Precision Displacement Measurement Research Articles

Super-resolution acoustic displacement metrology through topological pairs in orbital meta-atoms

The precise measurement of minute displacements using light is a common practice in modern science and technology. The utilization of sound for precision displacement metrology remains scarce due to the diffraction limit of half-wavelength, while it holds crucial applications in some specific scenarios, such as underwater environments, biological tissues, and complex machinery components. Here, we propose an approach to super-resolution acoustic displacement metrology by introducing the concept of topological pairs in orbital meta-atoms, drawing inspiration from the analogy of Cooper pairs observed in spinful electrons. The topological pairs are conjugately formed to create two distinct pathways in mode space that enable robust generation of interference. This allows the realization of acoustic analogue of Malus’s law and thereby enhances the resolution of displacement measurements. By incorporating a spiral twist configuration in orbital meta-atoms, we demonstrate the first acoustic prototype of a physical micrometer tailored for micron-scale displacement metrology. We observe experimentally a displacement resolving power of 1.2 μm at an audible frequency of 3.43 kHz, approximately 1/105 of the sound wavelength of 100 mm. Our work implies a new paradigm for precise displacement metrology within classical wave physics and lays the foundation for diverse acoustic applications.

High-Precision Chromatic Confocal Technologies: A Review

Chromatic confocal technology is widely used for precise, steady, and efficient displacement measurement in many industrial fields. It employs the confocal and dispersion principles to encode axial positions with the wavelengths of the reflected broad spectrum. The typical chromatic confocal sensor includes a light source, a dispersion objective, conjugate pinholes, and a spectral detection device. This study offers an overview of the current research on chromatic confocal technology. Because of its good performance in displacement detection, chromatic confocal technology has been widely used in contour measurement, biomedical imaging, and thickness measurements, as part of global and professional research. Due to its structural flexibility, it is also easily integrated into industrial equipment for in-machine and online profile measurements. It holds significant potential for future applications in industrial manufacturing and scientific research. However, there are also some challenges to be explored in terms of the broadband light source, dispersive optics design, and the balance between speed and accuracy in signal processing.

Signal generation in dynamic interferometric displacement detection.

Laser interferometry is a well-established and widely used technique for precise displacement measurements. In a non-contact atomic force microscope (NC-AFM), it facilitates the force measurement by recording the periodic displacement of an oscillating microcantilever. To understand signal generation in a NC-AFM-based Michelson-type interferometer, we evaluate the non-linear response of the interferometer to the harmonic displacement of the cantilever in the time domain. As the interferometer signal is limited in amplitude because of the spatial periodicity of the interferometer light field, an increasing cantilever oscillation amplitude creates an output signal with an increasingly complex temporal structure. By the fit of a model to the measured time-domain signal, all parameters governing the interferometric displacement signal can precisely be determined. It is demonstrated, that such an analysis specifically allows for the calibration of the cantilever oscillation amplitude with 2% accuracy.

Treating Tropospheric Phase Delay in Large-scale Sentinel-1 Stacks to Analyze Land Subsidence

Variations in the tropospheric phase delay pose a primary challenge to achieving precise displacement measurements in Interferometric Synthetic Aperture Radar (InSAR) analysis. This study presents a cluster-based empirical tropospheric phase correction approach to analyze land subsidence rates from large-scale Sentinel‑1 data stacks. Our method identifies the optimum number of clusters in individual interferograms for K‑means clustering, and segments extensive interferograms into areas with consistent tropospheric phase delay behaviors. It then performs tropospheric phase correction based on empirical topography-phase correlation, addressing stratified and broad-scale tropospheric phase delays. Applied to a six-year data stack along a 1000-km track in Iran, we demonstrate that this approach enhances interferogram quality by reducing the standard deviation by 50% and lowering the semivariance of the interferograms to 20 cm2 at distances up to 800 km in 97% of the interferograms. Additionally, the corrected time series of deformation shows a 40% reduction in the root mean square of residuals at the most severely deformed points. By analyzing the corrected interferograms, we show that our method improves the efficiency of country-scale InSAR surveys to detect and quantify present-day land subsidence in Iran, which is essential for groundwater management and sustainable water resource planning.

Smart DIC: User-independent, accurate and precise DIC measurement with self-adaptively selected optimal calculation parameters

Existing subset-based digital image correlation (DIC) must rely on user-selected key calculation parameters (i.e., subset size and shape function) to proceed with displacement/deformation analysis. However, the lack of clear guidelines for selecting these parameters leads to varying choices among users, thus introducing artificial uncertainty in DIC measurements. Previous theoretical analyses and experimental studies revealed that optimal calculation parameters must account for both local speckle pattern quality and deformation at each required point. That means these key parameters should vary at each calculation point, posing a significant challenge for optimal parameter selection. To tackle this challenge, a novel Smart-DIC is proposed to achieve user-independent, accurate and precise displacement field measurements. This method comprehensively considers the local speckle pattern quality and local deformation at each calculation point, and gives the explicit formulas to determine optimal calculation parameters. Based on these optimal calculation parameters, Smart-DIC outputs accurate and precise displacement measurements without the need for users’ inputs. To validate its metrological performance, numerical tests were processed using data from DIC Challenge 1.0 and real images of tensile tests of a commercial AL-based alloy. The experimental results underscore the capacity of Smart-DIC to efficiently achieve accurate and precise displacement measurements across various scenarios by automatically selecting optimal subset sizes and shape functions.

Controllable split polarization singularities for ultra-precise displacement sensing

The topic of optical precise displacement measurement has garnered significant attention and generated widespread interest recently. The use of optical singularity offers a potential solution for this purpose, although effectively manipulating the singularity in an ideal manner remains challenging. In this work, we propose a theoretical approach to achieve controllable position modulation of the C-point in the focal plane, whose spatial position can be easily modulated by adjusting the relative offset factor β and the offset angle α of an azimuthal polarization beam (APB), while the interval and orientation of the C-points can be flexibly regulated. Notably, the chiral polarization state undergoes a distinct reversal along the link-line connecting the two C-points, thereby providing a promising approach for accurate displacement sensing. To evaluate its sensing characteristics, the varying pattern of the scattered field intensity is monitored when sweeping a gold helix and nanoparticle along the link-line. The results of simulation quality index Q verify that the equilibrium factor of the scattering field possesses an obvious linear relationship with the displacement, signifying a precise sub-nanometric sensitivity. This research introduces new methods for the flexible control of polarization singularities in tightly focused fields, thereby enhancing the utilization of circular polarization properties near C-points for displacement sensing. These findings not only enrich the field of nanometer measurement technology but also pave the way for new avenues of research in this domain.

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.

Method for measuring time waveforms of minute sinusoidal displacements using continuous waves with a network analyzer

This study proposes a method for precise measurement of time waveforms of minute sinusoidal displacements using continuous waves. The technique involves measuring the S-parameter of ultrasonic waves reflected from an object undergoing sinusoidal vibration with a network analyzer. When the sinusoidal displacement is not sufficiently small, second-order side peaks emerge in its inverse Fourier transform, alongside the main and first-order side peaks. This method, which incorporates second-order side peaks previously overlooked, enhances the accuracy of measurements. It facilitates precise measurement of sinusoidal displacements ranging from 0.3 to 50 μm at frequencies between 10 and 300 Hz.

Research on image deformation monitoring algorithm based on binocular vision

Monitoring the deformation of critical structures such as tunnel、buildings and bridges is critical to ensure the safety of infrastructures. Non-contact deformation monitoring technology based on digital imagery has emerged as a prevalent and effective monitoring method, which enables cost-effective and efficient tracking of structural deformations. This paper aims to develop an automated deformation monitoring methodology using the binocular vision. First, standard preprocessing of digital images is performed through the integration of filtering algorithms and image enhancement techniques. Furthermore, by combining the Scale Invariant Feature Transform (SIFT) feature matching algorithm, the inverse compositional gauss–newton iterative algorithm, and interpolation methodologies, the planar displacement of the monitored targets can be calculated precisely, with sub-pixel precision being achieved. Subsequently, by adopting an enhanced Semi-Global Matching (SGM) algorithm, stereo matching of binocular images were accomplished. This process yields a disparity map, from which the depth map is computed. Then, precise measurement of the vertical displacement of the monitoring target can be obtained. This enables accurate measurement of three-dimensional displacements of the monitored targets. Finally, the developed methodology undergoes a comparative assessment against traditional measurement methods and existing algorithms to validate its measurement accuracy. The results prove that the deformation measurement technique based on binocular vision proposed in this paper captures structural deformation effectively. The accuracy surpasses that of existing measurement algorithms, and its efficiency outperforms traditional measurement methods.

Investigating paleoseismicity using high-resolution airborne LiDAR data - A case study of the Huangxianggou fault in the northeastern Tibetan plateau

Fault-offset landforms have long been recognized as holding important information about paleoseismic slip. Constructing an along-strike fault slip distribution could help reveal a fault's long-term rupture patterns and facilitate a more precise assessment of its future behavior. In this study, we documented the paleoseismic history of the Huangxianggou Fault, an oblique sinistral-thrust segment of the West Qingling Fault in the northeastern region of the Tibetan Plateau, using LiDAR-derived high-resolution DEM (0.1 m/pixel) and measurement of offset landforms. A total of 46 well-preserved and well-shaped landforms were chosen for horizontal and vertical displacement measurements, and the dense measurement data allow us to generate the cumulative offset probability distribution curves of horizontal and vertical displacements. Statistical analysis revealed at least seven surface-rupturing events, each with similar coseismic horizontal displacements of ∼7.0 m and vertical displacements of ∼0.7 m, in agreement with previous paleoseismic trench results. Using empirical relationships between moment magnitude and horizontal displacement, a plausible moment magnitude range of Mw7.3–7.7 was determined for these paleoearthquakes. Furthermore, by evaluating rupture parameters and fault slip rate, we determined a recurrence interval of 2.7–3.4 kyr for significant surface-rupturing events on this fault. The elapsed time since the last earthquake closely approaches this interval, suggesting a potential seismic risk for the Huangxianggou Fault. Our results emphasizes the importance of high-resolution topographic data in paleoseismic investigations, enabling the identification of numerous offset landforms and precise displacement measurements across faults. Paleoearthquake counts derived from horizontal and vertical displacement analyses were found to be consistent, highlighting the significance of vertical displacements in quantifying paleoearthquakes for strike-slip faults with a thrust component.

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.

(Digital Presentation) A Novel Method for Precise Measurement of Displacement Using Eddy Currents at High Temperature

In this paper, a novel method of measuring displacement using eddy currents at high temperature is presented. The measurement system consists of a sensing coil created on a PCB by patterns, a parallel turning circuit and a microcontroller including a signal processing unit. When the gap distance between the conductive target and the sensing coil changes, the inductance value of the coil varies by the influence of the eddy current. By detecting the change in the inductance, we have proposed a novel method to precisely measure the displacement of the coil. In order to make the optimal coil, a theoretical analysis was conducted using the inductance calculation theory, and the magnetic field distribution and inductance variation of the coil were analyzed using ANSYS Maxwell. Then, the coil was fabricated as a PCB, and the measured result value was compared with each analysis result, and the coil most suitable for the system was selected. The circuit was designed so that the characteristics of the synchronization amplification circuit in the detection system were minimized in temperature change, and the temperature characteristics were primarily corrected in hardware by adding a temperature correction circuit. The output value of the primarily corrected tuning amplification circuit improved the temperature characteristics of the sensor by secondarily correcting the temperature characteristics in firmware, and is designed to meet the IPC class 3 specification. The sensing range of the implemented measurement system was 0.0 ~ 3.8 mm, the nominal value of the fabricated sensing coil was 11.2uH, and the resonance frequency of the tuning circuit including the sensing coil was 300Khz. The operating temperature of the system is – 40 ~ 150 ℃ and the resolution is 0.15 mm within the range of 0.0 ~ 3.8 mm. From the experimental results, Comparing the change in inductance with respect to the moving distance of the measurement system and the displacement signal measured by the system, it can be seen that as the inductance increases, the displacement output increases, and as the inductance decreases, the displacement also decreases. Considering this, it was found through the system that inductance and output of displacement are correlated, and is seen operates stably at high temperature and has linearity. Figure 1

Novel measurement method for full-field bridge strain and displacement with limited long-gauge strain sensors

In efforts to resolve the limitations of incomplete bridge measurements in accurately identifying structural parameters, this study introduces a novel approach for precise measurement of full-field bridge strain and displacement using a limited number of long-gauge fibre Bragg grating strain sensors. This method consists of two algorithms: a double reconstruction algorithm for strain reconstruction and an improved conjugate beam algorithm (ICBA) for displacement identification. The dual reconstruction algorithm exploits proper orthogonal decomposition to establish a comprehensive mapping relationship between units, thereby achieving precise strain estimation. This intricate mapping process enables the algorithm to accurately compute strain responses. By leveraging the derived full-field strain data, the ICBA effectively captures complete displacement responses. The conventional sensor placement configuration monitors only a limited number of units. To enhance full-field measurement accuracy, this method categorizes unmonitored units into two levels based on sensor placement. The double reconstruction algorithm then estimates the strain response sequentially, contributing to enhanced precision. Numerical simulations validate the proposed method (PM), which is demonstrated to be efficient and robust under various vehicle loads, impact loads, and noised levels. A physical experiment further demonstrates the efficacy of the PM in practice. The results underscore the potency of the PM as powerful theoretical and practical approach for full-field strain and displacement measurement.

Rapid and high-precision displacement sensing based on the multiple mode dip areas in a SNAP microresonator.

Whispering gallery mode (WGM) microresonators offer significant potential for precise displacement measurement owing to their compact size, ultrahigh sensitivity, and rapid response. However, conventional WGM displacement sensors are prone to noise interference, resulting in accuracy loss, while the demodulation process for displacement often exhibits prolonged duration. To address these limitations, this study proposes a rapid and high-precision displacement sensing method based on the dip areas of multiple resonant modes in a surface nanoscale axial photonics microresonator. By employing a neural network to fit the nonlinear relationship between displacement and the areas of multiple resonant dips, we achieve displacement prediction with an accuracy better than 0.03µm over a range of 200µm. In comparison to alternative sensing approaches, this method exhibits resilience to temperature variations, and its sensing performance remains comparable to that in a noise-free environment as long as the signal-to-noise ratio is greater than 25dB. Furthermore, the extraction of the dip area enables significantly enhanced speed in displacement measurement, providing an effective solution for achieving rapid and highly accurate displacement sensing.

Quasi-static compression of shock loaded, single crystal tantalum micropillars

This paper presents the mechanical behaviour of single crystal Ta (6.5 GPa–22 GPa) 1-D shocked along the three principal crystallographic directions [100], [110] and [111]. Room temperature mechanical testing was carried out on micropillars to make possible precise load and displacement measurements. The findings exhibit a marked variation in the flow curve and strain hardening between the three orientations, and relative changes are noticed with shock loading. The yield strength (YS) increases linearly as a function of shock load. The YS was highest along [111] (282 MPa) compared with the [100] and [110] orientations (194 and 206 MPa). The strain hardening rates without pre-shock loading are found to be in the order [111] > [100] > [110] and this is not altered by pre-shock loading. Deformation was accomplished by slip on {112} planes. Further, assessments are considered to identify effective plastic strain accumulation during shock loading. The accumulation of effective plastic strain was found to be similar for all directions for shock loading up to 6.5 GPa, however, above 15 GPa the effective strain was lower for [110] compared to [100] and [111] directions. An attempt is made here to assess the flow curve hardening behaviour and variation in yield strength based on a different combination of pair orientation to throw some light into materials response at high-pressure shock loading.

Enhanced sensitivity and durability in photodetector of Ag/nanocellulose/Si via plasma-assisted synthesis.

Position-sensitive detectors (PSDs) based on the lateral photovoltaic effect (LPE) are widely used for precision displacement and angle measurement. However, high temperatures can lead to the thermal decomposition or oxidation of nanomaterials frequently utilized in PSDs, and can ultimately affect the performance. In this study, we present a PSD based on Ag/nanocellulose/Si that maintains a maximum sensitivity of 416.52 mV/mm, even at elevated temperatures. By encapsulating nanosilver in a nanocellulose matrix, the device demonstrates excellent stability and performance over a wide temperature range from 300 to 450 K. Its performance can be comparable to that of room temperature PSDs. An approach that uses nanometals to regulate optical absorption and the local electric field overcomes carrier recombination due to nanocellulose, enabling a breakthrough in sensitivity for organic PSDs. The results indicate that the LPE in this structure is dominated by local surface plasmon resonance, presenting opportunities for expanding optoelectronics in high-temperature industrial environments and monitoring applications. The proposed PSD offers a simple, fast, and cost-effective solution for real-time laser beam monitoring, and its high-temperature stability makes it ideal for a wide range of industrial applications.

Noncontact Structural Displacement Measurements Using a Low-Cost Motion Tracking System

Structural health monitoring (SHM) depends on precise displacement measurements to evaluate a structure’s condition. Current measurement systems face challenges such as contact-type restrictions, high costs, uniaxial limitations, and significant computational power requirements. A novel low-cost, non-contact displacement measurement system, called the HTC-VTS (Vive Tracking System), developed by Hongda International Electronics Co., Ltd. (New Taipei City, Taiwan), is proposed. The system setup and data acquisition of the HTC-VTS for SHM involve coordinate transformations to convert six degrees of freedom (DOFs) from raw motion data into 3-DOF structural displacement measurements. The HTC-VTS was experimentally validated using laboratory-scale free vibration tests on a cantilever beam and shaking table tests with actual bridge displacement measurements, demonstrating satisfactory performance in both scenarios. The proposed system expands the potential for cost-effective motion capture systems in both experimental and real-world structural applications.

Optical Grating Diffraction and Optical Beat Frequency Principle-Based Ultrahigh Resolution Displacement Measurement System

This research presents a novel displacement measurement system that combines optical grating diffraction, the optical Doppler principle, and the optical beat frequency principle. The system utilizes a double-frequency laser device, an interferometer, a measuring grating, and an electrical signal processing unit. By dividing the laser into reference light and measuring light and analyzing the beat frequency signal generated by the interaction of the measuring light and the reference light, the system achieves precise linear displacement measurements in two directions. The system offers sub-nanometer-grade or even higher resolution and accuracy, simultaneous measurement of horizontal large-stroke displacement and horizontal displacement, and exhibits advantages such as environmental insensitivity, high measurement accuracy, compact size, and lightweight. The proposed system finds potential applications in ultraprecise workpiece platform position measurement systems, contributing to the overall performance improvement of lithography machines.

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.

EDF laser displacement sensor based on bending characteristics of polarization-independent double-pass cascaded-chirped long-period fiber grating

In this study, we propose an Erbium-doped fiber (EDF) laser displacement sensor using bending characteristics of a cascaded-chirped long-period fiber grating (C-CLPG), in which the C-CLPG assisted by a Faraday rotator mirror (FRM), namely double-pass C-CLPG, shows a channeled spectrum and plays both the roles of wavelength tunable filter and sensor element. In the sensing scheme, the spectral shift of the channeled spectrum due to the displacement-induced bending deformation is utilized. Due to the FRM reflection, the double-pass C-CLPG has characteristics suitable for sensing: the polarization-independent channeled spectrum and the compensation effect for polarization variation in the sensor section. In the experiment, it is successfully demonstrated that the EDF laser in a sigma-type cavity configuration (EDFσL) using the double-pass C-CLPG enables precise displacement measurement based on the oscillation wavelength shift corresponding to the spectral shift of the double-pass C-CLPG. Further, the advantage of this EDFσL is confirmed by comparison with the conventional EDF ring laser using the single-pass C-CLPG.