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The phase-shifting interferometry has been intensively studied for more than half a century, and is still actively investigated and improved for more demanding precision measurement requirements. A proper phase-shifting algorithm (PSA) for phase extraction should consider various error sources including (i) the phase-shift errors, (ii) the intensity harmonics, (iii) the non-uniform phase-shift distributions and (iv) the random additive intensity noise. Consequently, a large pool of PSAs has been developed, including those with known phase shifts (abbreviated as kPSA) and those with unknown phase shifts (abbreviated as uPSA). While numerous evaluation works have been done for the kPSAs, there are very few for the uPSAs, making the overall picture of the PSAs unclear. Specifically, there is a lack of (i) fringe pattern parameters' restriction analysis for the uPSAs and (ii) performance comparison within the uPSAs and between the uPSAs and the kPSAs. Thus, for the first time, we comprehensively evaluated the pre-requisites and performance of four representative uPSAs, the advanced iterative algorithm, the general iterative algorithm (GIA), the algorithm based on the principal component analysis and the algorithm based on VU factorization, and then compare the uPSAs with twelve benchmarking kPSAs. From this comparison, the demand for proper selection of a kPSA, and the restriction and attractive performance of the uPSAs are clearly depicted. Due to the outstanding performance of the GIA, a hybrid kPSA-GIA is proposed to boost the performance of a kPSA and relieve the fringe density restriction of the GIA. Economic Development Board (EDB) Ministry of Education (MOE) Published version Economic Development Board - Singapore (S17-1579-IPP-II); Ministry of Education - Singapore (MOET2EP20220-0008).

Computer-Controlled Optical Surfacing (CCOS) has been greatly developed and widely used for precision optical fabrication in the past three decades. It relies on robust dwell time solutions to determine how long the polishing tools must dwell at certain points over the surfaces to achieve the expected forms. However, as dwell time calculations are modeled as ill-posed deconvolution, it is always non-trivial to reach a reliable solution that 1) is non-negative, since CCOS systems are not capable of adding materials, 2) minimizes the residual in the clear aperture 3) minimizes the total dwell time to guarantee the stability and efficiency of CCOS processes, 4) can be flexibly adapted to different tool paths, 5) the parameter tuning of the algorithm is simple, and 6) the computational cost is reasonable. In this study, we propose a novel Universal Dwell time Optimization (UDO) model that universally satisfies these criteria. First, the matrix-based discretization of the convolutional polishing model is employed so that dwell time can be flexibly calculated for arbitrary dwell points. Second, UDO simplifies the inverse deconvolution as a forward scalar optimization for the first time, which drastically increases the solution stability and the computational efficiency. Finally, the dwell time solution is improved by a robust iterative refinement and a total dwell time reduction scheme. The superiority and general applicability of the proposed algorithm are verified on the simulations of different CCOS processes. A real application of UDO in improving a synchrotron X-ray mirror using Ion Beam Figuring (IBF) is then demonstrated. The simulation indicates that the estimated residual in the 92.3 mm × 15.7 mm CA can be reduced from 6.32 nm Root Mean Square (RMS) to 0.20 nm RMS in 3.37 min. After one IBF process, the measured residual in the CA converges to 0.19 nm RMS, which coincides with the simulation.

Introducing a carrier into a fringe pattern makes the phase retrieval problem well-posed, and has become one of the pillar techniques in optical metrology. The carrier fringe pattern analysis for high-accuracy phase retrieval is hence important, for which, many well-known methods have been developed, such as the Fourier transform method, the windowed Fourier transform based methods (the windowed Fourier filtering and the windowed Fourier ridges), the spatial carrier phase-shifting method, and the sampling moire method. These methods were developed independently and seemingly different. The purpose of this paper is to reveal the close relationships between them, and to connect these methods into a tight-knit methodology family.

In this Letter, a deep learning solution (Y4-Net, four output channels network) to one-shot dual-wavelength digital holography is proposed to simultaneously reconstruct the complex amplitude information of both wavelengths from a single digital hologram with high efficiency. In the meantime, by using single-wavelength results as network ground truth to train the Y4-Net, the challenging spectral overlapping problem in common-path situations is solved with high accuracy.

An accurate and flexible real-time digital image correlation (RT-DIC) system utilizing a pipelined CPU and GPU parallel computing framework is proposed. First, the respective advantages of CPU and GPU in performing the fast Fourier transform-based cross-correlation (FFT-CC) algorithm and the inverse-compositional Gauss Newton (IC-GN) algorithm of the employed path-independent DIC (PI-DIC) method are elucidated. Second, based on the different properties and performances of CPU and GPU, a pipelined system framework unifying five Variants of combinations of CPU and GPU is proposed, which can be flexibly applied to various practical applications with different requirements of measurement scales and speeds. Last, both the accuracy and speed of the entire pipelined framework are verified by a PC implementation of the RT-DIC system integrating Variants 2–5. Variants 2 and 5 are also implemented on an iPhone 5S for the feasibility investigation of realizing a portable RT-DIC system on mobile devices using the same framework.

High-speed three-dimensional (3D) shape measurement techniques based on fringe projection profilometry (FPP) have undergone huge advances over the past two decades. However, accurate 3D displacement mapping and deformation analysis of dynamic scenes using FPP remains an unsolved problem. Because fringe patterns are projected rather than attached on the tested surfaces, the full-field point-to-point correspondence cannot be accurately established between any two 3D shape results. To deal with this challenge, a DIC-assisted FPP for high-speed 3D shape, displacement and deformation measurement of textured surfaces is proposed. Firstly, a high-speed 3D shape measurement system is adopted using our recently proposed robust and efficient Gray-coded coding strategy, which can accurately reconstruct full-field shape of discontinuous surfaces with rich texture information. Then, the modulation-based method is proposed to retrieve high-quality texture map from three phase-shifting fringe patterns, which can eliminate the adverse influence of the nonuniform and time-varying ambient light. By matching the retrieved surface texture images at difference states using DIC, accurate point tracking between the measured 3D shape data can be fulfilled, leading to precise 3D displacement and deformation measurement. Experiments have verified that the proposed method can achieve 3D shape, displacement and deformation measurement of dynamic scenes at a frame rate of 542 fps without any extra expense of hardware or calibration for the FPP system. The presented method is reliable and promising for further 3D displacement mapping and deformation analysis of dynamic scenes using FPP.

Phase unwrapping, either spatial or temporal, plays an important role in fringe projection profilometry (FPP) to recover a continuous phase map. Compared with the spatial phase unwrapping (SPU), the temporal phase unwrapping (TPU), including multi/two-frequency, phase coding, and gray code methods, is more widely used due to its ability to measure discontinuous objects. However, multiple patterns are required in TPU, which limits the measurement speed and the application of dynamic object measurement. To overcome this problem, different techniques, such as binary defocusing projection, two-plus-one phase-shifting algorithm, geometry/continuity constrained phase unwrapping, and ternary/quaternary gray code phase unwrapping have been proposed and actively studied recently, which either enhance the projection speed or reduce the number of projected patterns. However, there are very few studies on how these techniques affect the accuracy of TPU and which TPU method is most accurate under the scenario of high-speed measurement. This paper compares the accuracy of the two-frequency (TF), phase coding (PC), and gray code (GC) methods with different situations, including the traditional 8-bit focused FPP (aFPP), the high-speed binary defocused FPP (bFPP), and the geometry/continuity constrained binary defocused FPP (cFPP). We classify the phase unwrapping errors caused by system noises into uniformly and non-uniformly distributed errors, and analyze their distributions and rates in different TPU methods and different FPP systems. By comparative simulations and experiments, we find that, for low-frequency phase unwrapping, all the three TPU methods have a good result, while for high-frequency phase unwrapping which is desired in high-quality measurement, GC in aFPP and TF in cFPP provide higher accuracy. Thus, for measurement where accuracy is more concerned than the speed GC in aFPP is preferred, for dynamic measurement where extreme high speed is required, TF in cFPP is suggested.

Size prediction and garment customization are two main goals of body measurement for garment design. Traditional body measurement, involving manual measurement and trying clothes in person, is time-consuming and not cost-efficient. With the help of 3D body scanner and neural networks, body measurement can be fast and accurate, thus reducing the cost. This paper introduces neural network models to predict body sizes and the measurements used to customize clothes from various body data. Three kinds of input data are used: raw 3D point clouds of human bodies, key body locations, and estimated body measurements. Raw point clouds are collected by scanning the participants' body, and key body locations and estimated measurements are automatically computed by existing software based on the point clouds. Then the manual measurement is applied to the participants to obtain the size labels and useful measurements for garment customization, which are used as the ground-truth values of output data. Different network structures are utilized for different kinds of input data. The results show that neural networks can achieve decent performance in predicting measurements for making clothes. While the results of the three models are comparable, the feed-forward network model with estimated measurements achieves the best result in numerical measurement prediction. In terms of size label prediction, the models using estimated measurements achieve similar results, while the CNN model with key body locations and the simplified PointNet model applied on raw point clouds are unable to achieve high accuracy. The initial attempts show the potential of using networks for body measurement. The models can be further improved with a larger amount of data, in order to make it production-ready.

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

Precision optics have been widely required in many advanced technological applications. X-ray mirrors, as an example, serve as the key optical components at synchrotron radiation and free electron laser facilities. They are rectangular silicon or glass substrates where a rectangular Clear Aperture (CA) needs to be polished to sub-nanometer Root Mean Squared (RMS) to keep the imaging capability of the incoming X-ray wavefront at the diffraction limit. The convolutional polishing model requires a CA to be extended with extra data, from which the dwell time is calculated via deconvolution. However, since deconvolution is very sensitive to boundary errors and noise, the existing surface extension methods can hardly fulfill the sub-nanometer requirement. On one hand, the figure errors in a CA were improperly modeled during the extension, leading to continuity issues along the boundary. On the other hand, uncorrectable high-frequency errors and noise were also extended. In this study, we propose a novel Robust Iterative Surface Extension (RISE) method that resolves these problems with a data fitting strategy. RISE models the figure errors in a CA with orthogonal polynomials and ensures that only correctable errors are fit and extended. Combined with boundary conditions, an iterative refinement of dwell time is then proposed to compensate the errors brought by the extension and deconvolution, which drastically reduces the estimated figure error residuals in a CA while the increase of total dwell time is negligible. To our best knowledge, RISE is the first data fitting-based surface extension method and is the first to optimize dwell time based on iterative extension. An experimental verification of RISE is given by fabricating two elliptic cylinders (10 mm × 80 mm CAs) starting from a sphere with a radius of curvature around 173 m using ion beam figuring. The figure errors in the two CAs greatly improved from 204.96 nm RMS and 190.28 nm RMS to 0.62 nm RMS and 0.71 nm RMS, respectively, which proves that RISE is an effective method for sub-nanometer level X-ray mirror fabrication.

Speckle projection profilometry (SPP), which establishes the global correspondences between stereo images by projecting only a single speckle pattern, has the advantage of single-shot 3D reconstruction. Nevertheless, SPP suffers from the low matching accuracy of traditional stereo matching algorithms, which fundamentally limits its 3D measurement accuracy. In this work, we propose a single-shot 3D shape measurement method using an end-to-end stereo matching network for SPP. To build a high-quality SPP dataset for training the network, by combining phase-shifting profilometry (PSP) and temporal phase unwrapping techniques, high-precision absolute phase maps can be obtained to generate accurate and dense disparity maps with high completeness as the ground truth by phase matching. For the architecture of the network, a multi-scale residual subnetwork is first leveraged to synchronously extract compact feature tensors with 1/4 resolution from speckle images for constructing the 4D cost volume. Considering that the cost filtering based on 3D convolution is computationally costly, a lightweight 3D U-net network is proposed to implement efficient 4D cost aggregation. In addition, because the disparity maps in the SPP dataset should have valid values only in the foreground, a simple and fast saliency detection network is integrated to avoid predicting the invalid pixels in the occlusions and background regions, thereby implicitly enhancing the matching accuracy for valid pixels. Experiment results demonstrated that the proposed method improves the matching accuracy by about 50% significantly compared with traditional stereo matching methods. Consequently, our method achieves fast and absolute 3D shape measurement with an accuracy of about 100µm through a single speckle pattern.

Phase-extraction is important in various fields of optical metrology, for which, many phase-shifting algorithms have been developed. Among them, the advanced iterative algorithm (AIA) can accurately extract phase from fringe patterns with random unknown phase-shifts by iteratively estimating the phase and phase-shifts. However, these iterations make the AIA much slower than traditional phase-shifting algorithms. This problem is severer when both the pixel number and the frame number are large for high resolution and accuracy, restricting AIA’s wide application. In this paper, based on the detailed analysis of the algorithm’s structure, a fully parallelized GPU-based AIA (gAIA) is proposed for the first time. Without scarifying the phase extraction accuracy, the gAIA achieves 500 × speedup comparing with the sequential implementation on a single-core-CPU, and 10 × speedup comparing with the state-of-the-art partial GPU implementation which has a potential convergence issue. Also, for the first time, the real-time phase extraction with AIA is achieved by using a normal NVIDIA RTX 2080 Ti GPU, i.e., the proposed gAIA only takes 26.55 ms to extract phase from 13 frames of fringe patterns with 2048 × 2048 pixels per frame. Finally, through the implementation and testing of the gAIA, it is discovered that increasing the frame number has little effect on the speed performance, which is against our intuition. As a consequence, more frames can be used for gAIA to increase the phase extraction accuracy with little influence on the speed.

The effectiveness of the renowned empirical mode decomposition (EMD) is affected by the mode-mixing problem (MMP) if a signal contains intermittent modes. The ensemble EMD (EEMD) and several modified and extended algorithms solve this problem by adding random white noises. However, the necessary large size of the ensemble and the inevitable manual intervention limits the application of EEMD. In this letter, a novel regenerated phase-shifted sinusoid-assisted EMD (RPSEMD) is proposed. Sinusoids with different scales are iteratively generated and added to cope with all possible MMPs in different intrinsic modes (IMs), where each sinusoid is designed adaptively and automatically. Furthermore, the sinusoids are shifted for better retaining the details of each IM and eliminating the added sinusoids. In the comparison experiments, the RPSEMD provides more reasonable results with less computation time. Accepted Version

The transport of intensity equation (TIE) is an ideal candidate for phase imaging with partially coherent illuminations. TIE has the advantages of simplicity in phase calculation due to its closed-form solution and no requirement for a reference beam and phase unwrapping due to its non-interferometric nature. However, TIE requires multiple through-focus intensity images, and is very sensitive to image boundaries and noise. Thus, in this paper, we combine deep learning with TIE, abbreviated as dTIE. After being trained by TIE phase results, the dTIE retains the advantages of TIE, and overcomes the shortcomings of TIE as follows: (i) only one de-focus intensity image is required for phase imaging while the result is very close to the TIE result with SSIM index reaches 0.95, enabling more efficient phase imaging; (ii) the boundary problem automatically disappears due to the translation invariance of the convolutional networks; (iii) it is insensitive to noise even with very heavy noise. All these enhancements are verified in the application of dTIE for phase imaging of real cells.

Although the 3D-DIC method has matured both theoretically and technically, the 2D-DIC method still plays an important role in in-plane deformation measurements. However, the accuracy of 2D-DIC is affected by out-of-plane motion (including out-of-plane translation and out-of-plane rotation) and non-perpendicular alignment. To tackle this problem, we propose to directly measure these unfavorable error sources by cross-shaped structured light (CSSL) and the optical triangulation method. Subsequently, pseudo-strains are calculated and compensated using an integrated mathematical model developed in this paper. To avoid mutual interference between the structured light strips and the speckle image, color coding is also proposed to use different color information for 2D-DIC processing and error compensation. Experiments with controlled out-of-the-plane motions show that the mean error after compensation can be as small as 50με. Uniaxial tension tests were also conducted to verify the feasibility of the proposed method in the real material parameter estimation experiment. This work was supported by the China Scholarship Council (grant nos. 201906340036).

We present an erratum and generalization to our Letter [Opt. Lett. 45, 3115 (2020)OPLEDP0146-959210.1364/OL.392102]. This erratum corrects an error in Eq. (12), and the generalization converts R h to k h for more general situations of wavelengths. Neither has any influence on the conclusions of the original Letter.

Two-wavelength fringe projection profilometry (FPP) unwraps a phase with the unambiguous phase range (UPR) of the least common multiple (LCM) of the two wavelengths. It is accurate, convenient, and robust, and thus plays an important role in shape measurement. However, when two non-coprime wavelengths are used, only a small UPR can be generated, and the unwrapping performance is compromised. In this Letter, a spatial pattern-shifting method (SPSM) is proposed to generate the maximum UPR (i.e., the product of the two wavelengths) from two non-coprime wavelengths. For the first time, to the best of our knowledge, the SPSM breaks the constraint of wavelength selection and enables a complete (i.e., either coprime or non-coprime) two-wavelength FPP. The SPSM, on the other hand, only requires spatially shift of the low-frequency pattern with the designed amounts and accordingly adjusting the fringe order determination, which is extremely convenient in implementation. Both numerical and experimental analyses verify its flexibility and correctness.

Binary defocusing technique has been widely used in fringe projection profilometry for high-speed measurement. This technique projects designed binary patterns with a defocused projector to generate fringes for wrapped phase calculation, and n-ary simple codes (nSC) or n-ary gray codes (nGC) for phase unwrapping. The unwrapped phase reflecting the object surface profile is calculated by a phase-shifting algorithm with nSC/nGC phase unwrapping. However, it remains unclear which phase unwrapping method, nSC or nGC, is more appropriate for high-accuracy and high-speed measurement. This paper comprehensively compares nSC and nGC with the consideration of various factors, including the strategies for error removal, the base n, the step heights and invalid regions on the measured objects, defocusing level and noise level of the system. From simulations and experiments, we conclude that, (i) in general, nSC with a proposed identification and binary classification (IBC) method has a similar result as nGC; (ii) when accuracy is critical, binary simple code (nSC with n = 2) and binary gray code (nGC with n = 2) methods are recommended; (iii) when speed is critical, quaternary simple code (nSC with n = 4) method with continuity/geometry constraints is recommended.

Phase-shifting profilometry (PSP) has been widely used in three-dimensional (3-D) shape measurement because of its attributes of high-accuracy and high-resolution. However, PSP typically works under fluorescent light, flickering with a double frequency of the alternating current frequency, which may generate a non-ignorable phase error, and result in a PSP's measurement error, especially for PSP using a high sampling speed. We first mathematically describe the fluorescent light problem, model the PSP's phase error, and state the problem in high-speed PSP. Next, a fluorescent light error suppression (FLES) algorithm is proposed to suppress the phase error. Both the phase error model and the proposed algorithm are theoretically analyzed, and then numerically and experimentally verified. The provided numerical and experimental results coincide with the theoretical analysis. The proposed algorithm can reduce the phase error from 0.12 rad to a comparable level with system noise of 0.02 rad, which is significant for the accurate measurement of 3-D shapes for high-speed PSP in a fluorescent light environment.

We propose a wrapped phase denoising method based on convolutional neural networks (CNN), which can effectively denoise a noisy wrapped phase. The noisy numerator and denominator of the arctangent function are firstly denoised by CNN, and then the filtered numerator and denominator use the arctangent function to obtain the clean wrapped phase. We experimentally verify the denoising performance using various wrapped phase that contains different noise conditions, where the denoised wrapped phase can achieve a satisfactory unwrapping performance using the existing simple unwrapping method. In addition, the proposed method is further demonstrated through the comparison of the existing methods, and shows an accurate denoising result without adjusting any parameters.

Phase-shifting techniques are extremely important in modern optical metrology. The advanced iterative algorithm (AIA) is an elegant, flexible and effective phase-shifting algorithm that can extract phase from fringe patterns with arbitrary unknown phase-shifts. However, comparing it with traditional phase-shifting algorithms, AIA has not been sufficiently investigated on (i) its applicability to different types of fringe patterns; (ii) its performance with respect to different phase-shifts, frame numbers and noise levels and thus the possibility of further improvement; and (iii) the predictability of its accuracy. To solve these problems, a series of innovations are proposed in this paper. First, condition numbers are introduced to characterize the least squares matrices used in AIA, and subsequently a fringe density requirement is suggested for the success of AIA. Second, the performance of AIA regarding different phase-shifts, frame numbers and noise levels is thoroughly evaluated by simulations, based on which, an overall phase error model is established. With such understanding, three individual improvements of AIA, i.e., controlling phase-shifts, controlling frame numbers and suppressing noise, are proposed for better performance of AIA. Third, practical methods for estimating the overall phase errors are developed to make the AIA performance predictable even before AIA is executed. We then integrate all these three innovations into an enhanced AIA (eAIA), which solves all the problems we mentioned earlier. The significant contributions of eAIA include the insurability of the convergence, the controllability of the performance, and achievability of a desired accuracy. An experiment is carried out to demonstrate the effectiveness of eAIA. Economic Development Board (EDB) Published version Economic Development Board - Singapore (S17-1579-IPP-II).

Accurately extracting phase or phase derivative is the most important requirement in optical metrology. However, in practice, there are many error sources, among which nonlinear distortion in fringe patterns is often encountered. Several techniques have been proposed over time to remove the nonlinearity error. Among these techniques, the windowed Fourier ridges (WFR) algorithm has been shown to be an effective solution insensitive to nonlinearity, but it lacks a theoretical justification. In this paper, we theoretically analyze the local frequency estimation error and phase extraction error, which not only proves the mentioned insensitivity, but also supports the performance prediction and error control, and thus is very important and useful in optical measurement. The theoretical results have been verified by computer simulations. Other error sources such as model error and noise are also compared and discussed.

This paper presents a technique for real-time texture-less object recognition and tracking on mobile devices. Our proposed algorithm is an even lighter-weight version of the recent state-of-the-art binary-based texture-less object detector BIND (Binary Integrated Net Descriptor), primarily customized for mobile device applications. This modification, termed BIND-Lite, employs various techniques to overcome the low-computational power of current mobile devices, while mostly retaining the texture-less object detection robustness of the original BIND. On current generation mobile devices, BIND-Lite was able to achieve runtime rates of up to 30 frames per second. To evaluate our algorithm, we have also designed a mobile augmented reality application coined IMPRINT, which renders logos/images onto detected objects to showcase BIND-Lite in a real-time mobile augmented reality setting.

This paper presents some of the most widely accredited techniques used in the texture-less object recognition field. We analyze these works to study their methodologies to solving the texture-less problem, while introducing our own state-of-the-art solutions in this genre.

Due to their advantages of non-destructiveness, high accuracy, and high sensitivity, optical measurement techniques have been successfully applied to measure various important physical quantities in experimental mechanics, materials science, biomechanics, etc. In order to deal with increasingly larger amounts of data and increase accuracy, the computational burden of optical measurement techniques has become heavier. In the past decade, parallel computing devices have been applied to accelerate these techniques, among which graphics processing units (GPUs) have become mainstream due to their high parallelism, cost effectiveness, short development cycle, and transparent scalability. Additionally, compute unified device architecture (CUDA), invented by NVIDIA, provides an easy-to-use C/C++ programming interface, which has opened the possibility to program GPUs without having to learn complex shading languages and the graphics pipeline. This Spotlight not only demonstrates the power of GPUs in accelerating optical measurement algorithms but also provides a hands-on approach for the acceleration of existing sequential algorithms on CUDA-capable GPUs. Readers who understand basic C/C++ programming can then attempt to integrate CUDA with their existing optical algorithms for higher computing performance.

A sub-voxel digital volume correlation (DVC) method combining the 3D inverse compositional Gauss-Newton (ICGN) algorithm with the 3D fast Fourier transform-based cross correlation (FFT-CC) algorithm is proposed to eliminate path-dependence in current iterative DVC methods caused by the initial guess transfer scheme. The proposed path-independent DVC method is implemented on NVIDIA compute unified device architecture (CUDA) for GPU devices. Powered by parallel computing technology, the proposed DVC method achieves a significant improvement in computation speed on a common desktop computer equipped with a low-end graphics card containing 1536 CUDA cores, i.e., up to 23.3 times faster than the sequential implementation and 3.7 times faster than the multithreaded implementation of the same DVC method running on a 6-core CPU. This speedup, which has no compromise with resolution, accuracy and precision, benefits from the coarse-grained parallelism that the points of interest (POIs) are processed simultaneously and also from the fine-grained parallelism that the calculation at each POI is performed with multiple threads in GPU. The experimental study demonstrates the superiority of the GPU-based parallel computing for acceleration of DVC over the multi-core CPU-based one, in particular on a PC level computer.

A sub-pixel digital image correlation (DIC) method with a path-independent displacement tracking strategy has been implemented on NVIDIA compute unified device architecture (CUDA) for graphics processing unit (GPU) devices. Powered by parallel computing technology, this parallel DIC (paDIC) method, combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm for integer-pixel initial guess estimation, achieves a superior computation efficiency over the DIC method purely running on CPU. In the experiments using simulated and real speckle images, the paDIC reaches a computation speed of 1.66×105 POI/s (points of interest per second) and 1.13×105 POI/s respectively, 57–76 times faster than its sequential counterpart, without the sacrifice of accuracy and precision. To the best of our knowledge, it is the fastest computation speed of a sub-pixel DIC method reported heretofore.

The applications of windowed Fourier fringe analysis in the past decade are reviewed. Because fringe patterns from different optical measurement systems are similar, the reviewed applications are classified according to the functions of the windowed Fourier transform being used in fringe pattern analysis: denosing exponential phase fields, demodulating carrier fringe patterns, getting phase derivatives, and utilizing local properties. From these applications, the windowed Fourier transform is shown to be effective and versatile for fringe pattern analysis.

The initial guess transferring mechanism is widely used in iterative DIC algorithms and leads to path-dependence. Using the known deformation at a processed point to estimate the initial guess at its neighboring points could save considerable computation time, and a cogitatively-selected processing path contributes to the improved robustness. In this work, our experimental study demonstrates that a path-independent DIC method is capable to achieve high accuracy, efficiency and robustness in full-field measurement of deformation, by combining an inverse compositional Gauss–Newton (IC-GN) algorithm for sub-pixel registration with a fast Fourier transform-based cross correlation (FFT-CC) algorithm to estimate the initial guess. In the proposed DIC method, the determination of initial guess accelerated by well developed software library can be a negligible burden of computation. The path-independence also endows the DIC method with the ability to handle the images containing large discontinuity of deformation without manual intervention. Furthermore, the possible performance of the proposed path-independent DIC method on parallel computing device is estimated, which shows the feasibility of the development of real-time DIC with high-accuracy. ASTAR (Agency for Sci., Tech. and Research, S’pore) Accepted version

This paper presents BIND (Binary Integrated Net Descriptor), a texture-less object detector that encodes multi-layered binary-represented nets for high precision edge-based description. Our proposed concept aligns layers of object-sized patches (nets) onto highly fragmented occlusion resistant line-segment midpoints (linelets) to encode regional information into efficient binary strings. These lightweight nets encourage discriminative object description through their high-spatial resolution, enabling highly precise encoding of the objects edges and internal texture-less information. BIND achieved various invariant properties such as rotation, scale and edge-polarity through its unique binary logical-operated encoding and matching techniques, while performing remarkably well in occlusion and clutter. Apart from yielding efficient computational performance, BIND also attained remarkable recognition rates surpassing recent state-of-the-art texture-less object detectors such as BORDER, BOLD and LINE2D.

In this work, a visible light positioning (VLP) system using an image sensor (a smartphone camera) as the receiver is considered. We focus our research on the system acquisition time and success rate, both of which are largely determined by the employed positioning algorithm. To speed up the positioning process and enhance its robustness, we derive a close-form expression to determine the receiver's position and orientation using the singular value decomposition (SVD) technique, and a new SVD-based positioning algorithm is proposed accordingly. Simulation results prove that the proposed SVD-based positioning algorithm is 50–80 times faster than the conventional iterative Levenberg-Marquardt (LM) based algorithm and avoids possible failures caused by bad initial guesses.

Phase-shifting profilometry using binary patterns with projector defocusing has been widely used for high-speed 3D measurement. Recently, a ternary Gray-code based phase unwrapping method has been proposed, which enables to accurately unwrap the phase but reduces the required binary patterns. This paper presents a comparison between the ternary and the traditional binary Gray code-based phase unwrapping methods. NRF (Natl Research Foundation, S’pore) Published version

Phase-shifting profilometry combined with Gray-code patterns projection has been widely used for 3D measurement. In this technique, a phase-shifting algorithm is used to calculate the wrapped phase, and a set of Gray-code binary patterns is used to determine the unwrapped phase. In the real measurement, the captured Gray-code patterns are no longer binary, resulting in phase unwrapping errors at a large number of erroneous pixels. Although this problem has been attended and well resolved by a few methods, it remains challenging when a measured object has step-heights and the captured patterns contain invalid pixels. To effectively remove unwrapping errors and simultaneously preserve step-heights, in this paper, an effective method using an adaptive median filter is proposed. Both simulations and experiments can demonstrate its effectiveness.

Optical interferometric techniques offer non-contact, high accuracy and full filed measurement, which are very attractive in various research and application fields. Fringe patterns are the recorded results of these techniques and often require denoising at the pre-processing step to increase the accuracy and robustness of information retrieval. Among various fringe pattern denoising techniques, iterative and oriented denoising techniques based on partial differential equations in the spatial domain are effective and widely used. However, these techniques introduce errors near boundary areas if traditional image padding methods such as zero padding and symmetric padding are used. Due to a large number of iterations needed in these techniques, the error will flood from the boundary into the inner part of the fringe pattern. Since fringe patterns have a flow-like structure represented by fringe orientation, padding along the fringe orientation helps to reduce the error. An oriented padding method is thus proposed for iterative and oriented fringe pattern denoising techniques that require partial derivative estimations. Simulated fringe patterns are tested and quantitative results are given to demonstrate the performance of the proposed method. Experimental results are also given for verification.

In this Letter, for the first time, to the best of our knowledge, we propose a digital holographic reconstruction method with a one-to-two deep learning framework (Y-Net). Perfectly fitting the holographic reconstruction process, the Y-Net can simultaneously reconstruct intensity and phase information from a single digital hologram. As a result, this compact network with reduced parameters brings higher performance than typical network variants. The experimental results of the mouse phagocytes demonstrate the advantages of the proposed Y-Net.

We recently presented a method for dynamic phase retrieval in temporal speckle pattern interferometry using least squares method and windowed Fourier filtering. In this paper, we extend this method to dynamic 3D profiling with fringe projection as a novel alternative. The phase distributions of distorted fringe patterns are sequentially retrieved and automatically unwrapped. Since only one fringe pattern is required to reconstruct a profile at a time, the method is particularly suitable for dynamic measurement. Simulation and experimental examples are presented to validate the method.

Phase shifting profilometry (PSP) using binary fringe patterns with projector defocusing is promising for high-speed 3D shape measurement. To obtain a high-quality phase, the projector usually requires a high defocusing level, which leads to a drastic fall in fringe contrast. Due to its convenience and high speed, PSP using squared binary patterns with small phase shifting algorithms and slight defocusing is highly desirable. In this paper, the phase accuracies of the classical phase shifting algorithms are analyzed theoretically, and then compared using both simulation and experiment. We also adapt two algorithms for PSP using squared binary patterns, which include a Hilbert three-step PSP and a double three-step PSP. Both algorithms can increase phase accuracy, with the latter featuring additional invalid point detection. The adapted algorithms are also compared with the classical algorithms. Based on our analysis and comparison results, proper algorithm selection can be easily made according to the practical requirement.

This paper presents an algorithm coined BORDER (Bounding Oriented-Rectangle Descriptors for Enclosed Regions) for texture-less object recognition. By fusing a regional object encompassment concept with descriptor-based pipelines, we extend local-patches into scalable object-sized oriented rectangles for optimal object information encapsulation with minimal outliers. We correspondingly introduce a modified line-segment detection technique termed Linelets to stabilize keypoint repeatability in homogenous conditions. In addition, a unique sampling technique facilitates the incorporation of robust angle primitives to produce discriminative rotation-invariant descriptors. BORDER's high competence in object recognition particularly excels in homogenous conditions obtaining superior detection rates in the presence of high-clutter, occlusion and scale-rotation changes when compared with modern state-of-the-art texture-less object detectors such as BOLD and LINE2D on public texture-less object databases.

Capacitive touch technology is used in almost all electronic devices with a user interface these days. Improved resolution and better responsiveness is always sought after in industry. The standard sampling method for electrodes on a capacitive touch panel comprises of measuring charge at every single electrode one by one which causes latency if the screen size is big. Compressive sensing has recently been proposed as an alternative sampling technique for capacitive touch panels [1]. However the proposed methods do not take into account the characteristics of capacitive touch signals. By utilising the unique block sparse nature of capacitive touch signals, an accurate and efficient greedy algorithm based on the existing block sparse greedy algorithms is proposed for recovering position of finger on a capacitive touch panel. High accuracy and efficiency are demonstrated through numerical simulations and compared with other notable block-based algorithms.

With advantages such as non-destructiveness, high sensitivity and high accuracy, optical techniques have successfully integrated into various important physical quantities in experimental mechanics (EM) and optical measurement (OM). However, in pursuit of higher image resolutions for higher accuracy, the computation burden of optical techniques has become much heavier. Therefore, in recent years, heterogeneous platforms composing of hardware such as CPUs and GPUs, have been widely employed to accelerate these techniques due to their cost-effectiveness, short development cycle, easy portability, and high scalability. In this paper, we analyze various works by first illustrating their different architectures, followed by introducing their various parallel patterns for high speed computation. Next, we review the effects of CPU and GPU parallel computing specifically in EM & OM applications in a broad scope, which include digital image/volume correlation, fringe pattern analysis, tomography, hyperspectral imaging, computer-generated holograms, and integral imaging. In our survey, we have found that high parallelism can always be exploited in such applications for the development of high-performance systems.

Phase demodulation from a single fringe pattern is a challenging task but of interest. A quadratic phase matching and frequency-guided regularized phase tracker (QFGRPT) and a quadratic phase matching and frequency-guided sequential demodulation (QFSD) for demodulation of a single fringe pattern are proposed. The algorithms are characterized by their improvements on both robustness and accuracy, which are realized by quadratic phase matching and frequency guided scanning strategy, respectively. Quadratic phase matching improves accuracy compared with the existing regularized phase tracker techniques and the frequency-guided sequential demodulation technique using linear phase matching. Frequency guidance ensures high robustness compared with the recently published path-independent regularized phase-tracking technique. Demodulation results from computer-simulated and experimental fringe patterns using the proposed methods are demonstrated and analyzed.

Extracting phase distribution from arbitrary phase-shifted fringe patterns, if possible, is very useful in phase-shifting interferometry. The advanced iterative algorithm (AIA) is introduced and the windowed Fourier ridges and least squares fitting (WFRLSF) is proposed. Both algorithms are sensitive to noise, which limits their applications to almost perfect fringe patterns. The windowed Fourier filtering (WFF) algorithm is proposed for both pre-filtering and post-filtering to suppress the noise. Simulation results show that with the effective noise suppression, the phase error is reduced to less than 0.1 rad. Experimental examples are also given for verification. The almost identical results produced by the AIA and the WFRLSF suggest that both algorithms can be used for phase extraction with cross-validation.