Fringe Pattern Research Articles

Efficient and robust 3D reconstruction: Absolute phase extraction algorithm based on three gray images

The structured light three-dimensional (3D) measurement technology based on optical metrics has gained increasing applications, and there is a growing demand for capturing transient trajectory changes in dynamic scenes. Conventional temporal phase unwrapping (TPU) approaches often require multi-frequency fringe patterns for application. However, the inevitable conflict arises between the number of projected fringe patterns and the measurement speed. This paper proposes a highly accurate and robust 3D measurement method using only 3-step phase-shifting fringe patterns. To precisely reconstruct the 3D shape using the fewest fringe patterns, it is essential to extract as much information as possible from the available patterns. Therefore, we calculate the wrapped phase distribution using 3-step phase-shifting fringe patterns to ensure accuracy. Simultaneously, the trapezoidal phase-shifting method is employed to calculate the intensity ratio distribution. Through the proposed region-based indexing method, the intensity ratio map is transformed into an unwrapped phase map. Additionally, a novel self-correction method is introduced to correct the non-linear errors in the unwrapped phase map, which is then utilized for the calculation of the fringe order required for phase unwrapping. This high-speed measurement method utilizes only 3-step phase-shifting fringe patterns while retaining the advantages of TPU, meeting the requirements of high-speed and full-field measurements. Experimental results on both static and dynamic scenes validate the effectiveness and versatility of the proposed method, demonstrating its flexibility and simplicity in application. In our 3D measurement system, the method achieves 3D reconstruction of the dynamic object's trajectory at a measurement speed of 107 frames per second.

Radial vibration measurement of rotating shaft using constant density fringe pattern and line scan camera

The radial vibration signals of the rotor can provide abundant information about the health condition of the machine. In this paper, a simple vision-based measurement system is proposed to simultaneously measure two-dimensional displacements in radial directions for the rotating shaft, where the system consists of a constant density fringe pattern (CDFP), a line scan camera (LSC), and a lens. The CDFP should be installed around the surface of the rotating shaft to make the density of the fringe constant along the shaft axis, while the shaft axis is vertical to the optical axis of the LSC but not parallel to the line-array sensor of the LSC. Therefore, the density of the fringe imaged on the LSC is not constant because of the modulation of the circular surface of the shaft, and the distribution of the fringe density on the LSC is a U-shaped curve. Thus, the shaft centreline orbit can be tracked by the lowest point of the density distribution curve (DDC) of the fringe. Then, an efficient and accurate parameterized instantaneous frequency estimation method is employed to estimate the DDC of the fringe, because the variable density fringe can be regarded as an amplitude-modulated and frequency-modulated nonstationary signal whose instantaneous frequency function is equivalent to the DDC. Experimental results verify the feasibility and effectiveness of the proposed method by comparing it to the eddy current sensors.

A Vision-Based Bolt Looseness Detection Method for a Multi-Bolt Connection

Many vision-based bolt looseness detection methods that directly observe the bolts have been developed. However, these methods have many limitations in terms of the conditions and processes of their implementation. To address these problems, this paper proposed a fully automated vision-based bolt looseness detection method for a rigid multi-bolt connection. The proposed method combines digital shearing speckle pattern interferometry (DSSPI) and recurrent neural network (RNN) and involves capturing speckle fringe patterns under various looseness cases using the DSSPI system and classifying these patterns with an RNN model to detect the loose bolts. The proposed method can detect all the bolts within the measured surface at one time, which is efficient. On the other hand, it eliminates the need for prior information such as the initial angle and position of each bolt. It can even detect unseen bolts in multi-bolt connections, making it applicable for connections in complex structures in which occlusion often occurs. Additionally, the method eliminates the complex process of distortion rectification. These features make the method achieve a single-judgment time (four bolts at one detection) of only 4.70 millisecond with a detection accuracy over 99%, which has potential for the real-time detection of loose bolts in multi-bolt connections.

Simulation study of compressed ultrafast 3D imaging based on interferometry

Observing the 3D (three-dimensional) surface vibration in 100 MHz is challenging due to low speed of CCD/CMOS camera. In order to obtain the ultrafast dynamic 3D shape information, a compressed ultrafast 3D imaging framework based on interferometry is proposed in this paper. Based on this imaging framework, an reconstruction method combining plug and play-fast flexible denoising network is developed to recover high resolution interference fringe patterns and the corresponding 3D information. The simulation results show that the proposed method can observe the dynamic processes of the anti-phase vibration and the in-phase vibration of the crystal oscillator, therefore the dynamic 3D model is established. The proposed method outperforms other reconstruction methods in terms of average peak signal to noise ratio and structural similarity in recovery the ultrafast dynamic 3D surface.

Object image and modulation-based method to segment gear tooth flank region from interference fringe patterns

Object image and modulation-based method to segment gear tooth flank region from interference fringe patterns

Three-dimensional shape measurement technique for hot and shiny forging

For hot and shiny forging, rapid optical three-dimensional (3D) shape measurement can find the defects in time, improve manufacturing efficiency and reduce manufacturing cost. Optical 3D measurement of hot and shiny forging faces following three challenges. (a) Influence of blackbody radiation on the red band of visible light leads to saturation of captured fringe pattern. (b) Infrared band of blackbody radiation causes the camera to heat up. (c) Specular reflection of shiny forging leads to local saturation of captured fringe pattern. To address the above issues, we propose an effective optical 3D measurement scheme for hot and shiny forging in this paper. Firstly, the experiments demonstrate that the influence of blackbody radiation on visible light is concentrated in red light band and has no crosstalk in the blue light band, so we adopt blue light projection and blue light band-pass filter (BBF) to capture clear fringe pattern. Secondly, since the BBF cannot block the near-infrared component, we use an infrared light cutoff filter (ICF) to reduce the thermal effect of blackbody radiation. Finally, we analyze the Fourier transform (FT) spectrum of saturated fringe pattern caused by specular reflection, and propose an efficient Butterworth low-pass filtering (BLPF) method that does not require additional hardware, algorithm processing, and image assistance. The experimental results verify the effectiveness of the proposed scheme.

Thermo‐mechanical behavior of ball grid packages with different solder ball grid patterns investigated through moiré interferometry

AbstractPlastic ball‐grid array (PBGA) package assembly comprises various materials with different thermo‐mechanical properties, and the solder ball‐grid patterns can significantly influence the package deformation and solder ball stress. This study utilizes moiré interferometry to investigate the deformation behavior of wire bonded plastic ball‐grid array (WB‐PBGA) packages under varying temperatures. Real‐time moiré interferometry experiments were conducted to capture fringe patterns representing package deformation at different temperature stages. Experiments were conducted for three different wire bonded plastic ball‐grid array packages with distinct solder ball array configurations: full grid patterns (WB‐PBGA‐FG) and perimeter patterns with/without central connections (WB‐PBGA‐PC/P). The analysis revealed considerable variations in thermal strain distribution and positioning of the critical solder ball within the package assembly, depending on the solder ball‐grid pattern. Among these wire bonded plastic ball‐grid array packages, WB‐PBGA‐P/C exhibited the most substantial bending deformation, experiencing the highest effective strain, which directly impacts solder ball failure. These findings emphasize the importance of solder ball‐grid patterns in understanding the deformation behavior and reliability of WB‐PBGA packages under varying temperature conditions.

Artery Pulse Waveform Acquired with a Fabry-Perot Interferometer.

For most patients admitted to a hospital, it is a requirement to continuously monitor their vital signs. Among these are the waveforms from ECG and the pulmonary arterial pulse. At present, there are several electronic devices that can measure the arterial pulse waveform. However, they can be affected by electromagnetic wave radiation, and the fabrication of electronic sensors is complicated and contributes to the e-waste, among other problems. In this paper, we propose an optical method to measure arterial pulse based on a Fabry-Perot interferometer composed of two mirrors. A pulse sensor formed by an acrylic cell with a thin membrane is used to gather the vasodilatation of the wrist, forming an air pulse that is enacted by means of a tube to a metallic cell containing a mirror that is glued to a thin silicone membrane. When the air pulse arrives, a displacement of the mirror takes place and produces a shift of the interference pattern fringes given by the Fabry-Perot. A detector samples the fringe intensity. With this method, an arterial pulse waveform is obtained. We characterize this optical device as a test of concept, and its application to measuring artery pulse is presented. The optical device is compared to other electronic devices.

Hole Edge Metrology and Inspection by Edge Diffractometry

Abstract This article introduces a novel hole edge inspection and metrology technology by edge diffractometry, which occurs when light interacts with the hole edge. The proposed method allows for simultaneous characterization of hole part error and edge roughness conditions. Edge diffraction occurs as light bends at a sharp edge. Such a diffractive fringe pattern, the so-called interferogram, is directly related to edge geometry and roughness. Image-based diffractometry inspection technology was developed to capture the diffractive fringe patterns. The collected fringe patterns were analyzed through statistical feature extraction methods, and numerical results such as roundness index, concentricity, and via edge roughness (VER) were obtained. The results indicated that hole 1 had an average VER of 0.665 μm and a roundness index of 0.95, while hole 2 was measured an average VER of 0.753 μm and a roundness index of 0.96. Through-focus scanning optical microscopy (TSOM) was also utilized to perform three-dimensional characterization of hole features along the depth direction. As a result, the proposed method could characterize hole part error and evaluate its roughness conditions. This study showed the potential to be adapted for automatic optical inspection for advancing microelectronics and semiconductor packaging technology.

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.

Measurement technology based on a Stokes parametric polarization system

Structured light measurement systems often use polarization filters to reduce image interference from highly reflective areas. This method can be effective, but it may also reduce the brightness of specific areas, particularly overly dark portions, which can affect the accuracy of the measurement results. This paper proposes a measurement method for a polarization system based on Stokes parameters to solve the problem. After adjusting the polarization filter to angles of 0°, 45°, and 90°, the camera captures an image of the object and calculates the corresponding Stokes parameters to generate the expected polarization angle histogram. Then, based on the detailed information on the angle distribution, the accurate mathematical model is used to screen the interval, and the optimal polarization angle is determined by orthogonal processing while ensuring the signal-to-noise ratio and image quality. Finally, an image fusion technology synthesizes a set of fringe projection images with the preferred polarization angles. Experiments have shown that this new method effectively addresses the issue of interference in the highlighted region when using conventional polarization filters. Additionally, it significantly improves the quality of the fringe pattern. The polarization angle selection in the experimental process is made more rapid and accurate through the quantitative mathematical model calculation of the polarization angle, significantly improving the system’s measurement efficiency.

Coupling Michelson-like lateral shear interferometric microscopy with self-referencing numerical phase calibration for quantitative measurement of 3D surface morphology of biological cells

A Michelson interferometer is commonly used for evaluating the morphology of a cell. However, the interference imaging with reference and object beams is easily affected by external vibrations and environmental disturbances, leading to unstable interference patterns. In this paper, the three-dimensional surface morphology of the biological cell is evaluated by a new quantitative phase imaging method, which couples Michelson-like lateral shear interferometric microscopy with self-referencing numerical phase calibration. The Michelson-like lateral shear interferometric microscopy is constructed by replacing the two plane mirrors of the traditional Michelson interferometer with two common right-angle prisms and generates interference fringe patterns. The lateral shear is created and freely adjustable by simply translating/or rotating one right-angle prism. To calculate the phase information of the biological cells quantitatively, the classical Fourier transform method is used to process the recorded interferogram, and then the self-referencing numerical phase calibration method is utilized for acquiring accurate phase information. Successfully achieving quantitative phase imaging of a cell verifies the feasibility and practicability of the proposed method.

Frequency-domain searching algorithm in deflectometry for measuring the surface of a transparent planar element.

This Letter presents the frequency-domain searching algorithm in deflectometry (FSAD). By encoding specialized multi-frequency fringe patterns and employing a correlation searching algorithm, the limitations of existing frequency-domain methods can be overcome to some extent, thereby separating front and back surface reflections to obtain complete measurement data. The principles of FSAD are described in detail. In the experiment, a piece of window glass with thickness of 10 mm and a square area of 96 × 96 mm is measured to verify the proposed method.

A novel hybrid model based on integrating RGB and YCrCb color spaces for demodulating the phase map of fibres using a color phase-shifting profilometry technique

In this paper, a refined color phase- shifting profilometry technique is suggested for accurate examining of the phase and optical features of polymeric fibres. It is based on combining the RGB and the YCrCb color spaces. The primary components of the suggested model (RGCb) are red (R), green (G), and blue chrominance (Cb). This model is considered an early study in combining color spaces to demodulate the phase map of the tested fibre. The suggested model enhances affects that arise from color crosstalk and chromatic aberration, especially in the blue color channel. The Pluta polarizing interference microscope is utilised for capturing RGB interference fringe pattern for polypropylene (PP) fibre. The wrapped and unwrapped phase maps of this fibre are demodulated via the traditional, the corrected RGB color phase shifting algorithms and the suggested RGCb model. For evaluating the accuracy of the suggested model, the contour line method is used. The obtained results confirm that the demodulated phase using the suggested RGCb model has the least standard deviation from the reference phase value compared to the other two algorithms. The validation of the suggested model for investigating the optical properties of drawn fibres with a high order of fringe shift is checked. Based on the demodulated phase maps from the suggested model, the 2.5D birefringence profile of a PP fibre is examined.

Large-field and fast super-resolution microscopic imaging method based on laser interferometry

In recent years, structured illumination microscopy (SIM) has been drawing great attention for both technique development and application. However, conventional SIM, which uses a spatial light modulator (SLM) for fringe projection, often has a limited field of view. To meet the demand for high-throughput microscopic imaging in biomedicine research, a large-field super-resolution (SR) fluorescence microscopic imaging method based on laser interferometry was proposed. The method that combines a two-dimensional (2D) grating for fringe pattern projection and an SLM for selecting fringe orientation can break the limitation of fringe number limited by the digital projection devices. A spatial-domain reconstruction algorithm was developed to improve the computational speed of super-resolution imaging. Finally, an experimental platform for SIM microscopy was established. A large-field view of 1380 μm × 1035 μm under a 20×/NA0.75 objective is experimentally demonstrated, and an enhancement of 1.8-fold resolution is realized. The spatial-domain reconstruction algorithm can significantly improve the computational speed by approximately 10 times faster compared to the traditional frequency-domain algorithm.

Variable-frequency phase-shifting algorithm with least-squares iteration for hybrid errors reduction under structured-light illumination

In this paper, a novel variable-frequency phase-shifting algorithm is proposed to reduce hybrid errors under structured-light illumination, which combines a least-squares iteration with regularization processing. Theoretical formulas and related calculation techniques for the variable-frequency fringe model are respectively derived and proposed considering phase-shifting errors, temporal intensity fluctuations and Gamma distortion. From the perspective of theoretical model, it is successfully verified and implemented to establish a minimal and sufficient system of equations using a least number of fringe patterns. To tackle the challenge of solving numerous unknown parameters in the derived model caused by these sources, a grouped step-by-step strategy is adopted during the least-squares iteration process. Error point determination and compensation tricks are further developed to reduce the phase jump problem caused by underdetermined solution. A Gamma prediction technique based on bi-frequency single-frame fringe patterns is also put forward to enhance the accuracy of phase retrieval results. Corresponding simulation and experimental results have demonstrated that the proposed algorithm with attractive potentiality can achieve a significant enhancement in accuracy using the least number of phase-shifting fringe patterns (taking bi-frequency two-step as an example in this study) compared to other existing competitive techniques.

Deep learning-based frequency-multiplexing composite-fringe projection profilometry technique for one-shot 3D shape measurement

The pursuit of precise and efficient 3D shape measurement has long been a focal point within the fringe projection profilometry (FPP) domain. However, achieving precise 3D reconstruction for isolated objects from a single fringe image remains a challenging task in the field. In this paper, a deep learning-based frequency-multiplexing (FM) composite-fringe projection profilometry (DFCP) is proposed, where an end-to-end absolute phase retrieval network (APR-Net) is trained to directly recover the absolute phase map from a FM composite fringe pattern. The obtained absolute phase map exhibits exceptional precision and is devoid of spectrum crosstalk or leakage disturbance typically encountered in traditional FM techniques. APR-Net is intricately crafted, incorporating a nested strategy along with the concept of centralized information interaction. A diverse dataset encompassing various scenarios and free from spectrum aliasing is assembled to guide the training process. A seven-map loss calculation scheme is employed to guide the training process, of which the efficacy is proved through ablation experiments. In the first qualitative experiment, DFCP demonstrates comparable phase accuracy to ground truths with 47 fewer projected images, outperforming other three methods with mean absolute phase errors of 0.0052 rad, 0.1761 rad, 0.0169 rad, and 0.0139 rad. The second qualitative experiment and the quantitative evaluation respectively prove DFCP’s capability in high dynamic range 3D measurement and in precise 3D measurement, with sphere diameter errors of 0.0780 mm and 0.0726 mm, and a spherical centroid distance error of 0.0555 mm.

Interferometric characterization of high-frequency piezoelectric effects in hydroxyapatite thin films

Hydroxyapatite (HAp) qualities such as biocompatibility and piezoelectricity make it an excellent material for biomedical applications. Here, HAp thin film samples were fabricated onto silica substrates to study their piezoelectric behavior with optical interference. Thin solid films were deposited using previously synthesized HAp powder, sol-gel, and spin-coating techniques. The samples were characterized by scanning electron microscopy, energy dispersive X-ray, Raman, and UV-Vis spectroscopies. The statical piezoelectric effect of the samples was studied by using a finite element method and computational software. Additionally, an experimental Bode analysis allows computing the internal electrical components of the films using high-frequency AC voltage. The electrical behavior is related to the equivalent circuit of a piezoelectric crystal, which indicates the range of frequencies where the electromechanical effect is maximum. A Sagnac interferometer was used to characterize the strain in the HAp as a function of the electrical input frequency. The displacement of the interferometric fringe pattern allows us to estimate the change in the thickness of the sample and compute the piezoelectric constant. The synthesis of HAp thin films with piezoelectric properties provides an effective way to produce sensors and actuators for technological applications.

Reconstruction of transparent objects using phase shifting profilometry based on diffusion models

Phase shifting profilometry is an important technique for reconstructing the three-dimensional (3D) geometry of objects with purely diffuse surfaces. However, it is challenging to measure the transparent objects due to the pattern aliasing caused by light refraction and multiple reflections inside the object. In this work, we analyze the aliasing fringe pattern formation for transparent objects and then, propose to learn the front surface light intensity distribution based on the formation principle by using the diffusion models for generating the non-aliased fringe patterns reflected from the front surface only. With the generated fringe patterns, the 3D shape of the transparent objects can be reconstructed via the conventional structured light. We show the feasibility and performance of the proposed method on the data of purely transparent objects that are not seen in the training stage. Moreover, we found it could be generalized to other cases with local-transparent and translucent objects, showing the potential capability of the diffusion based learnable framework in tackling the problems of transparent object reconstruction.

Super-resolution based number-theoretical phase unwrapping method applicable to 2D spiral fringe patterns

Spiral interferometry is a technique that accurately measures changes in 3D structures or refractive indices by converting phase changes into spiral fringe patterns. The spiral fringe patterns consist of phase distributions, which are wrapped from 0 to 2π, requiring phase unwrapping techniques. Phase unwrapping transforms a discontinuous phase image from 0 to 2π into a continuous phase image, which can ultimately be reconstructed into 3D information. The 3D reconstructed information is affected by the unwrapped phase information with noise. Among the phase unwrapping methods, the number-theoretical phase unwrapping method used in 1D structured light is a unique approach that unwraps the phase into a step function. Due to its insensitivity to noise, this method is an effective solution for improving phase unwrapping in noisy environments. However, due to the same characteristics, the resolution inevitably decreases. In this paper, we propose a super-resolution based numerical unwrapping method applicable to two-dimensional spiral patterns. Based on multi-wavelength interpolation, this method not only retains the advantage of the number-theoretical phase unwrapping method, which is insensitive to noise, but also compensates for its disadvantage of resolution degradation. The proposed method uses the basic concept of generating sub-step information by multi-wavelength interpolation and performing super-resolution based on this concept. We perform simulations and experiments to verify the validity. As a result of the verification, it is confirmed that the super-resolution effect of the number-theoretical unwrapping in the 2D spiral fringe patterns can be achieved by the proposed method.