In-plane Displacement Measurement Research Articles

Orbital angular momentum beam-based interferometry for an in-plane displacement measurement.

In this Letter, a novel, to the best of our knowledge, robust interferometry based on orbital angular momentum (OAM) is proposed for an in-plane displacement measurement. A vortex beam (VB) is incident onto a diffraction grating, and the ±1st order diffraction beams with conjugate OAM interfere with each other. By demodulating the petal-like interferogram, the in-plane displacement of the grating can be determined. Theoretically, a 1° rotation of the interferogram corresponds to a displacement of 2.31 nm. Experimental results revealed that the maximum measurement error was less than 3.35%. The proposed measurement system combines the advantages of both OAM interferometry and grating interferometry. It adopts the grating pitch instead of the wavelength as the measurement reference, providing robust immunity to environmental disturbances while maintaining high resolution simultaneously.

Grating (Moiré) Microinterferometric Displacement/Strain Sensor with Polarization Phase Shift.

Grating (moiré) interferometry is one of the well-known methods for full-field in-plane displacement and strain measurement. There are many design solutions for grating interferometers, including systems with a microinterferometric waveguide head. This article proposes a modification to the conventional waveguide interferometer head, enabling the implementation of a polarization fringe phase shift for automatic fringe pattern analysis. This article presents both the theoretical considerations associated with the proposed solution and its experimental verification, along with the concept of in-plane displacement/strain sensing using the described head.

Experimental assessment of a low-cost aberration-free compact double aperture four-hololens imaging system: application to the enhancement of sensitivity and accuracy of in-plane displacement measurement

In this work, an experimental analysis of hololens imaging configuration consisting of four holographic lenses has been carried out to realize Duffy’s double aperture speckle interferometer. It is demonstrated that using holographic lenses recorded for typical f-number in the four-hololens imaging system, the sensitivity of measurement is not limited due to the f-number of the lens. However, the sensitivity can be significantly enhanced by increasing the angle between the plane and spherical waves while recording the holographic lenses. In-plane displacements were measured using holographic lenses recorded at nearly equal f-number and with different beam angles between the plane and spherical waves. Experimental results show that holographic lenses recorded with a large beam angle between the plane and the spherical waves give a higher measurement sensitivity in comparison to those holographic lenses that were recorded with a lower beam angle at an equal f-number. This work shows that a four-hololens imaging system can be used advantageously as a low-cost alternative to Duffy’s double aperture interferometer to overcome the need for expensive diffraction-limited low f-number lenses for higher measurement accuracy and sensitivity.

High-speed and high-precision measurement of biaxial in-plane displacements: tens of nanometers principle error suppression in microprobe sensors

When the microprobe sensor is faced with the demand of high-speed biaxial displacement measurement, due to the characteristics of phase generated carrier (PGC) technology, accompanying optical intensity modulation (AOIM) and unfavorable phase modulation depth (PMD) will bring about the tens of nanometer cyclic nonlinear errors, further hindering high-speed and high-precision measurement. Herein, a light source intensity stabilization system based on semiconductor optical amplifier (SOA) feedback control is achieved to eliminate the error caused by AOIM in the presence of high-frequency and large-amplitude laser modulation. Based on this, the reasons for large nonlinear errors in biaxial measurements and the inability to ensure the stability of the accuracy of multiple measurement axes are methodically examined, and an effective nonlinear error elimination methodology based on the normalized amplitude correction of active temperature scanning is proposed. The continuity and linearity of the temperature scanning are also discussed. The performed experiments show that the above approach is capable of reducing the displacement demodulation error from the nanometer scale to the sub-nanometer scale. Further, the nonlinear error is reduced to within 0.1 nm for both measurement axes and the performance becomes consistent. The dual-axis measurement resolution of the microprobe sensor reaches 0.4 nm and the measurement speed is better than 1.2 m/s with the standard deviation of lower than 0.5 nm.

Digital synchronous measurement method for two-dimensional in-plane displacement using check-code

The measurement of two-dimensional displacement is an essential aspect of ultra-precision manufacturing and product design. This paper introduces an innovative method that uses a four-reader probe and a group of check codes to achieve digital synchronous measurement of translational and rotational displacement. The measuring principle and two-dimensional coding method are modelled first, and several reader-code combinations are proposed. And then, the study conducts numerical simulations to investigate the effect of different factors on measurement accuracies, such as check code size, machining tolerance, and reader resolution, and the method’s accuracy and performance are evaluated based on the error distribution to determine the optimal system parameters for various applications. A specialized lab experiment is conducted to validate the accuracy and reliability of the proposed method. In conclusion, the proposed method is innovative and practical, which realizes the synchronous measurement of two-dimensional in-plane displacement instead of a simple combination of two one-dimensional sensors.

Research on full-field vibration displacement measurement based on grid CCD moiré method

The development of full-field, accurate vibration testing techniques has been vastly valued by the academic and engineering community. However, due to the limited data transmission speed of digital cameras, the contradiction between speed and resolution remains in the traditional full-field vibration measurement systems based on image measurement, failing to acquire high-resolution images at high-speed simultaneously. In this paper, a high-speed and high-resolution full-field vibration displacement measurement system is established based on the grid CCD moiré method. A periodic grid is arranged on the surface of the sample as a deformation carrier, and the periodic pixel of the digital camera is used as a reference grating that ‘enlarges’ the grid on the surface of the sample to form a grid CCD moiré with a geometry significantly larger than the original, capturing images for deformation analysis. This approach lowers the requirement of digital image resolution for high-resolution deformation measurement, reducing the contradiction between speed and resolution in full-field vibration measurement. In this paper, the principle and implementation of full-field vibration measurement using the CCD moiré method are introduced, and the experiment results of full-field in-plane vibration displacement measurement are included, verifying the effectiveness and reliability of the system.

Self-aligned single-electrode actuation of tangential and wineglass modes using PMN-PT

Considering the evolution of rotation sensing and timing applications realized in micro-electro-mechanical systems (MEMS), flexural mode resonant shapes are outperformed by bulk acoustic wave (BAW) counterparts by achieving higher frequencies with both electrostatic and piezoelectric transduction. Within the 1–30 MHz range, which hosts BAW gyroscopes and timing references, piezoelectric and electrostatic MEMS have similar transduction efficiency. Although, when designed intelligently, electrostatic transduction allows self-alignment between electrodes and the resonator for various BAW modes, misalignment is inevitable regarding piezoelectric transduction of BAW modes that require electrode patterning. In this paper transverse piezoelectric actuation of [011] oriented single crystal lead magnesium niobate–lead titanate (PMN–PT) thin film disks are shown to excite the tangential mode and family of elliptical compound resonant modes, utilizing a self-aligned and unpatterned electrode that spans the entire disk surface. The resonant mode coupling is achieved by employing a unique property of [011] PMN–PT, where the in-plane piezoelectric coefficients have opposite signs. Fabricating 1-port disk transducers, RF reflection measurements are performed that demonstrate the compound mode family shapes in the 1–30 MHz range. Independent verification of mode transduction is achieved using in-plane displacement measurements with Polytec’s laser Doppler vibrometer (LDV). While the tangential mode achieves a 40o/s dithering rate at 335 kHz resonant frequency, the n = 2 wine-glass mode achieves 11.46 nm tip displacement at 8.42 MHz resonant frequency on a radius of 60 μm disk resonator in air. A single electrode resonator that can excite both tangential and wine-glass modes with such metrics lays the foundation for a BAW MEMS gyroscope with a built-in primary calibration stage.

Multiple-beam grating interferometry and its general Airy formulae

Multiple-beam grating interferometry, a hybrid of the multiple-beam interference and grating interferometry, is introduced and conducted by building a Littrow-type cavity with a diffraction grating. Based on multi-beam interference and grating interferometry, mathematical derivation reveals that the fringes of the multi-beam grating interferometry follow a general form of Airy formulae, while the period of which is additively determined by phases from grating pitches and laser wavelength. Two crucial parameters, peak transmission and finesse describing brightness and sharpness of fringes, are defined and investigated, whose results reveal that fringe shape of multiple-beam grating interferometry is determined by amplitude coefficients of two surfaces forming the cavity and could be explained by multiple beam interference with intensity loss. Consistency of simulation and experiment results are proved and analyzed. Multiple-beam grating interferometry is promising for in-plane and multi-dimensional displacement measurements and might inspire novel enhancement for sensors and instruments based on Fabry-Pérot interferometry.

Two-Dimensional Displacement Sensor Based on a Dual-Cavity Fabry-Perot Interferometer

Simultaneously and independently measuring two-dimensional (2D) displacement, one-dimensional (1D) for out-of-plane measurement and 1D for in-plane measurement, is important for practical applications. Although extrinsic fiber Fabry-Perot interferometers (EFPIs) have been reported for highly precise out-of-plane displacement measurements for many years, simultaneous measurement of 2D displacement with sub-micrometer accuracy has not been realized by a monolithic EFPI as far as we know. In this paper, a monolithic dual-cavity EFPI to realize 2D displacement measurement of a target is reported. By quantitatively analyzing and experimentally calibrating the linear dependences of the in-plane displacement sensitivity and interception on the cavity length, the effect of out-of-plane displacement on the in-plane displacement measurement is removed, which is the basis of the 2D displacement detection. 2D random movement detection and the repeatability of the system are investigated experimentally. Within the range of ±7 μm for in-plane displacement, and 352 μm-358 μm for cavity length, demodulation errors better than 96 nm are achieved. The 2D displacement measurement system based on the dual-cavity EFPI with the advantages of noncontact, high accuracy and compact size is promising to be applied in the 2D acceleration measurement, 2D rotor vibration measurement, 2D precise positioning in semiconductor manufacture, thermal expansion coefficient measurement, and so on.

Analysis of double aperture hololens imaging system through simulation and experimentation for its application in speckle metrology

In-plane displacement measurement using Double exposure Speckle photography involves illumination of a rough surface by coherent source of light and formation of image of the object containing speckles on a high-resolution photosensitive film using imaging lenses corresponding to undeformed and deformed state of object. When doubly exposed and properly processed specklegram is illuminated with an unexpended laser beam, two slightly displaced speckles behave as two-point scatterer giving rise to young's type of speckle correlation fringes. From the measured value of fringe spacing, in-plane displacement occurred between the two exposures is measured. Monochromic aberrations of the imaging system lead to formation of deteriorated curved fringes which introduces error in measurement. Further, to measure in-plane displacement component with enhanced sensitivity of measurement, Duffy's double aperture interferometer is used where diffraction limited performance almost free from all monochromatic aberration is required over the two apertures. Sensitivity of measurement depends on separation between the two apertures. For achieving higher sensitivity of measurement, separation between the twin apertures should be large requiring low f-number imaging lens of large diameter for given focal length of the imaging lens. Conventional diffraction limited and almost aberration free lenses are costly and require tedious processing for their production. Present work presents detailed analysis of a four-hololens imaging system through simulation and experimentation to show that properly recorded and played back hololens imaging system may be used advantageously to achieve diffraction limited imaging performance almost free from all monochromatic aberrations. Further, it is shown that to minimize aberration for extended object field, a two-hololens imaging configuration corresponding to each aperture has to be utilized and to obtain appreciable illumination over the image plane the two lenses of each aperture should be kept in contact making the system compact. The experimentally obtained values of in-plane displacement using the compact version of the low f- number four-hololens imaging system are found to be in good agreement with theoretical predictions as well as results obtained for similar experimentation where Duffy's double aperture imaging configuration comprising of conventional imaging lens was used.

Experimental evaluation of the coefficients of thermal expansion in a composite laminate using digital image correlation

A procedure for measuring simultaneously the coefficients of thermal expansion (CET) in the in-plane and the thickness directions in L-shaped composite laminated samples is presented. Measurements are carried out using digital image correlation, from which the displacements in one of the faces of the samples are measured when de sample undergoes a temperature increment inside an oven. From the in-plane displacement measurements, the in-plane strain tensor components and the corresponding CTE are determined. Results show that the presented technique is capable of determining these CTE with high accuracy. Displacement measurements in the direction normal to the face, enables determining the rotation of the face and consequently the difference between the CTE in the thickness direction and the CTE in the in-plane direction affected by the curvature. Results obtained for the CTE in the thickness direction show, first, values significantly higher than the CTE of the material in the in-plane direction normal to the fibres and, second, a high dispersion from one stacking sequence to another. These discrepancies were expected and are caused by the misalignment of the fibres in the corner zone of the samples.

In-plane Displacement Measurement Based on Digital Holography and Digital Image Correlation

In-plane Displacement Measurement Based on Digital Holography and Digital Image Correlation

Single hololens imaging configuration in laser speckle photography for in-plane displacement measurement

Single hololens imaging configuration in laser speckle photography for in-plane displacement measurement

Perspective error reduction in 2D Digital Image Correlation measurements by combination with Defocused Speckle Imaging

2D Digital Image Correlation (2D DIC) enables full-field in-plane displacement measurement by tracking the physical surface texture in the recorded images. However, because camera magnification is inversely proportional to object distance, points along the imaged surface can have different scales and appear to move at different rates. Surface curvature and out-of-plane motions may thus lead to perspective errors that manifest as apparent strains, limiting the method suitable only for flat objects that move purely in-plane. Defocused Speckle Imaging (DSI) is a related optical method where the movements of a laser-illuminated surface are determined by tracking the scattered interference speckle pattern. When the camera is in focus, the speckles appear to move at the same rate with the physical surface. However, camera defocus causes the speckle motion to deviate from the actual surface motion. Interestingly, the observed speckle motion magnitude increases with positive defocus distance, which is contrary to the perspective effects inherent to 2D DIC. Remarkably, with optimized geometric arrangement, 2D DIC and DSI have perspective errors that are equal in magnitude but with opposite signs. It is thus possible to compensate perspective errors by performing DIC and DSI measurements simultaneously and simply calculating the average of the two signals. This article derives the proposed compensation principle analytically using simple geometric framework. An experimental demonstration shows that the combination of DIC and DSI reduces magnification-dependent perspective errors by 73%, and errors due to object rigid-body rotation by 86%.

Concept of an In-Plane Displacement Sensor Based on Grating Interferometry with a Stepwise Change of Sensitivity

Grating Interferometry, known in the relevant literature as the High Sensitivity Moiré Interferometry, is a method for in-plane displacement and strain measurement. The sensitivity of this method depends on the spatial frequency of the diffraction grating attached to the object under test. For typical specimen grating, with high spatial frequency of 1200 lines per mm, the basic sensitivity is 0.417 µm per fringe. A concept of in-plane displacement sensor based on Grating Interferometry with a stepwise change in sensitivity is presented. It is realized by using the specimen grating with lower spatial frequency. In this case, the grating has more higher diffraction orders and by selecting them appropriately, the sensitivity (chosen from 1.25 μm, 0.625 μm, or 0.417 μm) and the resulting measurement range (chosen from about 600 μm, 300 μm, or 200 μm) can be adjusted to the requirements of a given experiment. A special method of filtration is required in this case. Achromatic configuration with illumination grating was chosen due to its low sensitivity to vibration.

A digital image correlation-aided sampling moiré method for high-accurate in-plane displacement measurements

Sampling moiré method (SMM) is widely used for measuring high-accurate displacements and strains. However, it provides accurate measurement only when the displacement is smaller than half of grating pitch due to defects on phase difference calculation. To overcome the shortage of SMM, we improve the performance of SMM by adapting the integer-pixel digital image correlation (DIC). The improved SMM is capable of measuring much larger displacements than half of the grating pitch with high accuracy. Through computer simulation, we analysed the displacement measurement accuracy of the improved SMM under various grating pitches and sampling pitches with multiple noise levels. Then the proper range of sampling pitch was obtained. Two independent experiments with short- and long-range sight-distances, respectively, were conducted to validate the accuracy of the improved SMM successfully. In conclusion, with a mean measurement accuracy of up to 1/350 of a pitch, the improved SMM can be used for measuring high-accurate in-plane displacement whether the displacement is greater than a half of grating pitch or not.

Fracture toughness of ZrO2–SiC/MoSi2 composite ceramics prepared by powder metallurgy

ZrO2–SiC/MoSi2 composite ceramics were prepared by powder metallurgy. The room temperature and high temperature fracture toughness of 10 vol%ZrO2+MoSi2, 10 vol%ZrO2+10 vol%SiC + MoSi2, 20 vol%ZrO2+10 vol%SiC + MoSi2, 10 vol%ZrO2+20 vol%SiC + MoSi2 composite ceramics were studied. The room temperature fracture toughness was calculated by Vickers indentation crack. High temperature fracture toughness is measured by wavefront interference principle of moire interferometry and non-contact measurement of in-plane displacement. The synergistic effects mechanism of nano-ZrO2 and SiC particles on the fracture toughness of MoSi2 nanocomposite ceramics was discussed.

A Study on the Quantitative Measurement of In-plane Displacement of Carbon Steel for Machine Structures according to Rolling Direction using a dual-beam Shear Interferometer

A Study on the Quantitative Measurement of In-plane Displacement of Carbon Steel for Machine Structures according to Rolling Direction using a dual-beam Shear Interferometer

Subpixel sampling moiré method for in-plane displacement measurement considering the symmetric errors induced by interpolation.

Sampling moiré method (SMM) is a highly accurate vision-based deformation measurement method, whose measurement error is minimized when an integer that is closest to the grating pitch is selected as the sampling pitch. We propose a subpixel SMM by applying subpixel interpolation operation before the downsampling in traditional SMM; the sampling pitch was selected as a noninteger nearest to the grating pitch in the subpixel resolution image. Meanwhile, the average filter method was used to eliminate the symmetric error cause by interpolation. As a result, the period of moiré fringe was enlarged greatly, and the measurement accuracy was also increased. To investigate the efficiency of the subpixel SMM, a computer simulation was applied to analyze the accuracy of the subpixel SMM. Then a simple tensile experiment was conducted to validate the efficiency of this method, and the result of the subpixel SMM accorded well with the fiber Bragg grating. In summary, the proposed novel subpixel SMM is capable of being used for high accuracy in-plane deformation measuring.

Fracture behavior of additively printed ABS: Effects of print architecture and loading rate

Acrylonitrile Butadiene Styrene (ABS) is an inexpensive amorphous thermoplastic used for Additive Manufacturing (AM) of engineering parts. Fused Filament Fabrication (FFF) is commonly used to 3D print ABS, and it involves layer-by-layer deposition of melted thermoplastic wire through a heated nozzle along predetermined paths. The individual layers can also be configured differently and could introduce mechanical anisotropy into the final part in terms of weak planes between individual beads and layers even when the feedstock is isotropic. In this context, this research examines the dynamic fracture behaviors of three different print architectures, namely [0°/90°]n, [45°/−45°]n and [0°/45°/90°/−45°]n in-plane orientations, under stress-wave loading conditions and compares the results with the quasi-static counterparts. The dynamic experiments are carried out using a modified-Hopkinson pressure bar apparatus. The full-field measurement of in-plane displacements are performed using Digital Image Correlation (DIC) and ultrahigh-speed photography of V-notched specimens subjected to stress-wave loading. A novel method of analyzing DIC data by transferring it to a finite element environment to compute the J-integral using prevailing domain integral algorithms is introduced. Distinct crack initiation and growth behaviors with different failure modes are observed in the three architectures under static and dynamic loading conditions despite the macroscale elastic isotropy. The results favor [0°/45°/90°/−45°]n architecture due to a better crack growth behavior relative to the other two, raising the possibility of fracture performance enhancement by tailoring the build architecture.