Real Fringe Patterns Research Articles

Fringe pattern demodulation using the fan two-dimensional continuous wavelet transform conjugate to Shannon entropy.

This paper proposes an algorithm for phase demodulating fringe patterns using a two-dimensional continuous wavelet transform (2D-CWT). This algorithm exploits the isotropy property of the fan mother wavelet conjugated to Shannon entropy to perform the ridge extraction process by using only 2D-CWT arguments. The proposed algorithm's performance is shown through simulated fringe patterns corrupted by speckle noise. Also, to evaluate the accuracy of the ridge extracted from the modulus to that obtained from the arguments of 2D-CWT, the developed algorithm is compared to the maximum ridge extraction algorithm for 2D-CWT and cost function ridge extraction algorithm for 2D-CWT, which extract the ridge from the 2D-CWT modulus. Furthermore, we demonstrate the ability of the proposed algorithm to demodulate real fringe patterns derived from optical metrology for temperature measurement. The most important result of the proposed method is that it is provably optimal in estimating the 2D-CWT ridge of oriented fringes. The added strength of the algorithm is that it is simpler and has better resistance to speckle noise than previous methods because it employs scalograms of arguments, which are the origin of the definition of the ridge.

Wrap reduction algorithm for fringe projection profilometry

Carrier removal has been typically associated with wrap reduction, and its application has strongly been recommended as a previous step to phase unwrapping. In general, the carrier signal contributes to an increase of the number of wraps, and its removal leads to a reduction of the number of phase inconsistencies, having a positive impact on the subsequent unwrapping operation. In this paper, we show that phase wrap reduction can be better tackled by other alternative and more effective methods that exploit local information and attempt to also remove the signal component associated with the object’s surface. The results are analyzed on a series of real fringe patterns and confirm the better performance of the proposed method, which leads to signals with a lesser number of wraps than by just removing the carrier.

U-Net based neural network for fringe pattern denoising

Fringe patterns from different optical measurement systems are widely used in scientific and engineering applications. However, fringe patterns are often corrupted by speckle noise, which is necessary to be removed to accurately recover the information encoded in the phase of the fringe pattern. In this paper we propose a lightweight residual dense neural network based on the U-net neural network model (LRDUNet) for fringe pattern denoising. The encoding and decoding layers of the LRDUNet consist of grouped densely connected convolutional layers for the sake of reusing the feature maps and reducing the number of trainable parameters. Additionally, local residual learning is used to avoid the vanishing gradient problem and speed up the learning process. We compare the proposed method versus state-of-the-art methods and present a study of parameters where we demonstrate that computationally simpler versions of the proposed model are still quite competitive. Experiments on simulated and real fringe patterns show that the proposed method outperforms state-of-the-art methods by restoring the main features of the fringe patterns, achieving an average of 41 dB of PSNR on simulated images.

Single-shot phase extraction for fringe projection profilometry using deep convolutional generative adversarial network

This paper presents a single-shot phase extraction approach based on a deep convolutional generative adversarial network that generates a phase map and a quality mask from an input fringe pattern image. A novel loss function is proposed, and a large-scale (28 800 samples) real fringe pattern dataset is collected to train the network. The experiments demonstrate that the proposed method achieves significantly improved phase extraction accuracy and overcomes the main limitations of Fourier transform profilometry. In addition, the proposed method presents excellent performance for real-time computing, reaching approximately 100 f s−1 with a single GPU. Moreover, the proposed learning-based approach can automatically perform denoising and phase extraction, without any manually set parameters.

Augmented Lagrangian method for a total variation-based model for demodulating phase discontinuities

In this work, we reformulate the method presented in App. Opt. 53:2297 (2014) as a constrained minimization problem using the augmented Lagrangian method. First we introduce the new method and then describe the numerical solution, which results in a simple algorithm. Numerical experiments with both synthetic and real fringe patterns show the accuracy and simplicity of the resulting algorithm.

Binarization of ESPI fringe patterns based on local entropy.

The fringe skeleton method is the most straightforward analysis method for phase extraction and widely used in dynamic measurement. Binarization is often required in this method. In the traditional binarization methods, filtering is often a necessary step prior to binarization due to the influence of intrinsic speckle noises in ESPI fringe patterns. In this paper, we propose a binarization method based on local entropy and fuzzy c-means (FCM) clustering algorithm. In this method, the pixels in the given ESPI fringe pattern are clustered into white fringes and black fringes according to their local entropy instead of the original intensity information. There is no need to perform the filtering preprocessing, because the intrinsic speckle noises are utilized as essentials. We evaluate the performance of our method by applying it to the computer-simulated and real fringe patterns. Experimental results demonstrate that the proposed method can achieve the desired binarization results, and the binarization results can give desired skeleton results.

Fringe pattern denoising using spatial oriented gaussian filters

In this paper, it is proposed a gaussian convolution-based fringe pattern denoising method. As will be shown, this method is robust enough compared with some of the most outstanding methods in the literature. Additionally, the proposed method overcomes the problem of underperformance in low-frequency fringes that is common in most oriented filtering methods, while keeping the great advantages of convolution-based filters. The advantages of the proposed denoising method will be demonstrated with experiments realized over synthetic and real fringe patterns, and comparing the performance with four representative methods, already reported.

Binarization of optical fringe patterns with intensity inhomogeneities based on modified FCM algorithm

Binarization of fringe patterns is a commonly used process in the fringe skeleton method for optical fringe pattern analysis. Most of the existing binarization algorithms of fringe patterns are based on the determination of gray level threshold. However, spatial intensity inhomogeneity induced by the uneven illumination makes the gray level threshold hard to determine. In this paper, we present a method for the binarization of fringe patterns based on a modified Fuzzy c-means clustering (FCM) algorithm. This method permits the clustering of pixels influenced by their immediate surroundings. The pixels in the fringe pattern are clustered into white fringes and black fringes without calculating thresholds. We evaluate the performance of this method by applying it to computer-simulated and real fringe patterns. Experimental results demonstrate that the proposed method can achieve the desired binarization results and perform better than the previous binarization methods, under non-uniform illumination conditions.

Fringe pattern denoising based on deep learning

In this paper, deep learning as a novel algorithm is proposed to reduce the noise of the fringe patterns. Usually, the training samples are acquired through experimental acquisition, but these data can be easily obtained by simulations in the proposed algorithm. Thus, the time cost used for the whole training process is greatly reduced. The performance of the proposed algorithm has been demonstrated through the analysis on the simulated and real fringe patterns. It is obvious that the proposed algorithm has a faster calculation speed compared with existing denoising algorithm, and recovers the fringe patterns with high quality. Most importantly, the proposed algorithm may provide a solution to other denoising problems in the field of optics, such as hologram and speckle denoising.

Assessment of Fringe Pattern Decomposition with a Cross-Correlation Index for Phase Retrieval in Fringe Projection 3D Measurements.

Phase retrieval from single frame projection fringe patterns, a fundamental and challenging problem in fringe projection measurement, attracts wide attention and various new methods have emerged to address this challenge. Many phase retrieval methods are based on the decomposition of fringe patterns into a background part and a fringe part, and then the phase is obtained from the decomposed fringe part. However, the decomposition results are subject to the selection of model parameters, which is usually performed manually by trial and error due to the lack of decomposition assessment rules under a no ground truth data situation. In this paper, we propose a cross-correlation index to assess the decomposition and phase retrieval results without the need of ground truth data. The feasibility of the proposed metric is verified by simulated and real fringe patterns with the well-known Fourier transform method and recently proposed Shearlet transform method. This work contributes to the automatic phase retrieval and three-dimensional (3D) measurement with less human intervention, and can be potentially employed in other fields such as phase retrieval in digital holography.

Variational phase recovering without phase unwrapping in phase-shifting interferometry

ABSTRACTWe present a variational method for recovering the phase term from the information obtained from phase-shifting methods. First we introduce the new method based on a variational approach and then describe the numerical solution of the proposed cost function, which results in a simple algorithm. Numerical experiments with both synthetic and real fringe patterns show the accuracy and simplicity of the resulting algorithm.

Comparative analysis of gradient-field-based orientation estimation methods and regularized singular-value decomposition for fringe pattern processing.

Fringe orientation is an important feature of fringe patterns and has a wide range of applications such as guiding fringe pattern filtering, phase unwrapping, and abstraction. Estimating fringe orientation is a basic task for subsequent processing of fringe patterns. However, various noise, singular and obscure points, and orientation data degeneration lead to inaccurate calculations of fringe orientation. Thus, to deepen the understanding of orientation estimation and to better guide orientation estimation in fringe pattern processing, some advanced gradient-field-based orientation estimation methods are compared and analyzed. At the same time, following the ideas of smoothing regularization and computing of bigger gradient fields, a regularized singular-value decomposition (RSVD) technique is proposed for fringe orientation estimation. To compare the performance of these gradient-field-based methods, quantitative results and visual effect maps of orientation estimation are given on simulated and real fringe patterns that demonstrate that the RSVD produces the best estimation results at a cost of relatively less time.

Deformation-phase measurement by digital speckle correlation method

A novel algorithm which extracts the out-of-plane component of deformation phase from two continuous fringe patterns is proposed. The velocity field between two consecutive frames is estimated by digital speckle correlation method (DSCM). After that, according to the optical flow constrained equation, the whole-field deformation-phase map is obtained by the estimations of the velocity field and the local frequency of the original image. The operation of the proposed method is simple compared with other phase demodulation methods. Moreover, the new method works perfectly at the areas with dense fringes. In this paper, the proposed algorithm is introduced. Meanwhile, in order to verify the effectiveness, the new algorithm is applied to simulated interferogram and real fringe pattern with a centrally loaded and edge-clamped plate. The results of simulation and experiment show that the new method can demodulate the out-of-plane component of deformation phase from the visible in-plane velocity field without unwrapping process. Further, dynamic deformation-phase extraction will be realized when we know the time interval of two continuous images. The proposed algorithm provides a new approach for whole-field deformation-phase measurement and dynamic deformation measurement.

Shifting of wrapped phase maps in the frequency domain using a rational number

The number of phase wraps in an image can be either reduced, or completely eliminated, by transforming the image into the frequency domain using a Fourier transform, and then shifting the spectrum towards the origin. After this, the spectrum is transformed back to the spatial domain using the inverse Fourier transform and finally the phase is extracted using the arctangent function. However, it is a common concern that the spectrum can be shifted only by an integer number, meaning that the phase wrap reduction is often not optimal. In this paper we propose an algorithm than enables the spectrum to be frequency shifted by a rational number. The principle of the proposed method is confirmed both by using an initial computer simulation and is subsequently validated experimentally on real fringe patterns. The technique may offer in some cases the prospects of removing the necessity for a phase unwrapping process altogether and/or speeding up the phase unwrapping process. This may be beneficial in terms of potential increases in signal recovery robustness and also for use in time-critical applications.

Fast fringe pattern phase demodulation using FIR Hilbert transformers

This paper suggests the use of FIR Hilbert transformers to extract the phase of fringe patterns. This method is computationally faster than any known spatial method that produces wrapped phase maps. Also, the algorithm does not require any parameters to be adjusted which are dependent upon the specific fringe pattern that is being processed, or upon the particular setup of the optical fringe projection system that is being used. It is therefore particularly suitable for full algorithmic automation. The accuracy and validity of the suggested method has been tested using both computer-generated and real fringe patterns. This novel algorithm has been proposed for its advantages in terms of computational processing speed as it is the fastest available method to extract the wrapped phase information from a fringe pattern.

Morphological operation-based bi-dimensional empirical mode decomposition for automatic background removal of fringe patterns

A modified bi-dimensional empirical mode decomposition (BEMD) method is proposed for sparsely decomposing a fringe pattern into two components, namely, a single intrinsic mode function (IMF) and a residue. The main idea of this method is a modified sifting process which employs morphological operations to detect ridges and troughs of the fringes, and uses weighted moving average algorithm to estimate envelopes of the IMF, replacing respective local extrema detection and envelope interpolation of conventional BEMDs. The background intensity of the fringe pattern is automatically removed by extracting the single IMF, thereby relieving the mode mixing problem of the BEMDs. A fast algorithm based on 2D convolution is also presented for reducing the calculation time to several seconds only. This approach is applied to process simulated and real fringe patterns, and the results obtained are compared with Fourier transform, discrete wavelet transform, and other EMD methods. The MATLAB code is downloadable at http://gr.xjtu.edu.cn/web/zhouxiang.

Squeezed Carrier Interferogram for Wavelet Phase Recovery

The purpose of the present work is the use of the Phase evaluation CWT algorith m to extract the phase from squeezing interferogram. The squeezing interfero metry technique generates a spatial carrier interferogram named squeezed interferogram by numerical co mbination of M shifted fringes patterns. The M shifted fringes patterns are digitally generated fro m co mb ination of t wo π/2 shifted fringe patterns. Fro m squeezed interferogram the phase is extracted in wavelet domain using CWT algorith m which leads directly to the phase distribution without the complex step of phase unwrapping. Simu lated fringe pattern are used to test our technique and real fringe pattern are used to improve the accuracy of this technique.

Single Frame Fringe Pattern Analysis for Phase Recovery with Analytic Signal

We consider a new application of the normalized Hilbert-Huang transform to extract directly the phase from a single fringe pattern. We present a technique to provide, with good accuracy, the phase distribution from a single interferogram without unwrapping step and this by a new exploitation of the analytic signal corresponding to each intrinsic mode function, resulting from one-dimensional empirical mode decomposition of the fringe pattern. A theoretical analysis was carried out for this technique, followed by computer simulations and a real experimental fringe pattern for verification.

Influence of the volume speckle on fiber specklegram sensors based on four-wave mixing in photorefractive materials

In this work, the dependence on the speckle size in the performance of a micro displacement sensor based on fiber specklegrams stored in a photorefractive BSO (Bi 12SiO 20) crystal is experimentally demonstrated. In our experimental setup, a plastic optical fiber (POF) was used to generate a subjective speckle pattern which was recorded in the crystal by using a four-wave mixing arrangement in transmission geometry. The speckle size was controlled by modifying the diameter of a pupil aperture adjacent to a lens producing the image of the speckle. The signal speckle beam was mixed into the crystal with two counter propagating pump beams to generate a fourth beam which is proportional to the conjugate of the original speckle beam. Real time fringe patterns were obtained at the output of the system by producing micro displacements of the fiber output end. Increases of the phase conjugation reflectivity and the visibility of the fringe patterns were appreciated when the speckle length was increased by decreasing the pupil aperture diameter. This behavior allowed recovering the autocorrelation functions of fringe patterns associated to micro displacements that initially led to decorrelation, and therefore, to improve the dynamic range of the metrological system. Until the best of our knowledge this is the first report about the influence of the speckle size on fiber specklegrams sensors recorded on photorefractive materials by four-wave mixing.

Analysis of Digital Speckle‐Pattern Interferometry Fringe Patterns Issued from Transitory Mechanical Loadings

Abstract: During a dynamic mechanical loading, we cannot use a phase‐shifting technique because the mechanical parameters evolve according to the time. This problem can be avoided by the development of algorithms which can extract the mechanical information from only one fringe pattern. In this way, we present two algorithms, the modulated phase correlation (MPC) and the polynomial modulated phase correlation (pMPC). These processes are based on the use of the virtual fringe pattern which locally approaches the real fringe morphology. The similarity degree between real and virtual fringe pattern is estimated by digital correlation technique. When the best similarity is obtained, we suppose that the virtual phase function is very close to the real phase function. Some examples are presented to show the low noise sensitivity of these techniques. So, we propose to use the MPC or the pMPC algorithms to extract the relief from a single interferogram obtained by digital speckle‐pattern interferometry. In this paper, we present experimental tests of impact loading on plates. The frame rate is adapted to the dynamic conditions of loading. Recorded fringe patterns and results of the unwrapped phase demodulated with our algorithms are shown.