Fringe Images Research Articles

3D measurement method based on Gray code and single sine fringe image

3D measurement method based on Gray code and single sine fringe image

Restoration of X-ray phase-contrast imaging based on generative adversarial networks

For light-element materials, X-ray phase contrast imaging provides better contrast compared to absorption imaging. While the Fourier transform method has a shorter imaging time, it typically results in lower image quality; in contrast, the phase-shifting method offers higher image quality but is more time-consuming and involves a higher radiation dose. To rapidly reconstruct low-dose X-ray phase contrast images, this study developed a model based on Generative Adversarial Networks (GAN), incorporating custom layers and self-attention mechanisms to recover high-quality phase contrast images. We generated a simulated dataset using Kaggle’s X-ray data to train the GAN, and in simulated experiments, we achieved significant improvements in Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM). To further validate our method, we applied it to fringe images acquired from three phase contrast systems: a single-grating phase contrast system, a Talbot-Lau system, and a cascaded grating system. The current results demonstrate that our method successfully restored high-quality phase contrast images from fringe images collected in experimental settings, though it should be noted that these results were achieved using relatively simple sample configurations.

Robust function guided color encoded single fringe pattern and unwrapping method

Fringe Projection Profilometry (Fringe Projection Profilometry，FPP), renowned for its speed, precision, and automation advantages, has found extensive applications in industries such as mechanical processing and quality inspection. A critical challenge within fringe projection techniques involves ensuring robust unwrapping while minimizing the necessary fringe images. While various unwrapping methods exist to reduce the number of projected images, there is a deficiency in efficient unwrapping methods developed under the guidance of error analysis theory. In this study, we derive a robustness function from FPP's error theory to assess the unwrapping robustness of different encoded images. Using this robustness function, we select highly robust single-color encoded fringe images and achieve unwrapping robustness with minimal training cost based on a single fringe pattern. Furthermore, this unwrapping process does not necessitate the establishment of complex training databases, as the K-nearest neighbor (K-Nearest Neighbor，KNN) algorithm learns the correspondence between image tricolor grayscale values and fringe orders from multi-frequency unwrapping method. Finally, experimental validation through a checkerboard measurement confirms that the proposed method can achieve robust unwrapping with low training costs using only one encoded fringe, thereby affirming the effectiveness of the introduced robustness function and the feasibility of the designed color encoded single fringe pattern unwrapping method.

Deep learning based measurement accuracy improvement of high dynamic range objects in fringe projection profilometry

One of the key factors affecting the accuracy of three-dimensional (3D) measurement in fringe projection profilometry (FPP) is the phase retrieve accuracy. In the 3D measurement of high dynamic range (HDR) objects, fringe saturation and/or low contrast are difficult to avoid. A greater number of fringe images are needed for 3D measurement of HDR objects by traditional methods, which is unfavorable for the measurement of moving objects. In this paper, what we believe to be a new method to solve the phase demodulation problem of HDR objects using deep learning is proposed. In this method, a “many-to-one” mapping relationship is established using an improved UNet deep neural network. In addition, in order to obtain more saturated fringe information, π-shifted binary fringes were also used. This allows us to retrieve the wrapped phase of HDR objects quickly and accurately. Experimental results demonstrate the effectiveness and reliability of the proposed method.

High precision full-field vibration measurement by LDV-induced stroboscopic fringe projection

A method for full-field vibration measurement that combines Fourier Transform Profilometry (FTP) and Laser Doppler Vibrometry (LDV) is proposed and validated experimentally on various structures. This technique projects sinusoidal fringe patterns onto the test sample using a flashing LED at an oblique angle, while a CCD camera captures the fringe images vertically. Vibration data is derived from 3-D phase maps generated by applying FTP to these images and is further calibrated using a motorized translation stage. To improve the precision of FTP and extend the measurable frequency range beyond that of normal-rate cameras, initial single-point vibration data from the test sample is obtained using LDV. This prior information enables noise decoupling and down-sampling techniques to be employed. The experimental results confirm that this method can precisely reconstruct the high-order operational deflection shapes of vibration on structures with different materials, achieving a precise measurement for vibration amplitude of around 500 nm (1/2000 of fringe spacing) on a 10 cm x 10 cm plastic plate and a 2 cm x 14 cm aluminum beam with approximately 1 mm fringe spacing and 26° projection angle.

Experimental Study on the Reconstruction of a Light Field through a Four-Step Phase-Shift Method and Multiple Improvement Iterations of the Least Squares Method for Phase Unwrapping

Phase unwrapping technology can reflect the true phase information of an image, but it is affected by adverse factors such as noise, shadows, and fractures when extracting the true phase information of an object. Therefore, corresponding unwrapping algorithms need to be studied for different interference images. This paper summarizes and analyzes various phase unwrapping algorithms and ultimately selects the required method based on their advantages and disadvantages. Using the four-step phase-shift method to reconstruct the phase of the optical field and then combining it with the least squares method to unwrap the phase through multiple improvement iterations, the simulated collected interference fringe images are simulated using the MATLAB program to complete the phase unwrapping of the interference information field. Based on the analysis of the final experimental results, the reliability of this research method was verified.

Adaptive median filter salt and pepper noise suppression approach for common path coherent dispersion spectrometer

The Common-path Coherent-dispersion Spectrometer (CODES), an exoplanet detection instrument, executes high-precision Radial Velocity (RV) inversions by recording the phase shifts of interference fringes. Salt-and-pepper noise caused by factors such as improper operation of the CCD probe/analog-to-digital converter and strong dark currents may interfere with the phase information of the fringe. This lowers the quality of the interfering fringe image and significantly interferes with the RV’s inversion. In this study, an adaptive median filtering algorithm (CODESmF) based on submaximum and subminimum values is designed to eliminate the interference fringe image's salt-and-pepper noise as well as to reduce RV error. This allows the interference fringe image's phase information to be retained more completely. The algorithm consists of two major modules. Pixel Sub-extreme-based Filtered Noise Monitoring Module: discriminates signal pixels and noise pixels based on the submaximum and subminimum values of the pixels in the filtering window. Adaptive Median Filter Noise Suppression Module: the signal pixel is kept at the original value output, the noise pixel serves as the filtering window's center pixel, and the adaptive median filtering procedure is repeated numerous times with various filtering window sizes. According to the experimental findings, the CODESmF outperforms comparable algorithms and works better at recovering interference fringes. More than 90% of the phase/RV error caused by salt-and-pepper noise is typically eliminated by the CODESmF algorithm, and in certain circumstances, it can even remove roughly 98% of the phase error.

Recognition and separation of fringe patterns in deflectometric measurement of transparent elements based on empirical curvelet transform

In the deflectometric measurement of transparent elements, it is critical to separate the superposed fringes reflected from the front and rear surfaces to establish the pixel correspondences between the camera and screen pixels. But it is a challenging task due to the low reflectivity and uneven background of transparent elements. A reliable fringe separation method is proposed based on the empirical curvelet transform. The captured fringe images are decomposed into different modes according to their directions, periods, curvatures or modulation coefficients, and then a weighted-permutation-entropy-based fusing algorithm is developed to automatically aggregate those over-separated patterns. By employing the proposed method, the measurement accuracy is significantly improved, the number of demanded images is effectively reduced, and high-precision, automatic, and rapid measurement is thereby achieved. The measurement accuracy of spherical and cylindrical lenses can achieve 73 nm and 332 nm Root-of-Mean-Squares-Error, respectively.

Moiré fringe imaging of heterostructures by scanning transmission electron microscopy

A heterostructured crystalline bilayer specimen is known to produce moiré fringes (MFs) in the conventional transmission electron microscopy (TEM). However, the understanding of how these patterns form in scanning transmission electron microscopy (STEM) remains limited. Here, we extended the double-scattering model to establish the imaging theory of MFs in STEM for a bilayer sample and applied this theory to successfully explain both experimental and simulated STEM images of a perovskite PbZrO3/SrTiO3 system. Our findings demonstrated that the wave vectors of electrons exiting from Layer-1 and their relative positions with the atomic columns of Layer-2 should be taken into account. The atomic column misalignment leads to a faster reduction in the intensity of the secondary scattering beam compared to the single scattering beam as the scattering angle increases. Consequently, the intensity distribution of MFs in the bright field (BF)-STEM can be still described as the product of two single atomic images. However, in high angle annular dark field (HAADF)-STEM, it is approximately described as the superposition of the two images. Our work not only fills a knowledge gap of MFs in incoherent imaging, but also emphasizes the importance of the coherent scattering restricted by the real space when analyzing the HAADF-STEM imaging.

Wafer Edge Metrology and Inspection Technique Using Curved-Edge Diffractive Fringe Pattern Analysis

Abstract This paper introduces a novel wafer-edge quality inspection method based on analysis of curved-edge diffractive fringe patterns, which occur when light is incident and diffracts around the wafer edge. The proposed method aims to identify various defect modes at the wafer edges, including particles, chipping, scratches, thin-film deposition, and hybrid defect cases. The diffraction patterns formed behind the wafer edge are influenced by various factors, including the edge geometry, topography, and the presence of defects. In this study, edge diffractive fringe patterns were obtained from two approaches: (1) a single photodiode collected curved-edge interferometric fringe patterns by scanning the wafer edge and (2) an imaging device coupled with an objective lens captured the fringe image. The first approach allowed the wafer apex characterization, while the second approach enabled simultaneous localization and characterization of wafer quality along two bevels and apex directions. The collected fringe patterns were analyzed by both statistical feature extraction and wavelet transform; corresponding features were also evaluated through logarithm approximation. In sum, both proposed wafer-edge inspection methods can effectively characterize various wafer-edge defect modes. Their potential lies in their applicability to online wafer metrology and inspection applications, thereby contributing to the advancement of wafer manufacturing processes.

Single-Shot 3D Reconstruction via Nonlinear Fringe Transformation: Supervised and Unsupervised Learning Approaches.

The field of computer vision has been focusing on achieving accurate three-dimensional (3D) object representations from a single two-dimensional (2D) image through deep artificial neural networks. Recent advancements in 3D shape reconstruction techniques that combine structured light and deep learning show promise in acquiring high-quality geometric information about object surfaces. This paper introduces a new single-shot 3D shape reconstruction method that uses a nonlinear fringe transformation approach through both supervised and unsupervised learning networks. In this method, a deep learning network learns to convert a grayscale fringe input into multiple phase-shifted fringe outputs with different frequencies, which act as an intermediate result for the subsequent 3D reconstruction process using the structured-light fringe projection profilometry technique. Experiments have been conducted to validate the practicality and robustness of the proposed technique. The experimental results demonstrate that the unsupervised learning approach using a deep convolutional generative adversarial network (DCGAN) is superior to the supervised learning approach using UNet in image-to-image generation. The proposed technique's ability to accurately reconstruct 3D shapes of objects using only a single fringe image opens up vast opportunities for its application across diverse real-world scenarios.

Adaptive focus stacking for large depth-of-field microscopic structured-light 3D imaging

This paper presents an adaptive focus stacking method for large depth-of-field (DOF) 3D microscopic structured-light imaging systems. Conventional focus stacking methods typically capture images under a series of pre-defined focus settings without considering the attributes of the measured object. Therefore, it is inefficient since some of the focus settings might be redundant. To address this problem, we first employ the focal sweep technique to reconstruct an initial rough 3D shape of the measured objects. Then, we leverage the initial 3D data to determine effective focus settings that focus the camera on the valid areas of the measured objects. Finally, we reconstruct a high-quality 3D point cloud using fringe images obtained from these effective focus settings by focus stacking. Experimental results demonstrate the success of the proposed method.

A new method for visually and real-timely measuring stress and load distributions in bolt with photoelastic technology

After analyzing the stress characteristics of the bolt, we determined that it can be regarded as experiencing a planar stress state due to the absence of circumferential stress. Consequently, a photoelastic bolt specimen was fabricated by taking a slice across its diameter. Using a photoelastic bench, we collected interference fringe images of the photoelastic specimen under different loads. This method enabled us to visually and continuously measure the stress distributions within the specimen in real-time. Additionally, the load distribution ratio of each tooth was derived. By comparing these results with those obtained through numerical simulation, we were able to validate the reasonability of the theoretical assumption regarding the load distribution of each tooth in the bolt. Our method establishes a solid foundation and can be effectively utilized for precise thread connection design.

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.

Analysis and simulation of the effect of large optical range difference of common path coherent-dispersion spectrometer on the detection of exoplanet radial velocities

The Exoplanet Explorer common-path coherent-dispersion spectrometer (CODES) utilizes a unique combination of an asymmetric common path Sagnac interferometer and a low to medium resolution spectrometer. The ideal optical range difference (OPD) interval for CODES is OPD ∈ {15.06 mm, 19.45 mm}; however, the OPD of CODES is 64.3 mm to achieve better detection accuracy. Though they will increase the accuracy of detection, large OPDs outside of the ideal interval will also reduce the contrast of the interference fringes, making phase changes more hazy. This may also significantly affect the radial velocity inversion and reduce CODES's instrumental accuracy. This study creates an inverse tone mapping operator based on the photographic model and designs an inverse tone mapping algorithm called CODESCE. The outcomes of the experiments demonstrate that the tone mapping algorithm CODESCE in this work is appropriate for enhancing the contrast of interference fringe images with high OPD, and it can enhance the contrast of interference fringes by three orders of magnitude when OPD = 64.3 mm; the processed interference fringes are located in the range of interference fringe curves of the optimal OPD. By comparison with other current approaches, the suggested algorithm yields superior processing outcomes.

Weakly Supervised Depth Estimation for 3D Imaging with Single Camera Fringe Projection Profilometry.

Fringe projection profilometry (FPP) is widely used for high-accuracy 3D imaging. However, employing multiple sets of fringe patterns ensures 3D reconstruction accuracy while inevitably constraining the measurement speed. Conventional dual-frequency FPP reduces the number of fringe patterns for one reconstruction to six or fewer, but the highest period-number of fringe patterns generally is limited because of phase errors. Deep learning makes depth estimation from fringe images possible. Inspired by unsupervised monocular depth estimation, this paper proposes a novel, weakly supervised method of depth estimation for single-camera FPP. The trained network can estimate the depth from three frames of 64-period fringe images. The proposed method is more efficient in terms of fringe pattern efficiency by at least 50% compared to conventional FPP. The experimental results show that the method achieves competitive accuracy compared to the supervised method and is significantly superior to the conventional dual-frequency methods.

Theory and verification of moiré fringes for x-ray three-phase grating interferometer

Dual-phase and three-phase grating x-ray interference is a promising new technique for grating-based x-ray differential phase contrast imaging. Dual-phase grating interferometers have been relatively completely studied and discussed. In this paper, the corresponding imaging fringe formula of the three-phase grating interferometer is provided. At the same time, the similarities and differences between the three-phase grating interferometer and the dual-phase grating interferometer are investigated and verified, and that the three-phase grating interferometer can produce large-period moiré fringes without using the analyzing grating is demonstrated experimentally. Finally, a simple method of designing three-phase grating and multi-grating imaging systems from geometric optics based on the thin-lens theory of gratings is presented. These theoretical formulas and experimental results provide optimization tools for designing three-phase grating interferometer systems.

Depth–Depth of Focus Moiré Fringe Alignment via Broad-Spectrum Modulation

Alignment precision is a crucial factor that directly impacts overlay accuracy, which is one of three fundamental indicators of lithography. The alignment method based on the Moiré fringe has the advantages of a simple measurement optical path and high measurement accuracy. However, it requires strict control of the distance between the mask and wafer to ensure imaging quality. This limitation restricts its application scenarios. A depth–DOF (depth of focus) Moiré fringe alignment by broad–spectrum modulation is presented to enhance the range of the alignment signals. This method establishes a broad–spectrum Moiré fringe model based on the Talbot effect principle, and it effectively covers the width of dark field (WDF) between different wavelength imaging ranges, thereby extending the DOF range of the alignment process, and employs a hybrid of genetic algorithms and the particle-swarm optimization (GA–PSO) algorithm to combine various spectral components in a white spectrum. By calculating the optimal ratio of each wavelength and using white light incoherent illumination in combination with this ratio, it achieves the optimal DOF range of a broad–spectrum Moiré fringe imaging model. The simulation results demonstrate that the available DOF range of the alignment system has been expanded from 400 μm to 800 μm. Additionally, the alignment precision of the system was analyzed, under the same conditions, and the accuracy analysis of the noise resistance, translation amount, and tilt amount was conducted for the Moiré fringe and broad–spectrum Moiré fringe. Compared to a single wavelength, the alignment precision of the broad–spectrum Moiré fringe decreased by an average of 0.0495 nm, equivalent to a 1.5% reduction in the original alignment precision, when using a 4 μm mask and a 4.4 μm wafer. However, the alignment precision can still reach 3.795 nm, effectively enhancing the available depth of focus range and reducing the loss of alignment precision.

Novel sensor developments for photon science at the MPG semiconductor laboratory

The world of photon science experiences significant advancements since the advent of synchrotron light sources with unprecedented brilliance, intensity and pulse repetition rates, with large implications on the detectors used for instrumentation. Here, an overview about the work on this field carried out at the semiconductor laboratory of the Max-Planck-Society (MPG HLL) is given. Main challenges are high dynamic range to resolve faint features at the fringes of scatter images as well as structures in bright peaks, and high bandwidth to fully exploit the fast timing capability of the source. A newly developed device to improve the signal-to-noise-ratio (SNR) at high bandwidths is the so-called MARTHA (Monolithic Array of Reach-Through Avalanche Photodiodes) structure, which integrates an array of APDs on a monolithic substrate. The reach-through architecture assures near 100% fill factor and allows implementing a thin entrance window with optimized quantum efficiency for low energy X-rays. The structures operate in proportional mode with adjustable gain, and can serve as a drop-in replacement for PAD detectors in hybrid pixel systems. A more sophisticated solution for low to medium frame rate applications with high contrast requirement are pnCCDs with high dynamic range in the pixel area featuring DEPFET based readout nodes with non-linear amplification (NLA). The high dynamic range mode has been demonstrated for pnCCD devices with a pixel size down to 75 μm2. Framerates of up to 1 kHz are possible for a 1 Megapixel detector. Small size prototypes of these structures have recently been manufactured. Modified DEPFET structures with build-in non-linear amplification are also used to implement active pixel detectors optimized for high dynamic range. Successfully prototyped for the DSSC sensors (DEPFET Sensor with Signal Compression) at the XFEL, these structures are increasingly being used in applications requiring high contrast and intensity, e.g., TEM imaging. Charge handling capability and output characteristics can be tailored to the requirements, as well as pixel geometry and size. The large intrinsic gain of the DEPFET provides excellent SNR even at fast timing. Pixels can be read with a speed of 100 ns, the resulting frame rate depends on the degree of readout parallelization.

Design of an angle measurement system based on interferometric fringe imaging and its off-axis measurement accuracy

Design of an angle measurement system based on interferometric fringe imaging and its off-axis measurement accuracy