Physics-informed deep learning for fringe pattern analysis

Recently,deep learning has yielded transformative success across optics and photonics,especially in optical metrology.Deep neural networks (DNNs) with a fully convolutional architecture (e.g.,U-Net and its derivatives) have been widely implemented in an end-to-end manner to accomplish various optical metrology tasks,such as fringe denoising,phase unwrapping,and fringe analysis.However,the task of training a DNN to accurately identify an image-to-image transform from massive input and output data pairs seems at best naive,as the physical laws governing the image formation or other domain expertise pertaining to the measurement have not yet been fully exploited in current deep learning practice.To this end,we introduce a physics-informed deep learning method for fringe pattern analysis (PI-FPA) to overcome this limit by integrating a lightweight DNN with a learning-enhanced Fourier transform profilometry (Le FTP) module.By parameterizing conventional phase retrieval methods,the Le FTP module embeds the prior knowledge in the network structure and the loss function to directly provide reliable phase results for new types of samples,while circumventing the requirement of collecting a large amount of high-quality data in supervised learning methods.Guided by the initial phase from Le FTP,the phase recovery ability of the lightweight DNN is enhanced to further improve the phase accuracy at a low computational cost compared with existing end-to-end networks.Experimental results demonstrate that PI-FPA enables more accurate and computationally efficient single-shot phase retrieval,exhibiting its excellent generalization to various unseen objects during training.The proposed PI-FPA presents that challenging issues in optical metrology can be potentially overcome through the synergy of physics-priors-based traditional tools and data-driven learning approaches,opening new avenues to achieve fast and accurate single-shot 3D imaging.

A New Algorithm for Automatic Double Bright Fringe of Multiple-Beam Fizeau Fringe Skeletonization Using Fourier Transform Method of Fringe Pattern Analysis

The interferogram of multiple-beam Fizeau fringe technique plays an important role to investigate the optical properties of fiber because this interferogram provides us with useful information which can used to determine the dispersion curve of the fiber sample. A common problem in any interferogram analysis is the accuracy in locating fringe centers (fringe skeleton). There are a lot of computer-aided algorithms, which depend on the interferogram types, used to fringe skeleton extraction of various digital interferogram. In this paper, as far as I know, a novel algorithm for fringe skeleton extraction of double bright fringe of multiple-beam Fizeau fringe is presented. The proposed algorithm based on using the different order of Fourier transform and the derivative-sign binary image. Also the proposed algorithm has been successfully tested by using a computer simulation fringe and an experimental pattern. The results are compared with the original interferogram and shown a good agreement.

Impacts of Transportation Arteries on Land Use Patterns in Urbanrural Fringe: A Comparative Gradient Analysis of Qixia District, Nanjing City, China

Integrated transportation and land use studies are of major interest to planners because they consider the interaction between transportation development and land use change. Quantifying the impact of transport infrastructure on land use change is necessary for evaluating the role of transportation development in the process of land use and land cover change in the urban-rural fringe. Taking Qixia District of Nanjing City, Jiangsu Province, China as a typical urban-rural fringe area, this paper analyzes the patterns and charac- teristics of land use change along three major transportation arteries using land use data from 2000 and 2008. We examine the spatial differentiation and gradient of land use pattern around railway, expressway, and highway corridors to investigate whether land use change in the urban-rural fringe is related to distance from transportation arteries and to clarify the varying impacts of different forms of transport infrastructure on land use patterns. We find that construction land generally tends to be located close to major transportation arteries, and that railways have the most obvious influence on land use change in the urban-rural fringe, while the impact of expressways was not significant. We conclude that there exists a causal relationship between the presence of transportation arteries and land use change in the urban-rural fringe, but this relationship varies across different types of linear transnort infrastrncnlre.

A New'Condition and Applications in Fourier Analysis(Ⅱ)

As we already mentioned in [6], in Fourier analysis, since Fourier coefficients are computable and applicable, people have established many nice results by assuming monotonicty of the coefficients. Generally speaking, it became an important topic how to generalize monotonicity. In many studies the generalization follows by this way:

Multi-Resolution Fourier Analysis Part I: Fundamentals

In the first paper of this series, we propose a multi-resolution theory of Fourier spectral estimates of finite duration signals. It is shown that multi-resolution capability, achieved without further observation, is obtained by constructing multi-resolution signals from the only observed finite duration signal. Achieved resolutions meet bounds of the uncertainty principle (Heisenberg inequality). In the forthcoming parts of this series, multi-resolution Fourier performances are observed, applied to short signals and extended to time-frequency analysis.

Multi-Resolution Fourier Analysis Part II: Missing Signal Recovery and Observation Results

In this paper, we report application procedures and observed results of multi-resolution Fourier analysis proposed in the first part of this series. Missing signal recovery derived from multi-resolution theory is developed. It is shown that multi-resolution Fourier analysis enhances dramatically performances of Fourier spectra suffering limitations traced to implicit time windowing. Observed frequency resolutions, improvement of frequency estimations, contraction of spectral leakage and recovery of missing parts of finite duration signals are in accordance with theoretical predictions.

Simulation of X-ray Diffraction Line Broadening Caused by Stress Gradients and Determination of Stress Distribution by Fourier Analysis

Different physical, mechanical and chemical processes, such as： ion implantation, oxidation, nitridation and others create on the surface of materials residual stress state, characterized by high level and strong gradient. X-ray diffraction method widely used for stress measurements has some difficulties in interpretation of experimental data, when the depth of X-ray penetration is compared with thickness of surface layer where inhomogeneous stress distribution is localized. Early it has been shown by authors that diffraction line broadening occurs when analyzed surface is characterized by strong gradient. The interest to study the diffraction line broadening is connected to the possibility of obtaining information about parameters of surface stress distribution. In the present paper the convolution and deconvolution concepts of Fourier analysis were applied to study X ray diffraction line broadening caused by surface stress gradients. Developed methodology allows determining of stress distribution in superficial layers of materials.

Photoelastic Stress Analysis by Use of Hybrid Technique and Fringe Phase Shifting Method

Photoelastic fringe patterns for stress analysis are investigated by use of hybrid technique and fringe phase shift method. The first one is a hybrid method which combines the conformal mapping technique and measured data away from the edge of a geometric discontinuity. Photoelastic data are hybridized with complex variable/mapping techniques to calculate photoelastic stress-field around a circular hole or an elliptical hole in plates under uniaxial tensile loading. This method determines full-field stresses in perforated finite tensile plates containing either a circular or an elliptical hole. The second one is a fringe phase shift method to separate isochromatics and isoclinics from photoelastic fringes of a circular disk under diametric compression by use of phase shift method. Digitally determined isochromatics and isoclinics are agreed well with those of manual measurements.

Fringe removal algorithms for atomic absorption images:A survey

The fringe noises disrupt the precise measurement of the atom distribution in the process of the absorption images.The fringe removal algorithms have been proposed to reconstruct the ideal reference images of the absorption images to remove the fringe noises.However,the focus of these fringe removal algorithms is the association of the fringe removal performance with the physical systems,leaving the gap to analyze the workflows of different fringe removal algorithms.This survey reviews the fringe removal algorithms and classifies them into two categories:the imagedecomposition based methods and the deep-learning based methods.Then this survey draws the workflow details of two classical fringe removal algorithms,and conducts experiments on the abs DL ultracold image dataset.Experiments show that the singular value decomposition(SVD)method achieves outstanding performance,and the U-net method succeeds in implying the image inpainting idea.The main contribution of this survey is the interpretation of the fringe removal algorithms,which may help readers have a better understanding of the research status.

Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

Quality Guided Phase Unwrapping for Fringe Projection Profilometry

Fringe projection technique is a non-contact, full field 3-D shape measurement method. The object depth information is recorded in one or several deformed fringe patterns. The phase-shifting algorithm or the Fourier transform method can be used to extract the wrapped phase data. A phase unwrapping process is then applied to retrieve a continuous phase distribution, which represents the surface profile of the test object. In this paper, a quality-guided phase unwrapping approach is incorporated and two novel phase quality evaluation methods are proposed to facilitate the phase unwrapping process.

Holographic Deformation Measurement by a Spatial Carrier Fringe Technique

A carrier fringe techrtique for measuring surface deformation is described and verified by experiments. In contrast to conventional holography and fringe analysis, this holographic system is based on fibre optics and automatic spatial carrier fringe pattem analysis techniques Single-mode optic fibres are used to transfer both the object and reference beams. Carrier fringes are generated by simply translating the object beam between two exposures The Fourier transform is applied to the carrier fringe pattern to convert it to the spatial frequency domain, where it is processed The results are given for a centrally loaded disk, including a 3-D perspective plot of the out of plane deformation field, phase map, grey level map and contour map.

Improved Responses with Multitaper Spectral Analysis for Magnetotelluric Time Series Data Processing:Examples from Field Data

In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without a multitaper approach for spectral estimation.There are several common ways to increase the reliability of the Fourier spectral estimation from experimental(noisy)data;for example to subdivide the experimental time series into segments,taper these segments(using single taper),perform the Fourier transform of the individual segments,and average the resulting spectra.

基于Fourier变换红外光谱分析咖啡豆成分

采用Fourier变换红外光谱对不同产区、不同海拔的5组浅中烘焙的咖啡豆样品进行分析,根据官能团的红外光谱特征峰分析样品主要成分;为进一步分析5组样品的成分差异,对原始光谱进行二阶导数处理,结合聚类分析理论建立平均偏离分析方法,计算出5组样品间的平均偏离大小并进行分析.结果表明:5组样品的红外光谱特征峰峰形相似,即主要成分相同;根据红外光谱得到平均偏离大小与产区海拔差值呈正相关.研究结果为分析咖啡豆产区和海拔提供鉴别依据,并对红外光谱研究提供一定参考.

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

Enhanced Fourier Transform Using Wavelet Packet Decomposition

Many domains, including communication, signal processing, and image processing, use the Fourier Transform as a mathematical tool for signal analysis. Although it can analyze signals with steady and transitory properties, it has limits. The Wavelet Packet Decomposition (WPD) is a novel technique that we suggest in this study as a way to improve the Fourier Transform and get beyond these drawbacks. In this experiment, we specifically considered the utilization of Daubechies level 4 for the wavelet transformation. The choice of Daubechies level 4 was motivated by several reasons. Daubechies wavelets are known for their compact support, orthogonality, and good time-frequency localization. By choosing Daubechies level 4, we aimed to strike a balance between preserving important transient information and avoiding excessive noise or oversmoothing in the transformed signal. Then we compared the outcomes of our suggested approach to the conventional Fourier Transform using a non-stationary signal. The findings demonstrated that the suggested method offered a more accurate representation of non-stationary and transient signals in the frequency domain. Our method precisely showed a 12% reduction in MSE and a 3% rise in PSNR for the standard Fourier transform, as well as a 35% decrease in MSE and an 8% increase in PSNR for voice signals when compared to the traditional wavelet packet decomposition method.

Carbonization mechanism of bamboo (phyllostachys) by means of Fourier Transform Infrared and elemental analysis

通过测定在200-600℃炭化竹材得到的固体产物的碳、氢、氧元素的含量及它们的红外光谱,研究了在炭化过程中竹材中半纤维素、纤维素及木素的变化规律。结果表明,结合元素分析,红外光谱分析方法是研究竹材炭化机理的有效手段。在200℃以前,竹材中的半纤维素和纤维素的大量羟基断裂,并结合成水而失去。在200-250℃之间,竹材中的纤维素被降解,其中的吡喃型环也遭到破坏。并且木素中的甲氧基也被脱去。竹材中的木素网状结构在250-400℃之间遭到完全的破坏。竹炭中的碳原子在600℃已基本上完成了芳环化。图3表2参15。

Fringe pattern analysis using deep learning

In many optical metrology techniques,fringe pattern analysis is the central algorithm for recovering the underlying phase distribution from the recorded fringe patterns.Despite extensive research efforts for decades,how to extract the desired phase information,with the highest possible accuracy,from the minimum number of fringe patterns remains one of the most challenging open problems.Inspired by recent successes of deep learning techniques for computer vision and other applications,we demonstrate for the first time,to our knowledge,that the deep neural networks can be trained to perform fringe analysis,which substantially enhances the accuracy of phase demodulation from a single fringe pattern.The effectiveness of the proposed method is experimentally verified using carrier fringe patterns under the scenario of fringe projection profilometry.Experimental results demonstrate its superior performance,in terms of high accuracy and edge-preserving,over two representative single-frame techniques:Fourier transform profilometry and windowed Fourier transform profilometry.

基于Fourier Analysis对造球机开式齿轮异常情况的诊断

利用Fourier Analysis对造球机开式齿轮异常情况进行了诊断,诊断结果表明,Fourier Analysis结果与开式齿轮实际运行状况相吻合。通过Fourier频域分析解释了齿轮啮合频率及边频对造球机振动的影响,得出了开式齿轮的异常情况是由于齿轮磨损造成齿形误差的结论。这对造球机开式齿轮的修复或更换提供了科学的依据。

Local Fourier Analysis of Multigrid Methods with Polynomial Smoothers and Aggressive Coarsening

We focus on the study of multigrid methods with aggressive coarsening and polynomial smoothers for the solution of the linear systems corresponding to finite difference/element discretizations of the Laplace equation.Using local Fourier analysis we determine automatically the optimal values for the parameters involved in defining the polynomial smoothers and achieve fast convergence of cycles with aggressive coarsening.We also present numerical tests supporting the theoretical results and the heuristic ideas.The methods we introduce are highly parallelizable and efficient multigrid algorithms on structured and semi-structured grids in two and three spatial dimensions.