High-precision Displacement Measurement Research Articles

An Integrated High Precision Absolute Angular Displacement Sensor

Abstract This paper proposed a high precision absolute angular displacement time grating sensor, and was assembled into an integrated encoder. This absolute angle sensor contains two incremental sensors, namely, N1 measurement period fine measurement component and N2 measurement period coarse measurement component, N1 and N2 are mutually prime, and N1 > N2. The induction electrodes of the fine measurement component adopt differential design to minimize the effects of external electromagnetic interference and common mode interference between different sensing units so as to achieve high precision displacement measurement, the phase difference between two incremental sensor is used for absolute positioning. The reflecting ring design simplifies the structure of the encoder and facilitates sensor integration. The induction output signals of different components are cross connected through leads to the reflecting ring far away from the measurement component to the first harmonic error during the measurement period. The reading heads adopt a round, uniformly distributed design scheme, and the average effect of the whole circumference closed ring sampling scheme is beneficial for improving measurement accuracy and eliminating harmonic errors. A sensor prototype with a diameter of 83mm was manufactured and assembled into an integrated encoder. Experimental results show that the sensor achieve a precision of 12" over a full 360° measurement range and a resolution of 0.5", and it can realize absolute positioning.

Polarization beam splitter based on 2D transmissive grating

This paper introduces a two-dimensional transmissive grating polarization beam splitter (PBS) exhibiting exceptional polarization-sensitive properties with high diffraction efficiency. The optimized grating structure can concentrate the energy of TE-polarized light at the (0, ±1) orders and the energy of TM-polarized light at the (±1, 0) orders under normal incidence with a wavelength of 550nm. The polarization splitting diffraction efficiency (DE) of the grating can reach 40.17%, and the extinction ratio (ER) exceeds 18dB. This proposal marks the pioneering use of two-dimensional transmissive grating to achieve a polarization beam splitter in two perpendicular diffraction planes, presenting an innovative approach to the development of such devices. The proposed grating structure is simple, high-performing, tolerant, and applicable in a wide range of applications such as polarization imaging and high-precision two-dimensional displacement measurement.

Research on precision linear displacement measurement method based on closed loop phase-shift control of single alternating light field

Abstract A high-precision linear displacement measurement method based on the digital phase shift of a single light source is proposed. In this method, the light intensity of a four-channel sinusoidal transmission surface with a 90° difference in the spatial phase is modulated by a single channel alternating light, and four-channel alternating light intensity signal with the same time phase can be obtained. Two channels of standing wave signals with a time difference of 90° are obtained through micro-control digital phase shift processing. After differential amplification, an electric travelling wave signal containing position information of measurement object is synthesized by these two standing wave signals. By measuring the phase difference between the travelling wave and the reference signal, the high precision linear displacement can be measured. The principle of displacement measurement based on the modulation of a single-alternating light field and the principle of digital phase-shift of micro-control are introduced in detail. The feasibility of the method is verified through experiments. Finally, the sensor is optimized by analyzing the causes of error, and the measurement accuracy of ±0.2 μm is achieved within the 100 mm range with a 0.6 mm grating period.

A single-stage anchor-free rotating target visual detection algorithm suitable for flexible body vibration displacement measurement

The phenomenon of angular inclination of flexible structures during vibration poses a significant challenge to the applicability of visual vibration measurement methods because the target locked in the captured image will produce unknown geometric deformations such as scale, displacement, and angle in the time domain space, and the horizontal rectangular frame used for matching during target detection will also increase the false detection rate of the target due to the introduction of more background information. Such subtle geometric deformations and false detections can lead to severe fit errors in the displacement curves regressed by the visual vibration measurement algorithm. To effectively improve the accuracy and robustness of vibration image target recognition, this article takes the flexible body captured by a high-speed camera as the target of vibration displacement measurement. It introduces the rotating target detection method based on deep learning into the field of visual vibration measurement, which verifies the feasibility of the deep learning method in flexible body vibration measurement, and based on the deep convolutional neural network framework, a high-precision displacement measurement algorithm based on single-stage anchor-free rotating target detection is proposed. The algorithm in this article first uses the CSPDarknet backbone network to extract multi-scale features of flexible structural image sequences. It then uses PANet to fuse the top-down and bottom-up bidirectional feature maps of the four bridge target feature maps obtained through the backbone network. The shallow and deep information is used for semantic feature fusion and combined with the Coordinate Attention mechanism to achieve target finding and fine positioning on the feature map. Finally, we use the coordinates of the bounding box obtained from the test to regress the position offset of the object’s center point. To verify the accuracy of the algorithm in this article, we conducted experimental validation on the cable-stayed bridge model and the actual bridge and compared the performance with the traditional template matching algorithm, differential optical flow method, and various deep learning algorithms with different localization principles, as well as the displacement signals collected and processed by accelerometers. The experimental results of time-frequency characteristics analysis show that the vibration displacement trajectories regressed by the algorithm in this paper have the best overlap with the displacement measurements collected by the accelerometer, which verifies that the algorithm in this article has good application potential and implementation space in the field of condition monitoring of flexible structural bodies.

A 2-DOF drag-free control ground simulation system based on Stewart platform

Space-based gravitational wave detection missions use multiple satellites to form a very large scale Michelson laser interferometer in space. This requires extremely high precision displacement measurements at the picometer level between test masses even millions of kilometers apart. Drag-free control is a key technology to ensure the ultra-static and ultra-stable space experiment platform for space-based gravitational wave detection. This paper proposes an innovative ground simulation scheme for drag-free control principle based on the Stewart platform. The kinematics and dynamics modeling of the Stewart platform used in the experiment is presented. A drag-free ground simulation experimental equipment is designed and built. A two-degree-of-freedom (2-DOF) drag-free controller is designed based on the H∞ loop shaping algorithm which outperforms a PID controller in Simulink simulation. A semi-physical simulation experiment is conducted to verify the controller designed using rapid control prototyping technology. The experimental results show that the control performance reaches the limit accuracy of the hardware device, thus verifying the effectiveness of the drag-free control algorithm.

High-precision laser beam lateral displacement measurement based on differential wavefront sensing.

Accurately lateral displacement measurement is essential for a vast of non-contact sensing technologies. Here, we introduce a high-precision lateral displacement measurement method based on differential wavefront sensing (DWS). Compared to the conventional differential power sensing (DPS) method, the DWS method based on phase readout has the potential to achieve a higher resolution. The beam lateral displacement can be obtained by the curvature distribution of the wavefront on the surface of the detector. According to the theoretical model of the DWS method, the sensitivity of the lateral displacement can be greatly improved by increasing the wavefront curvature of the measured laser beam by means of lenses. An optical system for measuring the lateral displacement of the laser beam is built and calibrated by a high-precision hexapod. The experimental results show that the DWS-based lateral displacement measurement achieves a resolution of 40 pm/Hz1/2 (at 1-10 Hz) with a linear range of about 40 µm, which is consistent with the theoretical model. This technique can be applied to high-precision multi-degree-of-freedom interferometers.

An absolute ranging method based on FMCW principle using dual laser interferometry

The FMCW (Frequency Modulated Continuous Wave) laser interferometer can achieve high-precision displacement measurement by calculating the phase of the interference signal. Due to the need for continuous superposition of signal phases, the optical path and power supply cannot be interrupted during the measurement process. To solve this problem, this article proposes a new absolute ranging method—the decimal comparison method. Two distributed feedback lasers with different central wavelengths are used to measure the same target. The digital signal processing technology is used to solve the sampled interference signals, and the initial phase value corresponding to the decimal of interference is taken. Combined with the central wavelength of the two laser sources, the length variation of the F–P cavity corresponding to the number of interference periods is calculated. Finally, the optical path difference of the target is calculated by the established mathematical model. The experimental results show that this method can realize the absolute measurement of laser interferometry and can expand the application range of FMCW interferometry.

Ultra-Low Frequency High-Precision Displacement Measurement Based on Dual-Polarization Differential Fiber Heterodyne Interferometer

Picometer displacement measurement in the ultra-low frequency band below 1 Hz is highly demanded in the fields of geophysics and space exploration for the applications of hydrophones, geophones, drag-free space controllers, and so on. In this work, high-precision displacement detection in ultra-low frequency is achieved by proposing and demonstrating a dual-polarization differential fiber heterodyne interferometer. By injecting two orthogonal polarized lights into the dual-polarization differential fiber heterodyne interferometer, two optical interferences can be co-existed in a monolithic interferometer with a fully identical optical fiber path. Through the difference of the two optical interferometric phases, the light source noise and the fiber link noise can be well suppressed. Meanwhile, a pull-push type displacement sensing module is designed to double the displacement sensitivity as well as suppress the common-mode noise derived from the environmental fluctuation. Through the calibration experiment, the displacement sensitivity is obtained as 0.01634(±0.00022) rad/nm, which is consistent with the theoretical calculation. The displacement resolutions of 1.8 pm/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> at 0.1 Hz and 0.25 pm/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> at 1 Hz are achieved in the experiment, which is the superior displacement measurement level for this frequency band in the existing optic displacement sensors to our knowledge. The proposed fiber optic displacement sensor with ultra-high resolution in low frequency can be of great use in scientific research and precision engineering.

Displacement Measurement of Shaking Table Experiments Based on Binocular Vision and Subpixel Optimization

The shaking table experiment is a very useful tool to assess the seismic performance of structural models. However, there are many shortcomings in traditional displacement measurement methods. In this research, a binocular vision algorithm for accurately extracting the subpixel center of the circular target based on elliptic fitting is proposed. Firstly, the images are collected by two high-speed cameras and pre-processed to enhance their brightness and contrast. Then, an improved subpixel optimization method based on the Zernike moments and Canny operator is adopted to get accurate localization of extracted target points’ three-dimension coordinates. After comparing the displacement of target points with laser sensors, the results show that the proposed algorithm achieves high-precision displacement measurements and overcomes the problems that traditional methods hold.

Rotating box multi-objective visual tracking algorithm for vibration displacement measurement of large-span flexible bridges

Visual displacement measurement methods for flexible structural bodies like large-span bridges has gained wide popularity in recent years, but practical applications still have some limitations. For instance, when acquiring images of large-span flexible bridges at a distance, the slight angular tilt of the detection target due to irregular vibrations can cause extremely serious misfit errors in the displacement curves returned by the vision measurement algorithm. To improve the reliability of vibration displacement measurement of flexible structural bodies, this paper takes the bridge subjected to external excitation in the acquired image sequence as the object of vibration displacement measurement and uses a designed high-precision displacement measurement algorithm for a single-stage rotating target tracking anchor-free box to track the vibration displacement of the target in the flexible structural body. We first extract multi-scale feature information of bridge model image sequences using the improved YOLOv5-s backbone network and combine the Transformer self-attention mechanism with PANet to perform a top-down and bottom-up bi-directional fusion of target feature maps at three different scales to achieve semantic feature fusion of shallow and deep information. Second, the improved Efficient Decoupled Head performs the detection of rotating target centroid offset and bounding box size. Finally, the detected results are passed into the multi-objective tracking algorithm ByteTrack, which strengthens the spatio-temporal correlation between frames and obtains a better-fitting vibration displacement curve. The validation and comparison of traditional visual measurement methods and deep learning measurement methods on cable-stayed bridge models, small arch bridges, and large span bridges show that the vibration displacement trajectories regressed by the algorithm in this paper have the best fit with the actual vibration displacement trajectories, which also verifies that the algorithm in this paper has good potential for engineering applications and implementation space in the field of condition monitoring of flexible structural bodies.

Experimental observation of diffractive retroreflection from a dielectric metasurface

The non-specular reflection scenario is considered important for many practical applications of gratings because this regime corresponds to the maximum efficiency of diffraction. Retroreflection is a particular case of a non-specular scenario when a grating returns a large portion of the incident light back to its source. We propose a detailed quasi-optic (microwave) experimental study of the retroreflection phenomenon in dielectric metasurfaces. Our study is supplemented by an analytical description and full-wave numerical simulation. The experimental sample of the metasurface is constructed as an array of disk-shaped low-loss ceramic resonators inserted in a host with air-like material properties. To ensure efficient reflection, the metasurface is coated on one side with a metallic foil. The conditions of retroreflection for any direction and polarization of an incident wave are demonstrated in both far-field and near-field experiments. The main contribution to the non-specular reflection of the Mie-type (HE 11) mode of the disk-shaped resonators forming the metasurface is revealed. The high efficiency of retroreflection in both TE (transverse electric) and TM (transverse magnetic) polarizations allows us to consider our metasurface as a prototype of planar grating rulers for high-precision displacement measurements.

A Compact and High-Precision Three-Degree-of-Freedom Grating Encoder Based on a Quadrangular Frustum Pyramid Prism.

A compact and high-precision three-degrees-of-freedom (DOF; X, Y, and Z directions) grating encoder based on the quadrangular frustum pyramid (QFP) prisms is proposed in this paper to solve the insufficient installation space problem of the reading head of the multi-DOF in high-precision displacement measurement applications. The encoder is based on the grating diffraction and interference principle, and a three-DOF measurement platform is built through the self-collimation function of the miniaturized QFP prism. The overall size of the reading head is 12.3 × 7.7 × 3 cm3 and has the potential for further miniaturization. The test results show that three-DOF measurements can be realized simultaneously in the range of X-250, Y-200, and Z-100 μm due to the limitations of the measurement grating size. The measurement accuracy of the main displacement is below 500 nm on average; the minimum and maximum errors are 0.0708% and 2.8422%, respectively. This design will help further popularize the research and applications of multi-DOF grating encoders in high-precision measurements.

Accumulated Error Reduction of Linear Motor Mover Position Measurement Based on SKLM

Cumulative measurement error is the most critical factor affecting the accuracy of long-stroke displacement measurement. Based on the one-dimensional image gradient method and Smooth Kalman filter algorithm (SKLM), this paper proposes a long-stroke linear motor displacement cumulative error reduction and high precision measurement methods. First, according to the motion characteristics of the linear motor and the principle of image measurement, a one-dimensional speckle target image is generated, and the one-dimensional Barron gradient algorithm is used to calculate the displacement of adjacent frames quickly. Second, according to the rea-sons for the accumulated error of long-stroke displacement measurement, the smooth Kalman algorithm for optimized autoregressive data processing is introduced to optimally estimate the measured displacement of adjacent frames to realize the reduction of accumulated error. To improve the robustness of the measurement system, a wavelet soft threshold image filter is introduced to per-form noise reduction and restoration processing on the collected signal, and further realize the high-precision dis-placement measurement of the long-stroke linear motor. Simulations and experiments show that the method in this paper not only improves the measurement accuracy of adjacent frames, but also reduces the cumulative error of long-stroke displacement measurement. And under different working conditions, compared with other methods, it has higher accuracy and anti-interference.

Two-dimensional polarization beam splitter based on cylindrical nano grating

In this paper, we report on a two-dimensional (2D) reflective grating with excellent polarization selectivity and high diffraction efficiency (DE). Based on silver cylindrical nano arrays, the grating is calculated by rigorous coupled wave analysis (RCWA). Optimized results show that the energy of transverse electric (TE) polarization is diffracted into (0, ±1) reflection orders and the energy of transverse magnetic (TM) polarization is diffracted into (±1, 0) reflection orders under normal incidence at 780 nm incident wavelength, with extinction ratio (ER) over 30 dB. To the best of our knowledge, this is the first time that a two-dimensional polarization beam splitter (2D-PBS) based on 2D grating is proposed, which opens up a new direction for the development of PBS. The holographic exposure technology, dry etching, and electron beam evaporation were used to fabricate the 2D-PBS. Preliminary experiments indicate that the 2D grating is sensitive to the polarization states of incident light and can be applied in the wide field of optical communication, high precision displacement measurement, and so on.

Study on deformation measurement method based on structured light point clouds

For the requirement of structural deformation measurement, a deformation measurement method based on structured light point clouds is proposed. A structured light measurement system is built, and the calibration process based on the assumption of the projector's reverse camera and with the help of the checkerboard calibration board is completed. The pattern projected by the projector is designed by using a four-step phase-shift technique assisted by Gray code. By combining with system parameters which have been calibrated, the three-dimensional reconstruction of the object surface is completed. A structural deformation measurement method based on the statistical analysis of the distance between point clouds is proposed, and the principles of three points cloud distance calculation methods including point-to-point, point-to-surface and surface-to-surface are analyzed. The feasibility and accuracy of the deformation measurement method based on the structured light point cloud proposed in this paper are verified via experiments. Experimental results show that this method can achieve out-plane high-precision displacement measurement of structures.

Metrological support of video measuring systems

Test objects of various types are used when creating and using video measuring systems which are part of the robots` technical vision, television sights, triangulation measuring systems, as well as 3D scanners. At the same time, an individual test object is developed for each type of device. This paper considers the possibility of development and construction of test objects for calibration (verification) of 2D and 3D video measuring systems, which are used to measure the geometric parameters of twodimensional (2D) and three-dimensional (3D) objects, respectively. We propose to use a measure based on a liquid crystal monitor to calibrate 2D systems. The calibration of such measure is based on the use of a high-precision displacement measurement devices. They are a laser interferometer and subpixel image resolution algorithms. The measure corresponds to the standard of the 3rd category according to the State verification scheme for measuring instruments of length in the range of 1·10–9–100 m and wavelengths in the range of 0.2–50 microns. The measure can be used to measure the modulation transfer function (MTF) of a video system and the point spread function (PSF). We also propose to use gauge block and move it in space according to the specific program using a translator and an external linear encoder. We introduce the technical specifications of the developed measures that can be used as working standards for calibration (verification) of a wide class of video measuring systems.

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 0.1mm 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.

High speed time-of-flight displacement measurement based on dual-comb electronically controlled optical sampling.

We demonstrate a direct time-of-flight approach that utilizes dual-comb electronically controlled optical sampling (ECOPS) to measure small displacements. ECOPS is enabled by electrically controlling the repetition rate of one laser via an intracavity electric-optical modulator (EOM). The acquisition rate is set by the EOM modulation frequency, which is much higher than commonly used asynchronous optical sampling (ASOPS). In a proof-of-principle experiment, an 80-kHz acquisition rate is obtained with a pair of ∼105 MHz repetition rate Er-fiber lasers. At an average time of 30 ms, a measurement precision evaluated with Allan deviation reaches 26.1 nm for a 40-µm static displacement. In a dynamic measurement, a 500-Hz sinusoidal vibration with 15 µm amplitude has also been identified. The high-precision and high-speed displacement measurement technique can be potentially used in 3D surface profilometry of microelectronic step-structures and real-time monitoring of high frequency mechanical vibrations, etc.

High-precision displacement measurement algorithm based on a depth fusion of grating projection pattern.

Displacement measurement based on an image recognition algorithm has more advantages in the field of displacement measurement. Due to the uncertainty of image location, the accuracy of the displacement measurement algorithm studied in the previous stage is limited. To improve the accuracy of image-type displacement measurement, a high-precision displacement measurement algorithm based on depth fusion of the grating projection pattern is proposed. First, a line-scan image sensor and parallel light source are placed on both sides of the calibration grating. The marking pattern on the calibration grating is projected onto the image sensor through illumination of the parallel light source to realize the projection imaging. Then, the centroid algorithm is used to calculate the centroid of each line in the collected image, and the mean value of the centroid group is determined. Finally, a linear function is used to fit multiple centroids to calculate the endpoints of the subdivision region, and the subdivision operation is carried out according to a ratio algorithm. To test the performance of the proposed algorithm, a linear displacement measurement device with a 250 mm range and an angular displacement measurement device with a 100 mm diameter grating are both used for experiments. After testing, the linear measurement accuracy of the proposed algorithm is improved from 4.63 to 1.26 µm, and the angular displacement measurement accuracy is enhanced from 8.87 to 2.88''. The research in this paper provides a theoretical basis for high-performance displacement measurement.

Polarization-modulated grating interferometer by conical diffraction.

The grating interferometer in the Littrow configuration uses quarter wave plates (QWPs) to modulate the polarization in the measurement system to determine the autocollimation optical path. Fabrication errors and mounting errors of the QWPs lead to phase changes in the grating interferometer that generate measurement errors. As an alternative, we propose a grating interferometer that produces conical diffraction. Using the grating instead of QWPs to modulate the beam's polarization bypasses this source of error. A 45 mm range experiment was performed that yielded a repeated measurement error of 40 nm. Experiments show that the system has a simple structure and good repeatability and is capable of high-precision displacement measurements.