Drone-based displacement measurement of infrastructures utilizing phase information.

Drone-based inspections provide an efficient and flexible approach to assessing aging infrastructures while prioritizing safety. Here, we present a pioneering framework that employs drone cameras for high-precision displacement measurement and achieves sub-millimeter accuracy, meeting the requirements for on-site inspections. Inspired by the principles of human auditory equilibrium, we have developed an effective scheme using a group of strategical reference markers on the bridge girders to measure structural displacements in the bridge. Our approach integrates the phase-based sampling moiré technique with four degrees-of-freedom geometric modeling to accurately delineate the desired bridge displacements from camera motion-induced displacements. The proposed scheme demonstrates favorable precision with accuracy reaching up to 1/100th of a pixel. Real-world validations further confirmed the reliability and efficiency of this technique, making it a practical tool for bridge displacement measurement. Beyond its current applications, this methodology holds promise as a foundational element in shaping the landscape of future autonomous infrastructure inspection systems.

Three-dimensional dynamic measurement of unstable temperature fields by multi-view single-shot phase-shifting digital holography.

A multi-view phase measurement system based on single-shot phase-shifting digital holography is proposed to dynamically obtain three-dimensional (3-D) information of an unstable temperature field. The proposed system consists of a laser, three polarization imaging cameras, and the corresponding optical components. The laser beam emitted from the laser is separated by the fibers into three pairs that contain three object beams and three reference beams. The object beams pass through the object in three different directions and interfere with the reference beams at the image sensor plane respectively. The recording of the three cameras is triggered simultaneously, which enables the phase measurement of dynamic objects from different viewpoints. We successfully measured the 3-D distributions of an unstable temperature field in the experiments with the proposed system.

Stereo sampling moiré method for three-dimensional deformation mapping with a stereomicroscope.

Three-dimensional (3D) deformation distribution measurement is of great interest in applications of materials evaluation. In this study, we propose a stereo sampling moiré method for full-field 3D deformation measurement based on a stereomicroscope. From the phase analysis on the left and right image planes as well as the relationship between displacements in the world and image coordinate systems, the 3D displacements and the in-plane strains of the specimen can be acquired. We also propose a method to calibrate the microscope convergence angle using the grid pitch variation. The validation experiment shows that the difference between the out-of-plane displacement measured by the proposed method and the movement of the sample stage is less than 0.2 µm. The microscopic 3D displacements and the in-plane strain distributions of a carbon fiber reinforced plastic specimen in a three-point bending test are investigated.

Dynamic deformation measurement of dual-wavelength arbitrary phase-shifting digital holography with automatic phase-shift detection.

Dual-wavelength arbitrary phase-shifting digital holography with automatic phase-shift detection is first proposed in this study. Holograms with two wavelengths and the interference fringes used to detect the phase-shifting amount for each wavelength were simultaneously recorded in one image using the space-division multiplexing technique. Compared with conventional methods, the proposed approach can achieve simultaneous phase shifting of the reference beams of two wavelengths, which substantially reduces recording time and does not require excessive phase-shifting device precision. The proposed and conventional methods were quantitatively evaluated with numerical simulations, and a dynamic deformation measurement was obtained using the system. In the quantitative evaluation of the simulation, the root-mean-square errors of amplitude and phase images reconstructed by the proposed method were reduced by 12% and 19% compared to the conventional method, respectively. Both numerical simulations and experiments verified the effectiveness of the proposed method.

Multiplication sampling moire method for full-field deformation measurement of composite materials.

A multiplication sampling moire (MSM) method was proposed for robust deformation distribution measurement by performing phase analysis of the second harmonic (second-order frequency) of a single grating pattern. The MSM method has a very strong noise immunity because the second harmonic spectrum is far from the low-frequency region of the background noise in the frequency domain. Phase analysis of an experimental grid image on a carbon fiber-reinforced plastic (CFRP) specimen indicated that the MSM method effectively solved the problem of non-negligible phase measurement errors of conventional methods that extract the fundamental frequency of the grating, in the case of severe local noise. The displacement and strain distributions of CFRP in a tensile test were successfully measured. This method is suitable for deformation measurement of various composite materials.

Point defect detection and strain mapping in Si single crystal by two-dimensional multiplication moiré method.

Although defect detection is critical for evaluating the manufacturing processes of semiconductor materials and metals, the detection of crystal defects, especially point defects, over a large field of view still faces considerable challenges. Herein, we report on the development of a two-dimensional (2D) multiplication moiré method using digital image processing to simultaneously detect point and line defects in a wide field of view. Defect locations were automatically detected by employing the concept of a hybrid strain, that is, the absolute value of the product of the strain distributions in different principal directions. To demonstrate a typical application of the proposed method, the hybrid strain distribution in a Si single crystal was measured, and point defects were successfully detected by transmission electron microscopy. The effectiveness of the proposed method was experimentally verified based on the enlarged views of atomic structures at several detected defect locations. This method is capable of visualizing defects by magnifying the lattice distortion in situ, which is a good solution to the problem faced by traditional methods in detecting point defects. This study paves the way for the detection of vacancies, interstitial atoms, substitutional atoms, dislocations, slips, and interfaces in various crystal structures and 2D materials.

Wide-view and accurate deformation measurement at microscales by phase extraction of scanning moiré pattern with a spatial phase-shifting technique.

A scanning-based second-order moiré method is proposed for high-accuracy deformation measurement in a large field of view (FOV) by analyzing the phase distribution of a single-shot scanning moiré fringe image using a spatial phase-shifting technique. In this method, the grating pitch can be as small as around one pixel in the scanning moiré image to ensure a wide FOV, while high-precision phase measurement is achievable. The strain measurement accuracy has been verified from simulations at different grating pitches, applied strains, and noise levels. The simulation results show that the closer the grating pitch is to the scanning pitch, the smaller the strain measurement error, and the recommended pitch ratio is 0.9∼1.1. Furthermore, the feasibility of this method has been verified from a tensile experiment on an aluminum specimen under a laser scanning microscope with scanning moiré images recorded. The microscale strains of aluminum measured at different tensile loads agree well with the strain gauge results. As an integration of the scanning and sampling moiré methods, this method has the advantages of a large FOV, high accuracy, strong noise immunity, and visualization of magnified deformation. Compared with the traditional phase-shifting scanning moiré method, this method only needs to record a single scanning moiré image and is suitable for dynamic deformation analysis.

Random phase-shifting digital holography based on a self-calibrated system.

Random phase-shifting digital holography based on a self-calibrated system is proposed. In the proposed method, the hologram and the calibration interference fringes can be recorded simultaneously in a single image based on the space-division-multiplexing technique. Three randomly phase-shifted holograms and corresponding interference fringes are recorded, and the phase-shifting amount between each two adjacent holograms is calculated by the sampling Moiré method from the calibration interference fringes. A reflective object is used to demonstrate the effectiveness of the proposed method in the numerical and experiment.

Second-order moiré method for accurate deformation measurement with a large field of view.

In this study, we propose a second-order moiré method by performing digital sampling at two stages to realize high-accuracy deformation measurement in a wide field of view, where a grid image is recorded at a low magnification. Simulations have verified that this method has high strain measurement accuracy when the grid pitch is close to or even smaller than two pixels for both parallel and oblique grids with random noise. As an application, the two-dimensional microscale strain distributions of a carbon fiber reinforced plastic specimen when the grid pitch was about 2.1 pixels were presented. Shear strain concentration was detected before an interlaminar crack emerged, and tensile strain concentration was found prior to the occurrence of a transverse crack. The proposed method makes the two-step phase-shifting technique achieved indirectly, not only enlarging the field of view, but also maintaining the measurement accuracy.

Data of dynamic microscale strain distributions of Ti-6Al-4V alloys in dwell fatigue tests.

Dynamic microscale strain distributions with temporal resolution of 1 s in a smooth and a cracked Ti-6Al-4V alloys during one-cycle dwell fatigue tests are illustrated in videos (URL: https://drive.google.com/drive/folders/1pit_VV2apGOpETVfaJAAtL5Xl2CNOiJ3?usp=sharing). The tensile strain distributions were measured by the video sampling moiré method from the 1-µm-pitch grid images in a scanning electron microscope. The strain concentration factors of the smooth and the cracked specimens are 1.96 and 2.65, respectively. The plastic strain increment is 0.0007 during the displacement holding time of 591s in the smoothed specimen at maximum stress of 900 MPa., and 0.0008 during the displacement holding time of 593s in the cracked specimen at maximum stress of 870 MPa. The typical strain results are analyzed in 1-s-resolved strain mapping in Ti-6Al-4V alloys during dwell fatigue in SEM by video sampling moiré [1].

Interlaminar Shear Behavior of Laminated Carbon Fiber Reinforced Plastic from Microscale Strain Distributions Measured by Sampling Moiré Technique.

In this article, the interlaminar shear behavior of a [±45°]4s laminated carbon fiber reinforced plastic (CFRP) specimen is investigated, by utilizing microscale strain mapping in a wide field of view. A three-point bending device is developed under a laser scanning microscope, and the full-field strain distributions, including normal, shear and principal strains on the cross section of CFRP, in a three-point bending test, are measured using a developed sampling Moiré technique. The microscale shear strain concentrations at interfaces between each two adjacent layers were successfully detected and found to be positive-negative alternately distributed before damage occurrence. The 45° layers slipped to the right relative to the -45° layers, visualized from the revised Moiré phases, and shear strain distributions of the angle-ply CFRP under different loads. The absolute values of the shear strain at interfaces gradually rose with the increase of the bending load, and the sudden decrease of the shear strain peak value implied the occurrence of interlaminar damage. The evolution of the shear strain concentrations is useful in the quantitative evaluation of the potential interlaminar shear failure.

Nanometer-order thermal deformation measurement by a calibrated phase-shifting digital holography system.

A thermal deformation measurement system based on calibrated phase-shifting digital holography is proposed. Two synchronized ordinary CMOS cameras are used in the calibrated phase-shifting digital holography system. One is to record the holograms including the object information, and the other is to record the interference fringes to evaluate phase-shifting errors. The calibrated phase-shifting digital holography can provide the high quality reconstructed images which are applied to calculate the thermal deformation of the object. Meanwhile, the thermal images of the object at different temperatures are recorded by a thermal camera. Nanometer-order thermal deformation measurement of an electronic device is achieved in a real experiment. Our measurement system could be useful for electric packaging materials development or the system design.

Comparative study of sampling moiré and windowed Fourier transform techniques for demodulation of a single-fringe pattern.

Phase measurement techniques using a single-shot carrier fringe pattern play an important role in optical science and technology and have been widely used for various applications. In this paper, we focus on the comparative study of two major fringe analysis techniques, the sampling moiré (SM) and the windowed Fourier transform (WFT). While SM converts a single-fringe pattern to multiple phase-shifted moiré fringe patterns to extract the phase information in the spatial domain, WFT obtains the phase information in the windowed Fourier domain; thus, the two methods look entirely different. We evaluate the phase extraction errors of SM and windowed Fourier ridges (WFRs) as a typical WFT method for both linear and nonlinear phases with/without noise against the reference Fourier transform (FT) technique. For the simulated fringe patterns with linear or nonlinear phase and different random noise level, all the methods have high phase extraction accuracies. For a real experiment with more complicated phase and discontinuities, SM and WFR, both local methods, yield quite similar results and outperform FT.

Calibrated phase-shifting digital holography based on a dual-camera system.

A calibrated phase-shifting digital holography system based on the sampling Moiré technique is proposed. Two synchronized cameras are used in this system. One is to record the conventional holograms that include the object information, and the other is to record the interference fringes to analyze phase-shifting errors. An algorithm for improving the quality of the reconstructed images is proposed. In this Letter, the effectiveness of the proposed system and algorithm is demonstrated in four-step phase-shifting digital holography. The quality of the reconstructed images is greatly improved from both the numerical simulation and experiment.

Two-dimensional Moiré phase analysis for accurate strain distribution measurement and application in crack prediction.

Aimed at the low accuracy problem of shear strain measurement in Moiré methods, a two-dimensional (2D) Moiré phase analysis method is proposed for full-field deformation measurement with high accuracy. A grid image is first processed by the spatial phase-shifting sampling Moiré technique to get the Moiré phases in two directions, which are then conjointly analyzed for measuring 2D displacement and strain distributions. The strain especially the shear strain measurement accuracy is remarkably improved, and dynamic deformation is measurable from automatic batch processing of single-shot grid images. As an application, the 2D microscale strain distributions of a titanium alloy were measured, and the crack occurrence location was successfully predicted from strain concentration.

Micro/Nano-scale Strain Distribution Measurement from Sampling Moiré Fringes.

This work describes the measurement procedure and principles of a sampling moiré technique for full-field micro/nano-scale deformation measurements. The developed technique can be performed in two ways: using the reconstructed multiplication moiré method or the spatial phase-shifting sampling moiré method. When the specimen grid pitch is around 2 pixels, 2-pixel sampling moiré fringes are generated to reconstruct a multiplication moiré pattern for a deformation measurement. Both the displacement and strain sensitivities are twice as high as in the traditional scanning moiré method in the same wide field of view. When the specimen grid pitch is around or greater than 3 pixels, multi-pixel sampling moiré fringes are generated, and a spatial phase-shifting technique is combined for a full-field deformation measurement. The strain measurement accuracy is significantly improved, and automatic batch measurement is easily achievable. Both methods can measure the two-dimensional (2D) strain distributions from a single-shot grid image without rotating the specimen or scanning lines, as in traditional moiré techniques. As examples, the 2D displacement and strain distributions, including the shear strains of two carbon fiber-reinforced plastic specimens, were measured in three-point bending tests. The proposed technique is expected to play an important role in the non-destructive quantitative evaluations of mechanical properties, crack occurrences, and residual stresses of a variety of materials.

Digital sampling Moiré as a substitute for microscope scanning Moiré for high-sensitivity and full-field deformation measurement at micron/nano scales.

This study proposed to generate digital sampling Moiré fringes by two-pixel down-sampling as a substitute for microscope scanning Moiré fringes, and further reconstruct multiplication Moiré fringes for micron/nano-scale deformation measurement. The displacement and strain sensitivities of the proposed reconstructed multiplication Moiré method are 2 times higher in a wide field of view. Besides, two-dimensional deformation is easily measurable without rotating the sample stage or the scanning lines, no matter whether the scanning resolution is adjustable or not. As an example, the deformations of a carbon fiber reinforced plastic specimen were measured and analyzed. The proposed method effectively expands the application range of the Moiré technique to deformation measurement.

Accurate full-field optical displacement measurement technique using a digital camera and repeated patterns.

In this study, a novel, fast, and accurate in-plane displacement distribution measurement method is proposed that uses a digital camera and arbitrary repeated patterns based on the moiré methodology. The key aspect of this method is the use of phase information of both the fundamental frequency and the high-order frequency components of the moiré fringe before and after deformations. Compared with conventional displacement methods and sensors, the main advantages of the method developed herein are its high resolution, accuracy, speed, low cost, and easy implementation. The effectiveness is confirmed by a simple in-plane displacement measurement experiment, and the experimental results indicate that an accuracy of 1/1000 of the pitch can be achieved for various repeated patterns. This method is useful for various applications ranging from the study of displacement and strain distributions in materials science, the biomimetics field, and mechanical material testing, to secure the integrity of infrastructures.

Theoretical error analysis of the sampling moiré method and phase compensation methodology for single-shot phase analysis.

Recently, a rapid and accurate single-shot phase measurement technique called the sampling moiré method has been developed for small-displacement distribution measurements. In this study, the theoretical phase error of the sampling moiré method caused by linear intensity interpolation in the case of a mismatch between the sampling pitch and the original grating pitch is analyzed. The periodic phase error is proportional to the square of the spatial angular frequency of the moiré fringe. Moreover, an effective phase compensation methodology is developed to reduce the periodic phase error. Single-shot phase analysis can perform accurately even when the sampling pitch is not matched to the original grating pitch exactly. The primary simulation results demonstrate the effectiveness of the proposed phase compensation methodology.

Intensity range extension method for three-dimensional shape measurement in phase-measuring profilometry using a digital micromirror device camera.

Phase-measuring profilometry is an accurate and effective technique for performing three-dimensional (3D) shape and deformation measurements of diffuse objects by fringe projection. However, phase analysis cannot be performed in underexposed or overexposed areas of the detector when an object with wide reflectance is measured. A novel intensity range extension method using a digital micromirror device (DMD) camera is proposed. In the optics of the DMD camera, each pixel of the CCD corresponds exactly to each mirror of the DMD. The phase-shifted fringe patterns with high contrast can be easily captured by programming an inverse intensity pattern that depends on the reflectance of the object. Our method can provide a wider intensity range and higher accuracy for 3D shape measurement than other conventional methods in both underexposed and overexposed areas. The measurements of a replica of a metallic art object and a flat plane are analyzed experimentally to verify the effectiveness of our method. In the experiment, the percentage of invalid points due to underexposure and overexposure can be reduced from 20% to 1%.