Optically levitated micro gyroscopes with an MHz rotational vaterite rotor.

The field of levitated optomechanics has experienced significant advancements in manipulating the translational and rotational dynamics of optically levitated particles and exploring their sensing applications. The concept of using optically levitated particles as gyroscopes to measure angular motion has long been explored but has not yet been proven either theoretically or experimentally. In this study, we present the first rotor gyroscope based on optically levitated high-speed rotating particles. The gyroscope is composed of a micrometer-size ellipsoidal vaterite particle that is driven to rotate at MHz frequencies in a vacuum environment. When an external angular velocity is input, the optical axis deviates from its initial position, resulting in changes in the frequency and amplitude of the rotational signal. By analyzing these changes, the angular velocity of the input can be accurately detected, making it the smallest rotor gyroscope in the world. The angular rate bias instability of the gyroscope is measured to be 0.08°/s and can be further improved to as low as 10-9°/h theoretically by cooling the motion and increasing the angular moment of the levitated particle. Our work opens a new application paradigm for levitated optomechanical systems and may pave the way for the development of quantum rotor gyroscopes.

Gradient torque and its effect on rotational dynamics of optically trapped non-spherical particles in the elliptic Gaussian beam.

Rotational motion of the optically trapped particle is a topic of enduring interest, while the changes of angular velocity in one rotation period remain largely unexplored. Here, we proposed the optical gradient torque in the elliptic Gaussian beam, and the instantaneous angular velocities of alignment and fluctuant rotation of the trapped non-spherical particles are investigated for the first time. The fluctuant rotations of optically trapped particles are observed, and the angular velocity fluctuated twice per rotation period, which can be used to determine the shape of trapped particles. Meanwhile, a compact optical wrench is invented based on the alignment, and its torque is adjustable and is larger than the torque of a linearly polarized wrench with the same power. These results provide a foundation for precisely modelling the rotational dynamics of optically trapped particles, and the presented wrench is expected to be a simple and practical micro-manipulating tool.

A Miniature Optical Force Dual-Axis Accelerometer Based on Laser Diodes and Small Particles Cavities.

In recent years, the optical accelerometer based on the optical trapping force effect has gradually attracted the attention of researchers for its high sensitivity and high measurement accuracy. However, due to its large size and the complexity of optical path adjustment, the optical force accelerometers reported are only suitable for the laboratory environment up to now. In this paper, a miniature optical force dual-axis accelerometer based on the miniature optical system and a particles cavity which is prepared by Micro-Electro-Mechanical Systems (MEMS) technology is proposed. The overall system of the miniature optical levitation including the miniature optical system and MEMS particles cavity is a cylindrical structure with a diameter of about 10 mm and a height of 33 mm (Φ 10 mm × 33 mm). Moreover, the size of this accelerometer is 200 mm × 100 mm × 100 mm. Due to the selected light source being a laser diode light source with elliptical distribution, it is sensitive to the external acceleration in both the long axis and the short axis. This accelerometer achieves a measurement range of ±0.17 g-±0.26 g and measurement resolution of 0.49 mg and 1.88 mg. The result shows that the short-term zero-bias stability of the two orthogonal axes of the optical force accelerometer is 4.4 mg and 9.2 mg, respectively. The main conclusion that can be drawn is that this optical force accelerometer could provide an effective solution for measuring acceleration with an optical force effect for compact engineering devices.

Batch Manufacturing of Split-Actuator Micro Air Vehicle Based on Monolithic Processing Technology.

Microrobots have a wide range of applications. The rigid-flexible composite stereoscopic technology based on ultraviolet laser cutting technology is primarily researched for the design and manufacture of microrobots and has been used to fabricate microscale motion mechanisms and robots. This paper introduces a monolithic processing technology based on the rigid-flexible composite stereoscopic process. Based on this process, a split-actuator micro flapping-wing air vehicle with a size of 15 mm × 2.5 mm × 30 mm was designed. We proposed a batch manufacturing method capable of processing multiple micro air vehicles at the same time. The main structure of 22 flapping-wing micro air vehicles can be processed at the same time within the processing range of the composite sheet with an area of 80 mm × 80 mm, and the processing effect is good.

Centrifugal motion of an optically levitated particle.

Levitated optomechanical systems experience a tremendous development on detecting weak force and torque with the center of mass motion and rotation of the levitated particle. Here the levitated optomechanical system is established on a rotating platform, and the centrifugal motion of the particle is observed after rotating the optical platform. The centrifugal displacement of the particle is experimentally proven to show a quadratic function relation with the rotation speed, and the stiffness of the trap and the mass of the levitated particle are obtained from it separately. Furthermore, the centrifugal motion makes the particle deviate from the laser focus center, which would decrease the particle spin speed. These results will help to understand the centrifugal motion and fully consider this effect when the optomechanical system rotates.

Miniature Ultralight Deformable Squama Mechanics and Skin Based on Piezoelectric Actuation.

A miniature deformable squama mechanics based on piezoelectric actuation inspired by the deformable squama is proposed in this paper. The overall size of the mechanics is 16 mm × 6 mm × 6 mm, the weight is only 140 mg, the deflection angle range of the mechanical deformation is -15°~45°, and the mechanical deformation is controllable. The small-batch array processing of the miniature deformable squama mechanics, based on the stereoscopic process, laid the technological foundation for applying the deformed squama array arrangement. We also designed and manufactured a small actuation control boost circuit and a mobile phone piezoelectric control assistant application that makes it convenient to perform short-range non-contact control of the deformation of the squama. The proposed system arranges the deformed squamae into groups to form the skin and controlls the size and direction of the signals input to each group of the squama array, thereby making the skin able to produce different shapes to create deformable skin.

Damping Asymmetry Trimming Based on the Resistance Heat Dissipation for Coriolis Vibratory Gyroscope in Whole-Angle Mode.

Damping asymmetry is one of the most important factors that determines the performance of Coriolis Vibratory Gyroscope. In this paper, a novel damping tuning method for the resonator with parallel plate capacitors is presented. This damping tuning method is based on resistance heat dissipation and the tuning effect is characterized by the control force in Whole-Angle mode. As the damping tuning and stiffness tuning in the resonator with parallel plate capacitors are coupled with each other, a corresponding tuning system is designed. To verify the tuning effects, experiments are conducted on a hemispherical resonator gyroscope with Whole-Angle mode. The damping tuning theories is demonstrated by the testing results and 87% of the damping asymmetry is reduced by this tuning method with a cost of 3% decaying time. Furthermore, the angle-dependent drift in rate measurement after tuning is only 15.6% of the one without tuning and the scale factor nonlinearity decreases from 5.49 ppm to 2.66 ppm. The method can be further applied on the damping tuning in other resonators with symmetrical structure.

A Study on the Trimming Effects on the Quality Factor of Micro-Shell Resonators Vibrating in Wineglass Modes.

Frequency trimming based on mass and stiffness modification is an important post-fabrication process for micro-shell resonators (MSRs). However, the trimming effects on the quality factor are seldom studied, although they may have great influence on the performance of the resonator. This paper presents a study on the quality factor (Q-factor) variation of trimmed micro-shell resonators (MSR). Thermoelastic damping (QTED) and anchor loss (Qanchor) are found to be the dominant energy loss mechanisms resulting in the reduction of the overall Q-factor, according to finite element method (FEM). The effects of different trimming methods on QTED and Qanchor are studied here, respectively. It is found that trimming grooves ablated in the rim of the resonator can cause a ~1-10% reduction of QTED, and the length of trimming groove is positively related to the reduction of QTED. The reduction of QTED caused by the mass adding process is mainly related to the thermal expansion coefficient and density of the additive and contact area between the resonator and additive masses. Besides, the first and second harmonic errors caused by asymmetrical trimming can cause a 10-90% reduction of Qanchor. Finally, trimming experiments were conducted on different resonators and the results were compared with FEM simulation. The work presented in this paper could help to optimize the trimming process of MSRs.

Investigation on the Quality Factor Limit of the (111) Silicon Based Disk Resonator.

Quality factor is one of the most important parameters for a MEMS resonator. Most MEMS resonators are dominated by thermoelastic dissipation (TED). This paper demonstrates that the TED in a disk resonator that is made of (111) single-crystal silicon is surpassed by clamping loss. The stiffness-mass decoupling design method, combined with reducing the beam width, was used to engineer high QTED. Experiments show that Q of the (111) disk resonator have an upper boundary that is determined by the clamping loss caused by the unbalanced out-of-plane displacement. The origin of the out-of-plane displacement is explained by theory and simulation.

Analysis of the Damping Characteristics of Cylindrical Resonators Influenced by Piezoelectric Electrodes.

The cylindrical resonator gyroscope (CRG) is a typical Coriolis vibratory gyroscope whose performance is mostly influenced by the damping characteristic of the cylindrical resonator. However, the tremendous damping influences caused by pasting piezoelectric electrodes on the gyroscope, which degrades the performance to a large extent, have rarely been studied. In this paper, the dynamical model is established to analyze various forms of energy consumption. In addition, a FE COMSOL model is also created to discuss the damping influences of several significant parameters of the adhesive layer and piezoelectric electrodes, respectively, and then explicit influence laws are obtained. Simulation results demonstrate that the adhesive layer has some impact on the damping characteristic, but it not significant. The Q factor decreases about 30.31% in total as a result of pasting piezoelectric electrodes. What is more, it is discovered that piezoelectric electrodes with short length, locations away from the outside edges, proper width and well-chosen thickness are able to reduce the damping influences to a large extent. Afterwards, experiments of testing the Q factor are set up to validate the simulation values.

Analysis on Node Position of Imperfect Resonators for Cylindrical Shell Gyroscopes.

For cylindrical shell gyroscopes, node position of their operating eigenmodes has an important influence on the gyroscopes' performance. It is considered that the nodes are equally separated from each other by 90° when the resonator vibrates in the standing wave eigenmode. However, we found that, due to manufacturing errors and trimming, the nodes may not be equally distributed. This paper mainly analyzes the influences of unbalanced masses on the cylindrical resonators' node position, by using FEM simulation and experimental measurement.

A novel vibration mode testing method for cylindrical resonators based on microphones.

Non-contact testing is an important method for the study of the vibrating characteristic of cylindrical resonators. For the vibratory cylinder gyroscope excited by piezo-electric electrodes, mode testing of the cylindrical resonator is difficult. In this paper, a novel vibration testing method for cylindrical resonators is proposed. This method uses a MEMS microphone, which has the characteristics of small size and accurate directivity, to measure the vibration of the cylindrical resonator. A testing system was established, then the system was used to measure the vibration mode of the resonator. The experimental results show that the orientation resolution of the node of the vibration mode is better than 0.1°. This method also has the advantages of low cost and easy operation. It can be used in vibration testing and provide accurate results, which is important for the study of the vibration mode and thermal stability of vibratory cylindrical gyroscopes.

Structural-acoustic coupling effects on the non-vacuum packaging vibratory cylinder gyroscope.

The resonant shells of vibratory cylinder gyroscopes are commonly packaged in metallic caps. In order to lower the production cost, a portion of vibratory cylinder gyroscopes do not employ vacuum packaging. However, under non-vacuum packaging conditions there can be internal acoustic noise leading to considerable acoustic pressure which is exerted on the resonant shell. Based on the theory of the structural-acoustic coupling, the dynamical behavior of the resonant shell under acoustic pressure is presented in this paper. A finite element (FE) model is introduced to quantitatively analyze the effect of the structural-acoustic coupling. Several main factors, such as sealing cap sizes and degree of vacuum which directly affect the vibration of the resonant shell, are studied. The results indicate that the vibration amplitude and the operating frequency of the resonant shell will be changed when the effect of structural-acoustic coupling is taken into account. In addition, an experiment was set up to study the effect of structural-acoustic coupling on the sensitivity of the gyroscope. A 32.4 mV/°/s increase of the scale factor and a 6.2 Hz variation of the operating frequency were observed when the radial gap size between the resonant shell and the sealing cap was changed from 0.5 mm to 20 mm.

A study of the temperature characteristics of vibration mode axes for vibratory cylinder gyroscopes.

The zero bias stability, which is an important performance parameter for vibratory cylinder gyroscopes, is high sensitive to temperature change. It is considered that the varying temperature makes the vibration mode axes unstable, which has significant influence on the zero bias stability. This paper will investigate this problem in detail. First, the relationships between the angular positions of vibration mode axes and the zero bias are analyzed. Secondly, the thermal-modal model of the cylinder resonator with several defects such as mass imbalance, frequency split (FS), and geometry errors are developed by ANSYS. Simulation results show that with the increase of temperature, angular positions of the vibration mode axes obviously change, which leads to a dramatic zero bias drift. Finally, several major influence factors on the angular position stability of vibration mode axes, including frequency split, geometry errors, thermal elastic modulus coefficient (TEMC) and thermal expansion coefficient (TEC) are analyzed in detail. Simulation results in this paper will be helpful for deep understanding of the drift principle of zero bias induced by temperature for vibratory cylinder gyroscopes and also be helpful for further temperature compensation or control.

Sphere-to-sphere diffraction propagation method for a phase-retrieval algorithm in the measurement of optical surfaces.

We present an improved phase-retrieval algorithm that is based on the Sziklas and Siegman coordinate transformation (SSCT) and applied to optical surface testing. With the SSCT, a spherical-wave diffraction problem can be transformed into a plane-wave diffraction problem, and the fast Fourier transform can be applied directly in propagation computations. Compared with conventional diffraction propagation methods, the proposed method is simple and relatively fast, and the computation efficiency for the phase-retrieval algorithm can be increased to a certain degree. Analysis and simulation were performed for this method, and simulation results exhibit correct diffraction computation and good phase-retrieval capability. A practical 200 mm diameter, f/5 spherical surface was tested; testing results showed good agreement with that of a ZYGO interferometer, which confirmed the feasibility and accuracy of the proposed method.

Subsurface damage distribution in the lapping process.

To systematically investigate the influence of lapping parameters on subsurface damage (SSD) depth and characterize the damage feature comprehensively, maximum depth and distribution of SSD generated in the optical lapping process were measured with the magnetorheological finishing wedge technique. Then, an interaction of adjacent indentations was applied to interpret the generation of maximum depth of SSD. Eventually, the lapping procedure based on the influence of lapping parameters on the material removal rate and SSD depth was proposed to improve the lapping efficiency.