Fringe Pattern Research Articles

Optimized dithering approach for 3D shape measurement using a phase-based chaos genetic algorithm.

A binary defocusing method has a significant impact on improving 3D shape measurement quality for digital fringe projector (DFP) techniques. In this paper, an optimization framework using the dithering method is presented. This framework utilizes genetic algorithm and chaos maps to optimize the bidirectional error-diffusion coefficients. It can effectively avoid quantization errors of binary patterns in a specific direction and obtain the fringe patterns with better symmetry and higher quality. In the process of the optimization, chaos initialization algorithms are used to generate a series of bidirectional error-diffusion coefficients as initial individuals. Additionally, mutation factors generated by chaotic maps, compared with the mutation rate, determine whether the individual position will mutate. Both simulations and experiments demonstrate that the proposed algorithm can improve the quality of phase and reconstruction at different defocus levels.

High-flexibility and high-accuracy phase delay calibration method for MEMS-based fringe projection systems.

Microelectromechanical system (MEMS) mirror based laser beam scanning (LBS) projectors for fringe projection profilometry (FPP) are becoming increasingly popular attributing to their small size and low cost. However, the initial phase of the scanning MEMS mirror employed in an LBS projector may vary over time, resulting in unstable and distorted fringe patterns. The distorted fringe patterns will largely decrease the accuracy of the three-dimensional (3D) topographic reconstruction. In this paper, an efficient phase delay calibration method based on a unique fringe projection sequence and a corresponding image processing algorithm is proposed. The proposed method can compensate the phase uncertainty and variation with no need to add any extra components. One LBS projector has been constructed using a uniaxial electrostatic MEMS mirror that has a mirror size of 2.5 mm × 2.5 mm and a scanning field of view of 60 ∘ at its resonance of 1523 Hz. 3D reconstruction experiments are conducted to study how the 3D reconstruction results are affected by the phase delay. The standard deviation of a sphere reconstruction is improved from 2.05 mm to 0.20 mm after the positive phase delay deviation of 5 μs is compensated using this new calibration method.

Channel transformer U-Net: an automatic and effective skeleton extraction network for electronic speckle pattern interferometry.

The fringe skeleton extraction method may be the most straightforward method for electronic speckle pattern interferometry (ESPI) phase extraction. Due to ESPI fringe patterns having the characteristics of high noise, low contrast, and different fringe shapes, it is very difficult to extract skeletons from ESPI fringe patterns with high accuracy. To deal with this problem, we propose a skeleton extraction method based on deep learning, called channel transformer U-Net, for directly extracting skeletons from noisy ESPI fringe patterns. In the proposed method, the advanced channel-wise cross fusion transformer module is integrated into the design of deep U-Net architecture, and a loss function by combining binary cross entropy loss and poly focal loss is proposed. In addition, a marking algorithm is proposed for phase extraction, which can realize automatic identification of a skeleton line. The effectiveness of the above proposed algorithms has been verified by computer-simulated and real-dynamic ESPI measurements. The experimental results demonstrate that the proposed channel transformer U-Net can obtain accurate, complete, and smooth skeletons in all cases. The accuracy of the skeleton extraction obtained by our proposed network can reach 0.9878, and the correlation coefficient value can reach 0.9905. The skeleton line automatic marking algorithm has strong universality.

Fast fringe projection profilometry using 3 + 1 phase retrieval strategy and fringe order correction.

Fringe projection profilometry (FPP) has attracted wide attention in optical 3D measurement field for its high resolution, high accuracy, and simple system construction. However, the inherent requirements of FPP's measurement speed and accuracy are contradictory. We adopt a 3+1 phase retrieval strategy combining phase shift and the Hilbert transform algorithm to achieve high-speed, high-precision simultaneous measurements with only four binary fringe patterns. Furthermore, when using temporal phase unwrapping, fringe order errors (FOEs) are inevitable. Although these FOEs do not affect neighboring pixels, they are brought into the final point cloud coordinates by the absolute phase value. We propose a fringe order correction method to eliminate FOEs. The feasibility and effectiveness of this method are verified by the experimental results.

Influence of artificial notch length in composite material on damage indicator values

Novel experimental method, which provides visualization of interference fringe patterns caused by inserting of artificial notch of prefixed length in composite material, is developed. Deformation response to local material removing is measured by electronic speckle-pattern interferometry. Interferogram interpretation in terms of in-plane displacement components produces determination of two deformation parameters. These parameters represent current damage indicators, which are essential for quantitative description of damage accumulation inherent in fatigue loading of specimens with stress concentrators. Both damage indicators are derived on a base of direct physical measurements by fringe order counting. Analysis of uncertainties in damage indicators determination, which are connected with incorrect prescribing of artificial notch length, is presented. Keywords: composite materials, speckle-pattern interferometry, artificial notch, damage indicators.

Optical propagation of exciton polaritons in ultrathin van der Waals microcrystals down to few monolayers

The exciton polariton is a kind of quasiparticles and provides a promising opportunity to explore fundamental quantum phenomena for photonic applications. Transition-metal dichalcogenide (TMD) materials provide the platform of nanophotonics that supports the propagative exciton polaritons even at room-temperature. Previously, real space studies on thin flakes of TMDs by scattering-type scanning nearfield optical microscopy (s-SNOM) were limited to waveguide thickness down to 30 nm. In this work, we present the nano-optical imaging of ordinary transverse electric modes of exciton polaritons in MoS2 and WSe2 down to a few atomic layers, measured by atomic force microscope-based s-SNOM. Surprisingly, the interference fringe patterns can be observed clearly at the prepared ultrathin TMD flakes with thickness down to ~3 nm (4 ML) and ~8 nm (12 ML) for MoS2 and WSe2, respectively, which breaks greatly the previous measurement limitation. The wavevectors stay around 1.6k0−1.7k0 constantly when the thickness approaching to a few MLs, instead of 1k0 according to the theory. These modes are supported by the nearly-freestanding TMD microflakes in the form of three-layer symmetric waveguide to confine the exciton polaritons. Our results provide in-depth understanding and open new avenues to explore the polaritonic devices operating at the near infrared region based on ultrathin TMD materials.

Correction for a camera-projector 3D reconstruction system based on dithering fringe pattern

Correction for a camera-projector 3D reconstruction system based on dithering fringe pattern

Three-Dimensional Measurement Method for High Dynamic Range Surfaces Based on Adaptive Fringe Projection

As an optical measurement method, fringe projection three-dimensional (3D) measurement technology will have poor measurement effect due to overexposure or too dark of the fringes when measuring high dynamic range (HDR) surfaces. The adaptive fringe projection method is one of the effective methods to solve the HDR surfaces measurement, but pixel matching is the difficulty. The existing matching methods generally use phase for matching, which requires at least 24 additional patterns to be projected, seriously affecting the measurement efficiency. In order to solve these problems, an adaptive fringe projection measurement method using speckle pattern for pixel matching is proposed in this paper. First, two grayscale patterns are projected to calculate the adaptive projection intensity. Then a speckle pattern is projected to match the pixels of the captured pattern and the projected pattern. Finally, the adaptive fringe patterns are generated. Better than the methods before, only three additional patterns are needed to be projected to realize the measurement of the HDR surfaces. The experimental results show that the proposed method can reduce the number of projected patterns by more than 59.5% while achieving similar measurement accuracy, which greatly improves the measurement efficiency.

Влияние длины искусственного надреза в композиционном материале на величины индикаторов повреждаемости

Novel experimental method, which provides visualization of interference fringe patterns caused by inserting of artificial notch of prefixed length in composite material, is developed. Deformation response to local material removing is measured by electronic speckle-pattern interferometry. Interferogram interpretation in terms of in-plane displacement components produces determination of two deformation parameters. These parameters represent current damage indicators, which are essential for quantitative description of damage accumulation inherent in fatigue loading of specimens with stress concentrators. Both damage indicators are derived on a base of direct physical measurements by fringe order counting. Analysis of uncertainties in damage indicators determination, which are connected with incorrect prescribing of artificial notch length, is presented.

Deep learning enabled single-shot absolute phase recovery in high-speed composite fringe pattern profilometry of separated objects

Deep learning enabled single-shot absolute phase recovery in high-speed composite fringe pattern profilometry of separated objects

Pixel-Wise Phase Unwrapping With Adaptive Reference Phase Estimation for 3-D Shape Measurement

Phase unwrapping plays an important role in phase-based three-dimensional (3D) shape measurement. This paper proposes an effective pixel-wise phase unwrapping method without requiring additional fringe patterns. Firstly, compared with the geometric constraint-based (GCB) method which needs calibrate the fringe projection system and create a reference phase at the closest plane <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> within the measurement volume, the proposed method can adaptively and directly estimate the reference phase from the wrapped phase without system calibration and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> estimation. Secondly, based on the finding that the slope angle of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z_min</i> plane ignored by the GCB method has significant impact on the measurement range, thus the phase gradients that highly correlates with the optimal slope angle are involved into reference phase estimation. The wrapped phase can be pixel-by-pixel unwrapped by comparing with the reference phase. Both simulations and experiments have been conducted to demonstrate the efficiency of the proposed method. Compared with traditional two-frequency method and phase-coding method, the proposed method can improve the measuring speed by 2 times. Experiment results show that the proposed method can effectively remove the phase unwrapping errors and achieve the mean absolute phase error of 0.0137 rad, which has obvious advantages relative to traditional methods.

In-situ evaluation of interference fringe patterns to be generated by interference lithography

In-situ evaluation of interference fringe patterns to be generated by interference lithography

High-Dynamic-Range 3-D Shape Measurement With Adaptive Speckle Projection Through Segmentation-Based Mapping

The 3-D shape measurement of high-dynamic-range (HDR) scenes based on structured light projection is challenging because the conventional projection without considering the reflection distribution of the tested surface usually causes over-exposure and over-dark areas simultaneously in the captured images, which will lead to the failure or low accuracy of 3-D reconstruction. In this article, we propose a novel HDR 3-D surface measurement method based on adaptive speckle projection with fully considering the reflection distribution. An efficient segmentation-based mapping strategy is established to speed up the generation of adaptive speckle patterns, which segments the estimated mask with optimal projection intensity into multiple subregions by the eight-connected standard to raise mapping accuracy and project gray-coded and sinusoidal fringe patterns to build the pixelwise mapping relationship between binocular cameras and the projector for each subregion, respectively. Then the pixelwise intensity of projected speckle patterns can be accurately adjusted according to optimal intensity. The generated adaptive speckle pattern is used to scan the tested object, and high signal-to-noise-ratio (SNR) speckle images can be obtained for accurate and complete 3-D measurement. Experimental results verify that the point cloud produced by our method has obvious advantages compared with the traditional methods in terms of measurement accuracy, whose coverage is as large as 92.26% and the average distance (AD) relative to ground truth (GT) is as low as 0.128 mm. Meanwhile, the number of projected patterns for mapping is decreased by a third compared with the widely used mapping strategy.

Fringe Pattern Orthogonalization Method by Generative Adversarial Nets

Fringe Pattern Orthogonalization Method by Generative Adversarial Nets

Three-dimensional reconstruction of moving HDR object based on PSP

High quality 3D reconstruction of HDR object can be achieved by projecting extra fringe patterns with different intensity. However, it requires the object to be kept static. The object motion not only introduces phase shift among the fringe patterns, but also changes the position of the overexposure pixels. This paper proposes a new method to reconstruct the moving HDR object by utilizing the features of motion. For the specific point on the object, overexposure will not happen among all the fringe patterns as the overexposure position is changed with the motion. The unsaturation fringe patterns are selected from the captured fringe patterns and the correct phase information is retrieved based on unequal phase shift algorithm. The effectiveness of the proposed algorithm is verified by the experiments.

A rapid and accurate gamma compensation method based on double response curve fitting for high-quality fringe pattern generation

The gamma effect of structured light illumination devices and camera will yield undesired nonlinear phase errors both in fringe projection system and fringe reflection system. The existing nonlinear correction methods can be classified into two categories: actively modifying the fringe patterns before their projection, or passively compensating the phase error after the fringe patterns are captured. The former needs to capture lots of fringe patterns in advance, while the latter occupies measurement time. In this paper, a rapid and robust active gamma compensation method based on double response curve fitting is proposed for the first time. In the proposed method, the appropriate pre-coding gamma value is determined jointly by the two constructed response curves, so the correction results will not get worse when the number of projected grayscale images decreases and no more than 4 frames of grayscale images are required. Experimental results verified that this method is fast, accurate and easy to implement. With the proposed technique, high-accuracy measurement can be achieved with the conventional 3-step phase-shifting algorithm.

Identification of defects in composite laminates by comparison of mode shapes from electronic speckle pattern interferometry

A novel technique for identifying defects in carbon fibre reinforced plates has been developed. Firstly, modal analysis by impact excitation was performed to obtain the first five resonant frequencies for three defect-free and three defective specimens with in-plane fibre waviness. Then amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) was used to obtain the mode shapes at these frequencies. The contours of the nodal regions visible in the mode shapes were extracted using a specially-developed algorithm employing density-based spatial clustering of applications with noise (DBSCAN). Fourier descriptors, that are invariant to rotations, translations, and scaling, were used to decompose the contours to reduce data dimensionality and make comparisons. The differences in contours between the two sets of specimens showed that the 4th and 5th mode shapes can be used for identifying the presence of the waviness defects. This technique for nodal region comparison was found to greatly simplify the comparison of fringe patterns for the purpose of damage assessment and could potentially be used as part of validation procedures.

Polynomial color compensation model with neural network solver for color-coded fringe patterns in phase-measuring deflectometry

The total image display/projection and image acquisition time in a projector-based phase-measuring deflectometry (PMD) measurement is reduced when color-coded fringe patterns are used since only a single image of the fringe pattern is sufficient to extract phase information using the phase-stepping method. This benefit is, however, offset by the difficulty in resolving various sources of color intensity errors of the fringe patterns in the camera view, such as uneven illumination, color imbalance, color crosstalk, and deviation of color intensity response of the camera and the projector from the calibrated color targets. Thus, a polynomial color compensation model is proposed in this study to compensate for color intensity errors. The model coefficients were estimated using the relationship between the captured and targeted color intensities, which are sequences of monochromatic 8-bit red, green, and blue (RGB) images for projection. The model was applied to modify the color intensities of the generated fringe patterns before projection. The modified color fringe patterns were then used for PMD measurement on spherical concave and convex mirrors. Based on the experimental results, the root-mean-squared (RMS) color intensity errors in R, G, and B channels were reduced by 33.3%, 58.3%, and 36.4%, respectively, after conducting the polynomial color compensation. The RMS phase errors in the fringe patterns were reduced by 71.9%. The RMS height errors and the radius percentage errors of the reconstructed concave and convex heightmaps were 1.87 μm (0.12%) and 1.55 μm (0.17%), respectively. The performance of the proposed polynomial color compensation model in reducing color intensity errors of the captured fringe patterns for accurate PMD measurement was demonstrated successfully.

Application of optimized 2D S-transform in digital speckle interferometry phase pattern denoising

To address the problem of a large amount of noise in the phase pattern in digital speckle pattern interferometry, which seriously affects the phase reconstruction and measurement precision, a filtering method based on optimized 2D S-transform is proposed in this paper. The optimized 2D S-transform provides high signal-to-noise ratio denoising method by adding tilt factors and translation factors to keep the Gaussian window of the appropriate size at different frequency positions. The analysis results of different frequency fringe pattern denoising show that the criteria metrics indicator signal-to-noise ratio (SNR) of the results of the proposed method can reach at least 14.5435 dB and the criteria metrics peak signal-to-noise ratio (PSNR) can reach at least 19.4555 dB, which has better precision compared with the traditional method and solves the incongruity between the smoothness of low-density fringe and the integrity of high-density fringe.

Adaptive horizontal scaling method for speckle-assisted fringe projection profilometry.

Phase-shifting method is widely used in fringe projection profilometry to obtain high-precision wrapped phase maps. The wrapped phase map needs to be converted to an absolute phase map to recover 3D information. The speckle pattern based phase unwrapping method requires only one additional auxiliary pattern, showing great potential for fast 3D measurements. In this paper, a speckle assisted four-steps phase-shifting method was proposed for 3D measurements. This method requires five structured light patterns to complete 3D measurements, including four-steps phase-shifting fringe patterns and a speckle pattern which is used to remove phase ambiguity. The main challenge of speckle based phase unwrapping method is to overcome the mismatch problem which often occurs in some very steep surfaces. In order to improve the speckle matching accuracy, an adaptive horizontal scaling method was proposed. A voting strategy based on phase-connected regions was proposed to reduce the computational overhead. The experiments demonstrate its superior performance, and an accuracy of 0.21 mm was achieved.