Electronic Speckle Pattern Interferometry Fringe Research Articles

Digital phase-shift method based on distance mapping for phase recovery of an ESPI fringe pattern.

In view of the limitation of the traditional method to recover the phase of the single fringe pattern, we propose a digital phase-shift method based on distance mapping for phase recovery of an electronic speckle pattern interferometry fringe pattern. First, the direction of each pixel point and the centerline of the dark fringe are extracted. Secondly, the normal curve of the fringe is calculated according to the fringe orientation to obtain the fringe moving direction. Thirdly, the distance between each pixel point and the next pixel point in the same phase is calculated by a distance mapping method according to the adjacent centerlines; then the moving distance of the fringes is obtained. Next, combining the moving direction and moving distance, the fringe pattern after the digital phase shift is obtained by full-field interpolation. Finally, the full-field phase corresponding to the original fringe pattern is recovered by four-step phase shifting. The method can extract the fringe phase from a single fringe pattern through digital image processing technology. The experiments show that the proposed method can effectively improve the phase recovery accuracy of a single fringe pattern.

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.

Application of attention-DnCNN for ESPI fringe patterns denoising

Fringe patterns' denoising in electronic speckle pattern interferometry (ESPI) is an important step in phase extraction. In this study, we propose a new denoising method for ESPI fringe patterns based on a convolutional neural network (CNN). The proposed model which combines the attention mechanism and CNN is defined as attention-denoising CNN. In this model, owing to the attention mechanism, more attention will be paid to fringe information, and better filtering results will be achieved. The experimental results show that our proposed method can obtain excellent results, especially with high and large variation density ESPI fringe patterns.

Joint enhancement and denoising in electronic speckle pattern interferometry fringe patterns with low contrast or uneven illumination via an oriented variational Retinex model.

Simultaneous speckle reduction and contrast enhancement for electronic speckle pattern interferometry (ESPI) fringe patterns is a challenging task. In this paper, we propose a joint enhancement and denoising method based on the oriented variational Retinex model for ESPI fringe patterns with low contrast or uneven illumination. In our model, we use the structure prior to constrain the illumination and introduce a fractional-order differential to constrain the reflectance for enhancement, then use the second-order partial derivative of the reflectance as the denoising term to reduce noise. The proposed model is solved using the sequential method to obtain piecewise smoothed illumination and noise-suppressed reflectance sequentially, which avoids remaining noise in the illumination and reflectance map. After obtaining the refined illuminance and reflectance, we substitute the gamma-corrected illuminance into the camera response function to further adjust the reflectance as the final enhancement result. We test our proposed method on two non-uniform illumination computer-simulated and two low-contrast experimentally obtained ESPI fringe patterns. Finally, we compare our method with three other joint enhancement and denoising variational Retinex methods.

Binarization for low-quality ESPI fringe patterns based on preprocessing and clustering.

Massive inherent speckle noise and extremely low contrast make it difficult to binarize electronic speckle pattern interferometry (ESPI) fringe patterns. In this paper, we present a binarization based on preprocessing and fuzzy C-means (FCM) clustering for low-quality ESPI fringe patterns. First, we use the multiscale retinex (MSR) algorithm to enhance the original fringe pattern to improve the contrast between the bright and dark fringes. Then, the local entropy of the enhanced fringe pattern is calculated and the second-order oriented partial differential equation algorithm is introduced to filter the local entropy map. Finally, the FCM is applied to cluster the local entropy filtering map, and the pixels of the fringe pattern are classified into two categories: bright fringes and dark fringes. To verify the reliability and universality of the proposed method, we provide a qualitative evaluation of six experimental ESPI subtraction fringe patterns and two computer-simulated ESPI addition fringe patterns. Experimental results exhibit that the proposed method can provide good binarization performances.

Binarization of ESPI fringe patterns based on an M-net convolutional neural network.

The fringe skeleton method is the most straightforward method to estimate phase terms in electronic speckle pattern interferometry (ESPI). It usually needs to binarize the fringe patterns. However, the massive inherent speckle noise and intensity inhomogeneity in ESPI fringe patterns make it difficult to binarize the ESPI fringe patterns. In this paper, we propose a binarization method for ESPI fringe patterns based on a modified M-net convolutional neural network. Our method regards the binarization of fringe patterns as a segmentation problem. The M-net is an excellent network for segmentation and has proven to be a useful tool for skeleton extraction in our previous work. Here we further modify the structure of the previous network a bit to suit our task. We train the network by pairs of ESPI fringe patterns and corresponding binary images. After training, we test our method on 20 computer-simulated and three groups of experimentally obtained ESPI fringe patterns. The results show that even for fringe patterns with high noise and intensity inhomogeneity, our method can obtain good binarization results without image preprocessing. We also compare the modified M-net with a classic segmentation network, the U-net, and a residual encoder-decoder network (RED-net). The RED-net was used for binarization of document images. The experimental results prove the effectiveness of our method.

Skeleton extraction and inpainting from poor, broken ESPI fringe with an M-net convolutional neural network

Extracting skeletons from fringe patterns is the key to the fringe skeleton method, which is used to extract phase terms in electronic speckle pattern interferometry (ESPI). Because of massive inherent speckle noise, extracting skeletons from poor, broken ESPI fringe patterns is challenging. In this paper, we propose a method based on a modified M-net convolutional neural network for skeleton extraction from poor, broken ESPI fringe patterns. In our method, we pose the problem as a segmentation task. The M-net performs excellent segmentation, and we modify its loss function to suit our task. The broken ESPI fringe patterns and corresponding complete skeleton images are used to train the modified M-net. The trained network can extract and inpaint the skeletons simultaneously. We evaluate the performance of the network on two groups of computer-simulated ESPI fringe patterns and two groups of experimentally obtained ESPI fringe patterns. Two related recent methods, the gradient vector fields based on variational image decomposition and the U-net based method, are compared with our method. The results demonstrate that our method can obtain accurate, complete, and smooth skeletons in all cases, even where fringes are broken. It outperforms the two compared methods quantitatively and qualitatively.

Denoising for variable density ESPI fringes in nondestructive testing by an adaptive multiscale morphological filter based on local mean.

Analysis of speckle images with variable density fringes is a challenging task when electronic speckle pattern interferometry (ESPI) is used for nondestructive testing of defects. In this paper, an adaptive multiscale morphological filter based on local mean is proposed. First, the image is segmented, and the regions are divided into different density levels using local mean. Then, the structural elements that adapt to different density levels are designed, and the proper size of the structural elements is determined by an iterative procedure. Finally, the morphological open-closing filtering is conducted, and the block edges are smoothed by averaging. The proposed method was applied to computer-simulation fringes and fringes experimentally obtained from a prefabricated defect specimen under thermal loading and then compared with the commonly used methods, i.e., discrete cosine filter, wavelet filter, Lee filter, and nonlocal mean filter. The experimental results showed that the proposed method had the best performance in terms of noise reduction and edge preservation. With the capability of noise reduction for ESPI images of variable density fringes, the proposed method will be helpful to build a quantitative relationship between fringes and defects in the cases of nonuniform deformation of speckle interferometry, such as nondestructive defect detecting, thermal structural analysis, and heterogeneous materials mechanical analysis.

The oriented bilateral filtering method for removal of speckle noise in electronic speckle pattern interferometry fringes

In optical interferometry methods, a challenging problem is how to preserve the edges of all fringes perfectly whilst reducing speckle noise effectively. Directivity is an important characteristic of optical interferometry fringes, and it plays an extremely important role in directing the filtering process. Bilateral filtering is a well-known filtering method for edge-preserving in image processing. In this paper, we propose an oriented bilateral filtering method with special application for optical interferometry fringes by incorporating a directional mask to original bilateral filtering method. We test our oriented bilateral filtering method by applying it to four computer-simulated and one experimentally obtained ESPI fringe patterns, respectively, and compare it with the original bilateral filtering method and the tangent least-squares fitting filtering method. The experimental results demonstrate that the proposed method performs impressively in speckle reduction and fringe edge preservation.

Batch denoising of ESPI fringe patterns based on convolutional neural network.

The denoising of electronic speckle pattern interferometry (ESPI) fringe patterns is a key step in the application of ESPI. In this paper, we propose a method for batch denoising of ESPI fringe patterns based on a convolution neural network (CNN). In the proposed method, the network is first trained by our training dataset, which consists of the noisy ESPI fringe patterns and the corresponding noise-free images. We propose a new computer-simulated method of ESPI fringe patterns to create our training dataset. After training, the other multi-frame ESPI fringe patterns to be processed are fed to the trained network simultaneously, and the corresponding denoising images can be obtained in batches. We demonstrate the performance of the proposed method via application to 50 computer-simulated ESPI fringe patterns and three groups of experimentally obtained ESPI fringe patterns. The experimental results show that our method can obtain desired results even when the quality of ESPI fringe images is considerably low because of variable density, high noise, and low contrast, and our method can denoise multi-frame fringe patterns simultaneously. Moreover, we use the computer-simulated ESPI fringe patterns to train the network; after training, the trained network can be used to denoise either computer-simulated ESPI fringe patterns or the experimentally obtained ESPI fringe patterns. The proposed method is especially suitable for processing a large number of ESPI fringe patterns.

A clustering framework based on FCM and texture features for denoising ESPI fringe patterns with variable density

Denoising of electronic speckle pattern interferometry (ESPI) fringe patterns with variable density is challenging. In this paper, we present a method to denoise ESPI fringe patterns with variable density by constructing a clustering framework. The framework first clusters the variable density fringes into low density fringes and high density fringes according to the texture features of fringes by using fuzzy c-means (FCM) clustering algorithm. The texture features include energy, contrast, homogeneity and correlation, which can characterize the densities of fringes. Then, the effective existing methods are adopted to denoise the low and high density fringes individually. Finally, the filtered low and high density fringes are combined to obtain the final denoising results of the fringe patterns with variable density. With the help of proposed framework, variable density fringes can be clustered into low and high density fringes without calculating the density map of fringe pattern. Furthermore, the filtering strength applied in high density fringes can be different from that in low density fringes in a fringe pattern, which can improve the performance of any filtering method in the denosing of fringe patterns with variable density. Experiments on computer-simulated and experimentally obtained ESPI fringe patterns tested with several filtering methods show that the proposed framework provides consistently better results than denoising the image directly, in terms of signal-to-noise ratio, equivalent number of looks and edge preservation metrics.

Fully automated extraction of the fringe skeletons in dynamic electronic speckle pattern interferometry using a U-Net convolutional neural network

With the development of artificial intelligence technology, intelligent fringe processing is a goal of relevant researchers in optical interferometry. We propose an intelligent method to achieve fully automated extraction of the fringe skeletons in electronic speckle pattern interferometry (ESPI) based on U-Net convolutional neural network. In the proposed method, the network is first trained by the samples that consist of the noisy ESPI fringe patterns and the corresponding skeleton images. After training, the other multiframe ESPI fringe patterns are fed to the trained network simultaneously; the corresponding skeleton images can be obtained in batches. Using our method, it is not necessary to process fringe patterns frame by frame. Our method is especially suitable for multiframe fringe patterns processing. We apply the intelligent method to one computer-simulated and one real-dynamic ESPI measurement, respectively. For the simulated measurement, it takes just 40 s to obtain the skeleton images of 20 noisy ESPI fringe patterns using our method. Even for low-quality experimental obtained ESPI fringe patterns, our method can also give desired results.

A shape-preserving oriented partial differential equation based on a new fidelity term for electronic speckle pattern interferometry fringe patterns denoising

Oriented partial differential equations (OPDEs) have been demonstrated to be a powerful tool for preserving the integrity of fringes while filtering electronic speckle pattern interferometry (ESPI) fringe patterns. However, the main drawback of OPDEs-based methods is that many iterations are often needed, which causes the change in the shape of fringes. Change in the shape of fringes will affect the accuracy of subsequent fringe analysis. In this paper, we focus on preserving the shape of fringes while filtering, suggested here for the first time. We propose a shape-preserving OPDE for ESPI fringe patterns denoising by introducing a new fidelity term to the previous second-order single oriented PDE (SOOPDE). In our proposed fidelity term, the evolution image is subtracted from the shrinkage result of original noisy image by shearlet transform. Our proposed shape-preserving OPDE is capable of eliminating noise effectively, keeping the integrity of fringes, and more importantly, preserving the shape of fringes. We test the proposed shape-preserving OPDE on three computer-simulated and three experimentally obtained ESPI fringe patterns with poor quality. Furthermore, we compare our model with three representative filtering methods, including the widely used SOOPDE, shearlet transform and coherence-enhancing diffusion (CED). We also compare our proposed fidelity term with the traditional fidelity term. Experimental results show that the proposed shape-preserving OPDE not only yields filtered images with visual quality on par with those by CED which is the state-of-the-art method for ESPI fringe patterns denoising, but also keeps the shape of ESPI fringe patterns.

Image decomposition model Shearlet-Hilbert-L2 with better performance for denoising in ESPI fringe patterns.

In this paper, we propose an image decomposition model Shearlet-Hilbert-L2 with better performance for denoising in electronic speckle pattern interferometry (ESPI) fringe patterns. In our model, the low-density fringes, high-density fringes, and noise are, respectively, described by shearlet smoothness spaces, adaptive Hilbert space, and L2 space and processed individually. Because the shearlet transform has superior directional sensitivity, our proposed Shearlet-Hilbert-L2 model achieves commendable filtering results for various types of ESPI fringe patterns, including uniform density fringe patterns, moderately variable density fringe patterns, and greatly variable density fringe patterns. We evaluate the performance of our proposed Shearlet-Hilbert-L2 model via application to two computer-simulated and nine experimentally obtained ESPI fringe patterns with various densities and poor quality. Furthermore, we compare our proposed model with windowed Fourier filtering and coherence-enhancing diffusion, both of which are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. We also compare our proposed model with the previous image decomposition model BL-Hilbert-L2.

General filtering method for electronic speckle pattern interferometry fringe images with various densities based on variational image decomposition.

Filtering off speckle noise from a fringe image is one of the key tasks in electronic speckle pattern interferometry (ESPI). In general, ESPI fringe images can be divided into three categories: low-density fringe images, high-density fringe images, and variable-density fringe images. In this paper, we first present a general filtering method based on variational image decomposition that can filter speckle noise for ESPI fringe images with various densities. In our method, a variable-density ESPI fringe image is decomposed into low-density fringes, high-density fringes, and noise. A low-density fringe image is decomposed into low-density fringes and noise. A high-density fringe image is decomposed into high-density fringes and noise. We give some suitable function spaces to describe low-density fringes, high-density fringes, and noise, respectively. Then we construct several models and numerical algorithms for ESPI fringe images with various densities. And we investigate the performance of these models via our extensive experiments. Finally, we compare our proposed models with the windowed Fourier transform method and coherence enhancing diffusion partial differential equation filter. These two methods may be the most effective filtering methods at present. Furthermore, we use the proposed method to filter a collection of the experimentally obtained ESPI fringe images with poor quality. The experimental results demonstrate the performance of our proposed method.

Combination of oriented partial differential equation and shearlet transform for denoising in electronic speckle pattern interferometry fringe patterns.

It is a key step to remove the massive speckle noise in electronic speckle pattern interferometry (ESPI) fringe patterns. In the spatial-domain filtering methods, oriented partial differential equations have been demonstrated to be a powerful tool. In the transform-domain filtering methods, the shearlet transform is a state-of-the-art method. In this paper, we propose a filtering method for ESPI fringe patterns denoising, which is a combination of second-order oriented partial differential equation (SOOPDE) and the shearlet transform, named SOOPDE-Shearlet. Here, the shearlet transform is introduced into the ESPI fringe patterns denoising for the first time. This combination takes advantage of the fact that the spatial-domain filtering method SOOPDE and the transform-domain filtering method shearlet transform benefit from each other. We test the proposed SOOPDE-Shearlet on five experimentally obtained ESPI fringe patterns with poor quality and compare our method with SOOPDE, shearlet transform, windowed Fourier filtering (WFF), and coherence-enhancing diffusion (CEDPDE). Among them, WFF and CEDPDE are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. The experimental results have demonstrated the good performance of the proposed SOOPDE-Shearlet.

Gradient vector fields based on variational image decomposition for skeletonization of electronic speckle pattern interferometry fringe patterns with variable density and their applications.

The skeletonization methods based on gradient vector fields (GVFs) have been a powerful tool for electronic speckle pattern interferometry (ESPI) fringe patterns. However, the skeletonization of ESPI fringe patterns with variable density has been an open problem in this area. In this paper, we propose a novel method for calculating GVFs based on the variational image decomposition of ESPI fringe patterns with variable density. In the proposed method, the GVFs of low-density regions are described in Beppo-Levi space, the high-density regions in Hilbert space and the noise regions in curvelet space. The GVFs of a whole image are the sum of the decomposed GVFs of low-density regions and high-density regions. The skeletons of ESPI fringe patterns with variable density can be obtained based on the topological analysis of the GVFs of a whole image. We apply the proposed method to a computer-simulated and two experimentally obtained ESPI fringe patterns with variable density and compare them with the related skeleton methods based on GVFs. The experimental results have demonstrated that the proposed method outperforms the other methods, even when the quality of the ESPI fringe patterns is considerably low.

Variational image decomposition for estimation of fringe orientation and density from electronic speckle pattern interferometry fringe patterns with greatly variable density

Fringe orientation and density are important properties of fringes. The estimation of fringe orientation and density from electronic speckle pattern interferometry (ESPI) fringe patterns with greatly variable density is still a challenging problem faced in this area. We propose an effective method based on variational image decomposition to estimate fringe orientation and density simultaneously. The BL–Hilbert model is proposed to successfully decompose an ESPI fringe pattern with greatly variable density into two images: one only includes low density fringes and the other high density fringes. The density of the two decomposed images are uniform. We estimate the orientation and density of the two decomposed images by existing methods. The whole fringe orientation and density can be obtained by combining the corresponding results of the two decomposed images. We evaluate the performance of our method via application to the computer-simulated and experimentally obtained ESPI fringe patterns with greatly variable density and comparison with the widely used three methods.

Skeleton extraction and phase interpolation for single ESPI fringe pattern based on the partial differential equations.

A novel phase extraction method for single electronic speckle pattern interferometry (ESPI) fringes is proposed. The partial differential equations (PDEs) are used to extract the skeletons of the gray-scale fringe and to interpolate the whole-field phase values based on skeleton map. Firstly, the gradient vector field (GVF) of the initial fringe is adjusted by an anisotropic PDE. Secondly, the skeletons of the fringe are extracted combining the divergence property of the adjusted GVF. After assigning skeleton orders, the whole-field phase information is interpolated by the heat conduction equation. The validity of the proposed method is verified by computer-simulated and experimentally obtained poor-quality ESPI fringe patterns.

Two parabolic-hyperbolic oriented partial differential equations for denoising in electronic speckle pattern interferometry fringes.

Oriented partial differential equation (OPDE)-based filtering methods have been demonstrated to be a powerful tool for denoising while preserving all fringes. In this paper we propose new OPDE-filtering models, named parabolic-hyperbolic oriented partial differential equations (PH-OPDEs), based on variational methods. We test the proposed PH-OPDEs on two computer-simulated and two experimentally obtained ESPI fringe patterns with poor quality, and compare our models with related OPDE models. The experimental results have demonstrated that the new models have significantly better performance in numerical stability and computational efficiency as compared with the previous OPDE models.