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Abstract Fringe projection profilometry (FPP) has been widely applied to non-contact three-dimensional measurement in industries owing to its high accuracy and speed. The point cloud, which is a measurement result of the FPP system, typically contains a large number of invalid points caused by the background, ambient light, shadows, and object edge regions. Research on noisy point detection and elimination has been conducted over the past two decades. However, existing invalid point removal methods are based on image intensity analysis and are only applicable to simple measurement backgrounds that are purely dark. In this paper, we propose a novel invalid point removal framework that consists of two aspects: (1) A convolutional neural network (CNN) is designed to segment the foreground from the background of different intensity conditions in FPP measurement circumstances to remove background points and the most discrete points in background regions. (2) A two-step method based on the fringe image intensity threshold and a bilateral filter is proposed to eliminate the small number of discrete points remaining after background segmentation caused by shadows and edge areas on objects. Experimental results verify that the proposed framework (1) can remove background points intelligently and accurately in different types of complex circumstances, and (2) performs excellently in discrete point detection from object regions.

Fringe projection profilometry (FPP) has been widely applied to non-contact three-dimensional measurement in industries owing to its high accuracy and speed. The point cloud, which is a measurement result of the FPP system, typically contains a large number of invalid points caused by the background, ambient light, shadows, and object edge regions. Research on noisy point detection and elimination has been conducted over the past two decades. However, existing invalid point removal methods are based on image intensity analysis and are only applicable to simple measurement backgrounds that are purely dark. In this paper, we propose a novel invalid point removal framework that consists of two aspects: (1) A convolutional neural network (CNN) is designed to segment the foreground from the background of different intensity conditions in FPP measurement circumstances to remove background points and the most discrete points in background regions. (2) A two-step method based on the fringe image intensity threshold and a bilateral filter is proposed to eliminate the small number of discrete points remaining after background segmentation caused by shadows and edge areas on objects. Experimental results verify that the proposed framework (1) can remove background points intelligently and accurately in different types of complex circumstances, and (2) performs excellently in discrete point detection from object regions. [ABSTRACT FROM AUTHOR]

Fringe Projection Profilometry-FPP system is widely used for three-dimensional(3D) imaging. This system is promising. However, for the changing environmental conditions, the measurement object, system noise, and strong backlighting changing, it is difficult to obtain 3D image accurately by fringe analyzing methods such as Traditional Fourier Transform Method-TFFT in FPP System. Therefore, in this paper, the TFFT method is combined with various method and hybrid methods are formed. The aim is to investigate how these methods affect the accuracy of FPP system. To make this determination, from simulated fringe pattern, phase is calculated. Then the error values are obtained using these phase values. Consequently, it is seen from error results that TFFT with two Dimensional Empirical Mode Decomposition method-2D-EMD-FFT which gives the lowest error, is the most insensitive to the disruptive effects mentioned above. Moreover, it is the most stability and least affected by the geometric of the object under test. [ABSTRACT FROM AUTHOR]

Abstract In fringe projection profilometry based on temporal phase unwrapping, determining a fringe order map commonly requires a large number of fringes. To reduce the fringe number, this paper proposes a concise absolute phase retrieval algorithm just by projecting four fringes. The first two orthogonal fringes with relatively large frequency can collect reliable height information. The second two fringes are designed the same as the first two, but the only difference is that each 2π-phase of them is shifted by a unique amount, which can robustly label a large number of fringe orders. For decoding the fringes, we develop an average intensity one-time extraction algorithm, which allows for the rapid acquisition of the two pairs of alternating current components. From this, the wrapped phase containing height information and the stair-coded phase providing fringe orders can be directly extracted by arctangent operation in a point-to-point manner. Furthermore, we also develop a universal fringe order correction algorithm that can simultaneously correct the common errors and the misalignment between the wrapped phase and fringe orders. Experiment results demonstrate that this method achieves comparable accuracy and adaptability to the phase-coding method, while utilizing two fewer fringes.

Abstract Recent advances in imaging sensors and digital light projection technology have facilitated rapid progress in 3D optical sensing, enabling 3D surfaces of complex-shaped objects to be captured with high resolution and accuracy. Nevertheless, due to the inherent synchronous pattern projection and image acquisition mechanism, the temporal resolution of conventional structured light or fringe projection profilometry (FPP) based 3D imaging methods is still limited to the native detector frame rates. In this work, we demonstrate a new 3D imaging method, termed deep-learning-enabled multiplexed FPP (DLMFPP), that allows to achieve high-resolution and high-speed 3D imaging at near-one-order of magnitude-higher 3D frame rate with conventional low-speed cameras. By encoding temporal information in one multiplexed fringe pattern, DLMFPP harnesses deep neural networks embedded with Fourier transform, phase-shifting and ensemble learning to decompose the pattern and analyze separate fringes, furnishing a high signal-to-noise ratio and a ready-to-implement solution over conventional computational imaging techniques. We demonstrate this method by measuring different types of transient scenes, including rotating fan blades and bullet fired from a toy gun, at kHz using cameras of around 100 Hz. Experiential results establish that DLMFPP allows slow-scan cameras with their known advantages in terms of cost and spatial resolution to be used for high-speed 3D imaging tasks.

The radial displacement of hydrogen storage composite overwrapped pressure vessel (COPV) is a key factor related to the collapse failure and burst pressure. However, there is still lack of effective method to monitor the radial displacement during the hydrostatic test and service process of the vessels. This paper proposed a method to measure the radial displacement based on fringe projection profilometry (FPP). Hydrostatic test with a composite overwrapped pressure vessel verifies the proposed method. The variation of displacement changing with inner pressures observed in the experiments is in agreement with that obtained from finite element analysis. Also Computed Tomography (CT) scanning is conducted and a widely spread micro defects is found in the composite layer of the cylinder. 78.9% of the total observed defects are small (<1000 mm2). In regions where large-sized defects (>1000 mm2) are concentrated, the total area of defects reaches 16,200 mm2. According to the statistical analysis, the strong correlation is found between the defects area and radial displacement. • Presented a novel method based on fringe projection profilometry (FPP) for monitoring the deformation of composite overwrapped pressure vessels (COPVs) during hydrostatic testing. • Employing 3D point clouds from FPP to reconstruct the cylinder and measure radial displacement. • The variation trend of radial displacement with pressure obtained by experiments is consistent with the finite element results. • Utilized Computed Tomography (CT) to detect and quantify micro delamination defects in the cylinders. • A significant correlation was found between the area of defects and radial displacement, while the relationship between the number of defects and radial displacement was less pronounced. [ABSTRACT FROM AUTHOR]

Recent advances in imaging sensors and digital light projection technology have facilitated rapid progress in 3D optical sensing, enabling 3D surfaces of complex-shaped objects to be captured with high resolution and accuracy. Nevertheless, due to the inherent synchronous pattern projection and image acquisition mechanism, the temporal resolution of conventional structured light or fringe projection profilometry (FPP) based 3D imaging methods is still limited to the native detector frame rates. In this work, we demonstrate a new 3D imaging method, termed deep-learning-enabled multiplexed FPP (DLMFPP), that allows to achieve high-resolution and high-speed 3D imaging at near-one-order of magnitude-higher 3D frame rate with conventional low-speed cameras. By encoding temporal information in one multiplexed fringe pattern, DLMFPP harnesses deep neural networks embedded with Fourier transform, phase-shifting and ensemble learning to decompose the pattern and analyze separate fringes, furnishing a high signal-to-noise ratio and a ready-to-implement solution over conventional computational imaging techniques. We demonstrate this method by measuring different types of transient scenes, including rotating fan blades and bullet fired from a toy gun, at kHz using cameras of around 100 Hz. Experiential results establish that DLMFPP allows slow-scan cameras with their known advantages in terms of cost and spatial resolution to be used for high-speed 3D imaging tasks. [ABSTRACT FROM AUTHOR]

A highly robust dual-frequency hierarchical temporal phase unwrapping (DHTPU) based on the novel spatial computer-generated Moiré profilometry (SCGMP) is proposed. The method requires only three patterns: a high-frequency fringe to provide robust surface information, a multi-period low-frequency fringe to eliminate the 2π-phase ambiguities, and a flat pattern to remove the average intensity of the two fringes. In decoding, different from traditional Moiré profilometries that rely on spectrum filters, SCGMP only employs spatial-domain calculations to extract the wrapped phase, thereby preserving more detailed information. Furthermore, we fully explore SCGMP's capability to significantly alleviate phase ambiguity and provide an algorithm to determine the maximum measurable height range for a fixed system, enabling the direct extraction of the continuous basic phase from the multi-period low-frequency fringe. Consequently, the proposed basic phase exhibits an enhanced signal-to-noise ratio, compared to the traditional basic phase derived from the single-period fringes, effectively releasing the high-frequency restriction in the traditional DHTPU. The experimental results verify that the proposed DHTPU method has considerable accuracy and great potential for high-speed measurements, due to there being only three shots required. [ABSTRACT FROM AUTHOR]

This work presents TTFDNet, a transformer-based and transfer learning network for end-to-end depth estimation from single-frame fringe patterns in fringe projection profilometry. TTFDNet features a precise contour and coarse depth (PCCD) pre-processor, a global multi-dimensional fusion (GMDF) module and a progressive depth extractor (PDE). It utilizes transfer learning through fringe structure consistency evaluation (FSCE) to leverage the transformer's benefits even on a small dataset. Tested on 208 scenes, the model achieved a mean absolute error (MAE) of 0.00372 mm, outperforming Unet (0.03458 mm) models, PDE (0.01063 mm) and PCTNet (0.00518 mm). It demonstrated precise measurement capabilities with deviations of ~90 μm for a 25.4 mm radius ball and ~6 μm for a 20 mm thick metal part. Additionally, TTFDNet showed excellent generalization and robustness in dynamic reconstruction and varied imaging conditions, making it appropriate for practical applications in manufacturing, automation and computer vision. [ABSTRACT FROM AUTHOR]

With its its ability to non-contact measure three-dimensional information of objects and its extremely high accuracy advantage in close range, structured light 3-D measurement is widely used in various fields. However, some application scenarios, such as measuring moving objects and performing measurements in confined spaces, impose requirements for high speed and miniaturization in structured light 3-D measurement. Therefore, we propose a real-time structured light 3-D measurement system on FPGA. This system employs a four-step phase-shifting method to compute wrapped phases, complemented Gray code for phase unwrapping, and a cubic polynomial fitting approach for calculating the 3-D coordinates of points. We have proposed the optimized pipeline structure for each module. We have also proposed an optimized on-chip buffer structure to further improve throughput. The 3-D measurement speed of the proposed method can reach 76.9 fps, when the clock frequency is 100 MHz, and the image size is 2448 × 2048. [ABSTRACT FROM AUTHOR]

In the fringe projection profilometry (FPP), the traditional phase-shifting (TPS) algorithm and the Fourier transform (FT) algorithm are beset with a conundrum where measurement efficiency and conflicts with measurement accuracy, thereby limiting their application in dynamic three-dimensional (3D) measurements. Here, we propose a phase shift generation (PSG) method, which acquires the sinusoidal fringes by sparse sampling and reconstructs the complete phase-shifting sequence by generating the missing fringes with superimposed coupling of adjacent fringes. According to our proposed PSG method in which the sinusoidal fringe sequence size is about half of the TPS method, meaning that the PSG method will be timesaving in the phase-shifting sequence sampling process. Moreover, because of the utilization of multiframe fringes, our PSG method allows for a more accurate measurement than the FT method. Both simulation and experimental results demonstrate that our proposed PSG method can well balance the measurement accuracy and efficiency with a lower sampling rate, bearing a great potential to be applied in both scientific and industrial areas. [ABSTRACT FROM AUTHOR]

Phase unwrapping is an important research direction in fringe projection profilometry. Improving the accuracy of phase unwrapping from a single wrapped phase map has been a research focus. Existing the deep learning mathods for phase unwrapping from a single wrapped phase map suffer from accuracy issues when dealing with noise, the large variation range of phase surfaces, or isolated area. In this paper, we propose a novel approach to address these challenges. We treat the phase unwrapping problem as a semantic segmentation problem and introduce a new stage to the high resolution network. Additionally, we add an object contextual representation module. This approach allows us to predict the fringe order map from a single wrapped phase map without the need for any pre-process or post-process. Our method can accurately recover the phase information of objects under various challenging conditions. We validate the effectiveness and superiority of our approach by comparing it with Three deep learning methods for spatial phase unwrapping and one traditional spatial phase unwrapping method, qualitatively and quantitatively.

In 2019, the Event Horizon Telescope (EHT) released the first-ever image of a black hole event horizon. Astronomers are now aiming for higher angular resolutions of distant targets, like black holes, to understand more about the fundamental laws of gravity that govern our universe. To achieve this higher resolution and increased sensitivity, larger radio telescopes are needed to operate at higher frequencies and in larger quantities. Projects like the next-generation Very Large Array (ngVLA) and the Square-Kilometer Array (SKA) require building hundreds of telescopes with diameters greater than 10 ms over the next decade. This has a twofold effect. Radio telescope surfaces need to be more accurate to operate at higher frequencies, and the logistics involved in maintaining a radio telescope need to be simplified to support them properly in large quantities. Both of these problems can be solved with improved methods for surface metrology that are faster and more accurate with a higher resolution. This leads to faster and more accurate panel alignment and, therefore, a more productive observatory. In this paper, we present the use of binocular fringe projection profilometry as a solution to this problem and demonstrate it by aligning two panels on a 3-m radio telescope dish. The measurement takes only 10 min and directly delivers feedback on the tip, tilt, and piston of each panel to create the ideal reflector shape. Highlights: Current methods for measuring and aligning radio telescope dishes are insufficient for future astronomy requirements. We've developed a 3D scanning method for measuring full aperture dishes outdoors that is faster, easier, and more reliable than current methods. We demonstrated the method by aligning two panels on a 3-m dish to a high accuracy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The aero-engine serves as the "heart" of an aircraft and is a primary factor determining the aircraft's performance. Among the crucial components in the core of aero-engines, aero-engine compressor blades stand out as extremely important. They are not only numerous but also characterized by a multitude of parameters, making them the most complex parts in an aero-engine. This paper aims to address the trade-off between accuracy and efficiency in the existing measurement methods for asymmetric blades. Non-contact measurements were conducted using a structured light system composed of a stereo camera and a DLC projector. The point cloud data of the blades are processed using methods such as the PCA (Principal Component Analysis) algorithm, binary search, and least squares fitting. This paper established a fringe-projection profilometry light sensor system for the multi-view measurement of the blades. High-precision rotary tables are utilized to rotate and extract complete spatial point cloud data of aviation blades. Finally, measurements and comparative experiments on the blade body are conducted. The obtained blade point cloud data undergo sorting and denoising processes, resulting in improved measurement accuracy. The measurement error of the blade chord length is 0.001%, the measurement error of blade maximum thickness is 0.895%, compared to CMM (Coordinate Measuring Machine), where the measurement error of chord is 0.06%. [ABSTRACT FROM AUTHOR]

A highly robust dual-frequency hierarchical temporal phase unwrapping (DHTPU) based on the novel spatial computer-generated Moiré profilometry (SCGMP) is proposed. The method requires only three patterns: a high-frequency fringe to provide robust surface information, a multi-period low-frequency fringe to eliminate the 2π-phase ambiguities, and a flat pattern to remove the average intensity of the two fringes. In decoding, different from traditional Moiré profilometries that rely on spectrum filters, SCGMP only employs spatial-domain calculations to extract the wrapped phase, thereby preserving more detailed information. Furthermore, we fully explore SCGMP’s capability to significantly alleviate phase ambiguity and provide an algorithm to determine the maximum measurable height range for a fixed system, enabling the direct extraction of the continuous basic phase from the multi-period low-frequency fringe. Consequently, the proposed basic phase exhibits an enhanced signal-to-noise ratio, compared to the traditional basic phase derived from the single-period fringes, effectively releasing the high-frequency restriction in the traditional DHTPU. The experimental results verify that the proposed DHTPU method has considerable accuracy and great potential for high-speed measurements, due to there being only three shots required.

Close-range photogrammetry methods are widely used for non-contact and accurate measurements of surface shapes. These methods are based on calculating the three-dimensional coordinates of an object from two-dimensional images using special digital processing algorithms. Due to the relatively complex measurement principle, the accurate estimation of the photogrammetric measurement error is a non-trivial task. Typically, theoretical estimations or computer modelling are used to solve this problem. However, these approaches cannot provide an accurate estimate because it is impossible to consider all factors that influence the measurement results. To solve this problem, we propose the use of physical modelling. The measurement results from the photogrammetric system under test were compared with the results of a more accurate reference measurement method. This comparison allowed the error to be estimated under controlled conditions. The test object was a flexible surface whose shape could vary smoothly over a wide range. The estimation of the measurement accuracy for a large number of different surface shapes allows us to obtain new results that are difficult to obtain using standard approaches. To implement the proposed approach, a laboratory system for the error estimation of close-range photogrammetric measurements was developed. The paper contains a detailed description of the developed system and the proposed technique for a comparison of the measurement results. The error in the reference method, which was chosen to be phasogrammetry, was evaluated experimentally. Experimental testing of the stereo photogrammetric system was performed according to the proposed technique. The obtained results show that the proposed technique can reveal dependencies that may not be detected by standard approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a non-contact continuous respiration monitoring method based on Fringe Projection Profilometry (FPP). This method aims to overcome the limitations of traditional intrusive techniques by providing continuous monitoring without interfering with normal breathing. The FPP sensor captures three-dimensional (3D) respiratory motion from the chest wall and abdomen, and the analysis algorithms extract respiratory parameters. The system achieved a high Signal-to-Noise Ratio (SNR) of 37 dB with an ideal sinusoidal respiration signal. Experimental results demonstrated that a mean correlation of 0.95 and a mean Root-Mean-Square Error (RMSE) of 0.11 breaths per minute (bpm) were achieved when comparing to a reference signal obtained from a spirometer. [ABSTRACT FROM AUTHOR]

Fringe projection profilometry (FPP) has been widely used for 3D reconstruction, surface measurement, and reverse engineering. However, if the surface of an object has a high reflectivity, overexposure can easily occur. Image saturation caused by overexposure can lead to an incorrect intensity of the captured pattern images, resulting in phase and measurement errors of FPP. To address this issue, we propose a phase retrieval method for the 3D shape measurement of high-reflectivity surfaces based on π phase-shifting fringes. Our method only requires eight images to be projected, including three single-frequency three-step phase-shifting patterns and one pattern used to provide phase unwrapping constraints, called conventional patterns, as well as the π phase-shifting patterns corresponding to the four conventional patterns, called supplemental patterns. Saturated pixels of conventional fringes are replaced by unsaturated pixels in supplemental fringes to suppress phase retrieval errors. We analyzed all 16 replacement cases of fringe patterns and provided calculation methods for unwrapped phases. The main advantages of our method are as follows: (1) By combining the advantages of the stereo phase unwrapping (SPU) algorithm, the number of projected fringes is reduced. (2) By utilizing the phase unwrapping constraint provided by the fourth fringe pattern, the accuracy of SPU is improved. For highly reflective surfaces, the experimental results demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Fringe Projection Profilometry (FPP) is a cost-effective and non-destructive method, typically used for measuring finer features and reconstructing 3D topography of objects. However, to use the FPP method for measuring the dynamic topography of powder bed and printed layers during Laser Powder Bed Fusion (LPBF) based additive manufacturing (AM) process, unique challenges exist due to the varying material properties and ambient conditions in the build chamber. In this work, we aim to enhance the discernibility, accuracy, and resolution of FPP in the specific application scenario of measuring layer-wise surface topography during LPBF AM by integrating our recently developed LPBF-specific FPP sensing model that features localized sensor calibration and Fourier filter-aided unwrapping with an equipment-based High dynamic range (HDR) method and machine learning (ML) aided FPP data analysis. First, a projector based HDR method is applied to mitigate the shadowing and intensity saturation problems by projecting sinusoidal fringe patterns of varying intensities. Secondly, a ML framework is developed to improve the surface topography measurement accuracy (RMSE from 10.57 μm to 7.49 μm or even 4.35 μm for directly measurable points) and enhance resolution that is currently subjected to hardware limitations (from 38 μm to 5 μm laterally and from 10 μm to 1 μm vertically). Several different types of candidate neural networks (NNs) are trained and tested using the in-situ FPP measurement data and ex-situ standard optical microscopy characterization data. Multiple NN-based models are resulted and compared in terms of their ability to enhance the accuracy and resolution of FPP's end-result (height measurement). By selecting the best-performance NN enabled image super resolution model, the proposed ML integrated HDR FPP method is expected to measure the surface topography of printed layers during LPBF-AM more capably and efficiently, thus advancing the existing state-of-the-art methods towards the desired online inspection of LPBF print defects. • Machine learning enhanced high dynamic range (HDR) fringe projection profilometry (FPP). • Mitigate intensity saturation and shadowing in in-situ laser powder bed fusion (LPBF) monitoring. • Improve measurement accuracy of LPBF-specific FPP, e.g., RMSE reduced from 10.57 μm to 4.35 μm. • Machine learning based super resolution model to enhance resolution (∼8 times improvement shown). • Application in detection of microscale (5 μm wide, 1 μm high) features and defects during LPBF. [ABSTRACT FROM AUTHOR]

Fringe projection profilometry (FPP) plays an important role in the quality control of complex surface workpieces. Simulation using realistic image synthesis referring to physical sensors provide valid measures for the design and optimization of FPP systems. In the simulation of FPP, ray tracing can simulate the fringe image acquisition process, considering the comprehensive influence of light source, camera and object attributes. Therefore, a measurement simulation system of FPP based on ray tracing is developed in this paper. The simulation model and measurement principle of FPP are introduced. On this basis, the methodology of simulating camera imaging by ray tracing is proposed, including scene construction, ray generation and gray value calculation. Principle experiments are carried to verify the accuracy and efficiency of simulation system, and comparative experiments are conducted for demonstrating its reproducibility to physical system. The proposed system provides a convenient and accurate mean for analyzing measurement errors and optimizing inspection strategy.

The gear is very important component in the means of transportation. A method for inspection of helix angle on pitch cylinder and reverse design of helical gear based on digital fringe projection profilometry, which is capable of high accuracy and high speed, is presented in this manuscript. The governing equation with 35 unknown parameters that represent the phase-to-height relationship is derived in case of arbitrary arrangement of the camera and projector in the presented work. The least-squares orthogonal distance fitting (LSODF) approach is employed for inspection and reverse design of helical gear. The appropriate mathematical equation of tooth profile of helical gear is proposed. The estimation error of helix angle on pitch cylinder is lower than 0.0166 degree. [ABSTRACT FROM AUTHOR]

We propose a novel hybrid FPP-DIC technique to measure an object's shape and deformation in 3D simultaneously by using a single 3CCD color camera, which captures the blue fringe patterns and red fluorescent speckles within the same image. Firstly, red fluorescent speckles were painted on the surface of the specimen. Subsequently, 12 computer-generated blue fringe patterns with a black background were projected onto the surface of the specimen using a DLP projector. Finally, both the reference and deformed images with three different frequencies and four shifted phases were captured using a 3CCD camera. This technique employed a three-chip configuration in which red–green–blue chips were discretely integrated in the 3CCD color camera sensor, rendering independent capture of RGB information possible. Measurement of out-of-plane displacement was carried out through the implementation of Fringe Projection Profilometry (FPP), whereas the in-plane displacement was evaluated using a 2D Digital Image Correlation (DIC) method by leveraging a telecentric-lens-based optical system. In comparison to the traditional FPP-DIC hybrid methodology, the present approach showed a lower incidence of crosstalk between the fringe patterns and speckle patterns while also offering a corrective for the coupling of the in-plane displacement and out-of-plane displacement. Experimental results for the in-plane cantilever beam and out-of-plane disk comparisons with the traditional 3D-DIC method indicated that the maximum discrepancy obtained between FPP-DIC and 3D-DIC was 0.7 μm and 0.034 mm with different magnifications, respectively, validating the effectiveness and precision of the novel proposed FPP-DIC method. [ABSTRACT FROM AUTHOR]

The quick and accurate retrieval of an object's height from a single fringe-pattern in Fringe Projection Profilometry has been a topic of ongoing research. While existing single-shot fringe-to-depth CNN methods can directly generate height map from one pattern, their accuracy lags behind traditional phase-shifting techniques. To improve accuracy, we propose a U-shaped High-resolution Network (UHRNet). The network utilizes U-Net's encoding-decoding structure as the backbone, employing Multi-Level Conv Blocks and High-resolution Fusion Blocks to extract features. Additionally, a compound loss function, combining Structural Similarity Index Measure Loss (SSIMLoss) and chunked L2 loss function, is devised to enhance the details of 3D reconstruction. Our method has been experimentally proven to be efficient with an average RMSE of 0.443 mm, which is 64.67% lower than hNet and 33.31% lower than ResUNet. These results indicate that the proposed approach significantly enhances the accuracy of 3D reconstruction from a single fringe-pattern. [ABSTRACT FROM AUTHOR]

In the fringe projection profilometry (FPP), the traditional phase-shifting (TPS) algorithm and the Fourier transform (FT) algorithm are beset with a conundrum where measurement efficiency and conflicts with measurement accuracy, thereby limiting their application in dynamic three-dimensional (3D) measurements. Here, we propose a phase shift generation (PSG) method, which acquires the sinusoidal fringes by sparse sampling and reconstructs the complete phase-shifting sequence by generating the missing fringes with superimposed coupling of adjacent fringes. According to our proposed PSG method in which the sinusoidal fringe sequence size is about half of the TPS method, meaning that the PSG method will be timesaving in the phase-shifting sequence sampling process. Moreover, because of the utilization of multiframe fringes, our PSG method allows for a more accurate measurement than the FT method. Both simulation and experimental results demonstrate that our proposed PSG method can well balance the measurement accuracy and efficiency with a lower sampling rate, bearing a great potential to be applied in both scientific and industrial areas.

In three-dimensional (3D) shape measurement based on fringe projection, various factors can degrade the quality of the point cloud. Existing point cloud filtering methods involve analyzing the geometric relationship between 3D space and point cloud, which poses challenges such as complex calculation and low efficiency. To improve the accuracy and speed of point cloud filtering, this paper proposes a new point cloud filtering method based on image segmentation and the absolute phase for the 3D imaging obtained by fringe projection. Firstly, a two-dimensional (2D) point cloud mapping image is established based on the 3D point cloud obtained from fringe projection. Secondly, threshold segmentation and region growing methods are used to segment the 2D point cloud mapping image, followed by recording and removal of the segmented noise region. Using the relationship between the noise point cloud and the absolute phase noise point in fringe projection, a reference noise-free point is established, and the absolute phase line segment is restored to obtain the absolute phase of the noise-free point. Finally, a new 2D point cloud mapping image is reconstructed in 3D space to obtain a point cloud with noise removed. Experimental results show that the point cloud denoising accuracy calculated by this method can reach up to 99.974%, and the running time is 0.954 s. The proposed method can effectively remove point cloud noise and avoid complex calculations in 3D space. This method can not only remove the noise of the 3D point cloud but also can restore the partly removed noise point cloud into a noise-free 3D point cloud, which can improve the accuracy of the 3D point cloud. [ABSTRACT FROM AUTHOR]

Intensity saturation can induce phase error and, thus, measurement error in fringe projection profilometry. To reduce saturation-induced phase errors, a compensation method is developed. The mathematical model of saturation-induced phase errors is analyzed for N-step phase-shifting profilometry, and the phase error is approximately N-folder of the frequency of the projected fringe. Additional N-step phase-shifting fringe patterns with initial phase-shift π/N are projected for generating a complementary phase map. The final phase map is obtained by averaging the original phase map extracted from the original fringe patterns and the complementary phase map, and then the phase error can be canceled out. Both simulations and experiments demonstrated that the proposed method can substantially reduce the saturation-induced phase error and realize accurate measurements for a highly dynamic range of scenarios. [ABSTRACT FROM AUTHOR]

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In phase-shifting fringe projection profilometry, nonlinearities of the used devices affect measurement accuracy by induing harmonics in fringe signals. The resulting errors are manifested as ripple artifacts in the measured phase maps. Especially when phase shifts are not uniform, the error artifacts have unpredictable profiles and complicated frequency components thus being not easy to eliminate. To solve this problem, this paper suggests a method for suppressing effects of fringe harmonics when using arbitrary phase shifts. For doing it, this paper derives the frequency transfer function that explicitly represents the response of the phase-shifting algorithm to each order of fringe harmonics, and then uses this function to deduce a method that allows one to estimate the coefficients of harmonics from spectrum of the calculated complex fringe pattern. By iteratively subtracting off the estimated harmonics from the calculated complex fringe pattern, fringe phases are calculated accurately. Simulation and experimental results demonstrate that this method significantly suppresses the influence of fringe harmonics on measurement results and, simultaneously, it preserves edges and details of the measured object from being blurred. • The frequency transfer function that represents response of least-squares phase-shifting algorithm to each order of fringe harmonic is deduced. • A novel non-filtering method for suppressing harmonics-caused errors is proposed. • This method can work well with few to three uniform or non-uniform phase shifts and can preserve details of the object from being blurred. [ABSTRACT FROM AUTHOR]

• The non-ideal linewidth of the line laser causes the window smoothing effect in MEMS-based FPP systems. • The first interpretable laser influence model is proposed to quantify window smoothing effect. • A novel method for evaluating MEMS FPP systems is designed by using laser parameters. • An optimal fringe number calibration method is proposed to maximize the accuracy of any given MEMS FPP system. The reconstruction using MEMS micro-vibration mirrors is the most promising. However, the influence mechanism of the line laser, which serves as the sole light source of MEMS-based systems, on reconstruction is unclear. To fill this theoretical gap, we propose the first interpretable laser influence model called the window smoothing model. This model reveals the window smoothing effect of laser beam scanning and quantifies its impact on modulation intensity through a decay factor. Given the absence of lens defocusing issues, the window smoothing effect becomes the primary factor affecting the contrast of fringe patterns. Therefore, a novel method using laser parameters to evaluate system accuracy is introduced. Leveraging these insights, we further propose an optimal fringe number calibration method, also based on laser parameters, to maximize the reconstruction accuracy of any given system. Finally, experimental results validate the effectiveness of the proposed method. As the first model tailored for MEMS systems, the window smoothing model is interpretable, highly accurate, and universal. Therefore, this model can provide new insights and a theoretical foundation for achieving high-performance MEMS-based reconstruction. [ABSTRACT FROM AUTHOR]

• A new method is proposed for Fringe Projection Profilometry (FPP) to obtain more accurate extrinsic parameters. • Reconstruction residuals of a standard plane and dumbbell bats are set as the objective function in the proposed algorithm. • Low-frequency reconstruction errors introduced by calibration errors in extrinsic parameters are compensated. • The method is applicable to all FPP systems calibrated with stereo vision models to improve the measurement accuracy. Fringe projection profilometry (FPP) is a wildly used three-dimension reconstruction method, where the reconstruction accuracy is closely related to the calibration precision. However, various sources of error in the calibration process can result in inaccurate calibration results. In particular, the calibration results of extrinsic parameters are more likely to deviate from the true values, which in turn leads to low-frequency errors in the reconstruction results. In order to obtain the extrinsic parameters closer to the true values, a simple but effective method is proposed in this paper. The proposed method utilizes the standard plane and the dumbbell bat, which are commonly used in measurements, to optimize the extrinsic parameters. First, the standard plane and dumbbell bat are reconstructed using the initial calibration results to transfer the errors in the extrinsic parameters to the plane fitting residuals, as well as to the fitting residuals for the radius and the center distance of dumbbell bat. The residuals and errors are then minimized using nonlinear optimization, resulting in the more accurate extrinsic parameters. Experimental results demonstrate that the proposed method can effectively compensate the calibration error of the extrinsic parameters. The root mean square (RMS) error of planar reconstruction is reduced from 0.0291 mm to 0.0106 mm, which is reduced by about 63.6 %. The RMS error of spherical reconstruction is reduced from 0.0358 mm to 0.0166 mm, which is about 53.6 %. The measurement accuracy of the FPP system is further improved. [ABSTRACT FROM AUTHOR]

• A theoretical analysis of factors affecting accuracy is conducted, and an error transformation equation is derived. • A novel accuracy quality function is developed to assess measurement accuracy using in-situ images with current settings. • An in-situ exposure time optimization is introduced to minimize phase error globally using only two images for unknown objects. Fringe projection profilometry (FPP) has become one of the most powerful techniques for three-dimensional (3D) non-contact measurement. However, in practical scenarios, the various reflectivity of the unknown measured objects often greatly makes the system unable to achieve the theoretical precision under the same system parameter settings. Therefore, the adaptively system parameter setting is essential to be developed. In this paper, we propose a novel metric model, i.e. the accuracy quality function, for initial accuracy evaluation using in-situ acquired images under the current parameter settings. The causes that potentially affects the ultimate accuracy are analyzed via theoretical derivation and further adopted within the evaluation model. In addition, an optimal exposure selection method based just two images is carried out to fast adjusting. Experimental results demonstrated that the proposed accuracy quality model aligns well with the actual condition. Under optimal exposure, it achieved a significant reduction in phase error by 36.15% and by 21.39% in low- and high- exposure, highlighting its strong performance and potential for high-accuracy and in-situ 3D shape measurement applications. [ABSTRACT FROM AUTHOR]

• A deep learning fringe projection profilometry with geometric constraints is proposed. • The reference phase is used to transform the phase unwrapping problem into the regression problem for phase difference. • The proposed method can achieve single-shot high-resolution 3D measurement. • The importance of the reference phase for single-frame deep learning-based phase unwrapping in FPP is demonstrated. • The proposed method enables motion artifact-free 3D measurements of dynamic scenarios. Single-shot three-dimensional (3D) measurement has always been the ultimate goal of fringe projection profilometry (FPP). Some studies have shown that deep learning outperforms traditional algorithm in analyzing single fringe pattern for complex scenarios. However, accurately phase unwrapping for a single wrapped phase map remains a significant challenge. In this paper, we propose a deep learning-based fringe projection profilometry. This method considers the geometric constraints of the measurement system. With the reference phase generated by the calibration parameters and appropriately designed intermediate variables based on physical models and prior knowledge, the proposed method is capable of recovering high-quality absolute phase from a single fringe pattern at the accuracy sufficiently high to rival traditional multi-frame algorithms. In addition, as far as FPP is concerned, the significance of the reference phase generated by the calibration parameters of the measurement system for deep learning-based single-frame phase unwrapping is experimentally demonstrated. Experiments on both static and dynamic scenarios show that the proposed method can achieves motion-artifact-free and high-resolution single-shot 3D measurements in various complex scenarios using only a single-frequency fringe projection. [ABSTRACT FROM AUTHOR]

• A novel composite fringe projection profilometry based on deep learning is proposed for single-shot 3D measurement. • This article proposes for the first time to incorporate three frequencies fringe patterns into one composite grayscale fringe pattern instead of the composite color fringe pattern. • The method proposed in this article can predict high-precision sinusoidal fringes with corresponding frequencies through Haar-like composite fringes. • The proposed two-stage, one-to-three deep learning network can predict the corresponding frequency fringe images and phase-shifting fringe images robustly and accurately. • The proposed method can achieve effective and robust phase unwrapping based on only one composite fringe pattern. The efficiency and precision of 3D shape reconstruction has been a focus in the fringe projection profilometry (FPP). However, achieving high-quality 3D measurement for isolated or overlapping objects from single fringe image is still a challenging task in the field. In this paper, a binocular composite grayscale fringe projection profilometry (BCGFPP) based on deep learning is proposed, in which a two-stage one-to-three network (TO Net) is trained to predict the images required for phase unwrapping. The obtained absolute phase map exhibits high precision and eliminates deviation error and periodic ambiguity typically encountered in traditional sinusoidal composite fringe coding scheme. Haar transform principle is employed to form a Haar-like composite fringe pattern (HCFP), which consists of three different frequencies, serving as the input. TO Net architecture is designed to predict images required by the tri-frequency four-step phase-shifting method (TFPM). Further, the absolute phase is calculated and the disparity map is obtained by matching the absolute phase of the left and right cameras. Finally, the 3D shape of the object can be restored by the system calibration parameters. Experimental results demonstrate the approach can greatly reduce the number of fringes required and achieve the accuracy of the absolute phase close to the training set. [ABSTRACT FROM AUTHOR]

• The projection points tracking method for motion-induced error reduction is proposed. • The digital image correlation method is introduced to fringe projection profilometry. • Fringe patterns for 3D shape measurement are corrected at sub-pixel level. Fringe projection profilometry is a significant method for three-dimensional measurement due to its non-contact and high accuracy. However, the motion-induced error will lead to the loss of measurement accuracy in dynamic scenes due to the disruption of the phase measurement process. In this paper, we introduce a novel motion error model that considers object motion causes the misalignment of the projection points on the camera, and propose the projection points tracking method to reduce the motion-induced error. First, the speckle pattern is added to projection sequences, after which the projection point displacements are determined using the digital image correlation (DIC) method between the adjacent speckle patterns. Finally, the fringe patterns are corrected using the image remapping method to calculate the 3D shape. Quantitative analysis and dynamic measurement experiments verify the feasibility of the proposed method. Different from 3D-DIC, we use one camera-projector system to realize high-accuracy measurement in dynamic scenes. [ABSTRACT FROM AUTHOR]