, operated in the n = 2 wineglass mode. Firstly, the elastic properties including elastic matrices and orthotropic elasticity values of (100) and (111) silicon wafers were calculated using the direction cosines of transformed coordinate systems. The (111) wafer was found to be in-plane isotropic. Then, the frequency splits of the n = 2 mode ring gyroscopes of two wafers were simulated using the calculated elastic properties. The simulation results show that the frequency split of the (100) ring gyroscope is far larger than that of the (111) ring gyroscope. Finally, experimental verifications were carried out on the micro-gyroscopes fabricated using deep dry silicon on glass technology. The experimental results are sufficiently in agreement with those of the simulation. Although the single crystal silicon is anisotropic, all the results show that compared with the (100) ring gyroscope, the frequency split of the ring gyroscope fabricated using the (111) wafer is less affected by the crystal direction, which demonstrates that the (111) wafer is more suitable for use in silicon ring gyroscopes as it is possible to get a lower frequency split.

Decreasing Frequency Splits of Hemispherical Resonators by Chemical Etching.

The hemispherical resonator gyroscope (HRG) has attracted the interest of the world inertial navigation community because of its exceptional performance, ultra-high reliability and its potential to be miniaturized. These devices achieve their best performance when the differences in the frequencies of the two degenerate working modes are eliminated. Mechanical treatment, laser ablation, ion-beams etching, etc., have all been applied for the frequency tuning of resonators, however, they either require costly equipment and procedures, or alter the quality factors of the resonators significantly. In this paper, we experimentally investigated for the first time the use of a chemical etching procedure to decrease the frequency splits of hemispherical resonators. We provide a theoretical analysis of the chemical etching procedure, as well as the relation between frequency splits and mass errors. Then we demonstrate that the frequency split could be decreased to below 0.05 Hz by the proposed chemical etching procedure. Results also showed that the chemical etching method caused no damage to the quality factors. Compared with other tuning methods, the chemical etching method is convenient to implement, requiring less time and labor input. It can be regarded as an effective trimming method for obtaining medium accuracy hemispherical resonator gyroscopes.

Automatic Frequency Tuning Technology for Dual-Mass MEMS Gyroscope Based on a Quadrature Modulation Signal.

In order to eliminate the frequency mismatch of MEMS (Microelectromechanical Systems) gyroscopes, this paper proposes a frequency tuning technology based on a quadrature modulation signal. A sinusoidal signal having a frequency greater the gyroscope operating bandwidth is applied to the quadrature stiffness correction combs, and the modulation signal containing the frequency split information is then excited at the gyroscope output. The effects of quadrature correction combs and frequency tuning combs on the resonant frequency of gyroscope are analyzed. The tuning principle based on low frequency input excitation is analyzed, and the tuning system adopting this principle is designed and simulated. The experiments are arranged to verify the theoretical analysis. The wide temperature range test (-20 ∘ C ⁻60 ∘ C ) demonstrates the reliability of the tuning system with a maximum mismatch frequency of less than 0.3 Hz. The scale factor test and static test were carried out at three temperature conditions (-20 ∘ C, room temperature, 60 ∘ C), and the scale factor, zero-bias instability, and angle random walk are improved. Moreover, the closed-loop detection method is adopted, which improves the scale factor nonlinearity and bandwidth under the premise of maintaining the same static performances compared with the open-loop detection by tuning.

Structural Analysis of Disk Resonance Gyroscope.

In this paper, we present two design methods to improve the performance of disk resonator gyroscope (DRG), including decreasing the frequency split and increasing the quality factor (Q). The structure parameters, which can affect the frequency split and Q value were concluded with the help of the FEM software. Meanwhile, devices with different parameters were designed, fabricated, and tested, and the experimental result was in accordance with the simulation. With the proposed methods, the DRG was selected with a high Q value and a low frequency split to satisfy the demand of high performance. The weakness and future works were pointed at last.

Carotid dual-energy CT angiography: Evaluation of low keV calculated monoenergetic datasets by means of a frequency-split approach for noise reduction at low keV levels.

BACKGROUND AND PURPOSE: Calculated monoenergetic ultra-low keV datasets did not lead to improved contrast-to-noise ratio (CNR) due to the dramatic increase in image noise. The aim of the present study was to evaluate the objective image quality of ultra-low keV monoenergetic images (MEIs) calculated from carotid DECT angiography data with a new monoenergetic imaging algorithm using a frequency-split technique. MATERIALS AND METHODS: 20 patients (12 male; mean age 53±17 years) were retrospectively analyzed. MEIs from 40 to 120 keV were reconstructed using the monoenergetic split frequency approach (MFSA). Additionally MEIs were reconstructed for 40 and 50 keV using a conventional monoenergetic (CM) software application. Signal intensity, noise, signal-to-noise ratio (SNR) and CNR were assessed in the basilar, common, internal carotid arteries. RESULTS: Ultra-low keV MEIs at 40 keV and 50 keV demonstrated highest vessel attenuation, significantly greater than those of the polyenergetic images (PEI) (all p-values <0.05). The highest SNR level and CNR level was found at 40 keV and 50 keV (all p-values <0.05). MEIs with MFSA showed significantly lower noise levels than those processed with CM (all p-values <0.05) and no significant differences in vessel attenuation (p>0.05). Thus MEIs with MFSA showed significantly higher SNR and CNR compared to MEIs with CM. CONCLUSION: Combining the lower spatial frequency stack for contrast at low keV levels with the high spatial frequency stack for noise at high keV levels (frequency-split technique) leads to improved image quality of ultra-low keV monoenergetic DECT datasets when compared to previous monoenergetic reconstruction techniques without the frequency-split technique.