The geometric phase analysis method based on the local high resolution discrete Fourier transform for deformation measurement

Dai, Xianglu; Xie, Huimin; Wang, Huaixi; Li, Chuanwei; Liu, Zhanwei; Wu, Lifu

doi:10.1088/0957-0233/25/2/025402

Cited by 23 publications

(16 citation statements)

References 30 publications

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“…The reason is that wavelet transform is not adapted here because the frequency of the carrier is known a priori and is only slightly modulated by straining. The use of the FT in the particular case of grids is mentioned in or in for instance. In these last references, this gave birth to the so‐called Geometric Phase Analaysis (GPA) briefly described in Section 4.3.…”

Section: Processing Grid Images To Extract Displacement and Strain Fimentioning

confidence: 99%

“…Retrieving the phase distributions (one along the x ‐direction, one along the y ‐direction) of a grid image using the FT consists in calculating the FT of this image, filtering the corresponding spectrum by considering, in turn, a zone surrounding the peaks of each of the first harmonics ( f , 0) and (0, f ), performing the IFT of each of these zones, and finally extracting the phase distribution of each result . This procedure should be applied to both the reference and the current grid images to deduce the phase change between these two configurations.…”

Section: Processing Grid Images To Extract Displacement and Strain Fimentioning

confidence: 99%

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The Grid Method for In‐plane Displacement and Strain Measurement: A Review and Analysis

Grédiac

Sur

Blaysat

2016

Strain

141

162

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The grid method is a technique suitable for the measurement of in-plane displacement and strain components on specimens undergoing a small deformation. It relies on a regular marking of the surfaces under investigation. Various techniques are proposed in the literature to retrieve these sought quantities from images of regular markings, but recent advances show that techniques developed initially to process fringe patterns lead to the best results. The grid method features a good compromise between measurement resolution and spatial resolution, thus making it an efficient tool to characterise strain gradients. Another advantage of this technique is the ability to establish closed-form expressions between its main metrological characteristics, thus enabling to predict them within certain limits. In this context, the objective of this paper is to give the state of the art in the grid method, the information being currently spread out in the literature. We propose first to recall various techniques that were used in the past to process grid images, to focus progressively on the one that is the most used in recent examples: the windowed Fourier transform. From a practical point of view, surfaces under investigation must be marked with grids, so the techniques available to mark specimens with grids are presented. Then we gather the information available in the recent literature to synthesise the connection between three important characteristics of full-field measurement techniques: the spatial resolution, the measurement resolution and the measurement bias. Some practical information is then offered to help the readers who discover this technique to start using it. In particular, programmes used here to process the grid images are offered to the readers on a dedicated website. We finally present some recent examples available in the literature to highlight the effectiveness of the grid method for in-plane displacement and strain measurement in real situations.

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Section: Processing Grid Images To Extract Displacement and Strain Fimentioning

confidence: 99%

Section: Processing Grid Images To Extract Displacement and Strain Fimentioning

confidence: 99%

The Grid Method for In‐plane Displacement and Strain Measurement: A Review and Analysis

Grédiac

Sur

Blaysat

2016

Strain

141

162

View full text Add to dashboard Cite

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“…Various Fourier-based image processing techniques can be used to process grid images to retrieve phase, displacement and strain maps, for instance sampling moiré [40], geometric phase analysis [41] and Windowed Fourier Transform (WFT). Concerning the WFT, two main approaches can be considered, either taking, in the Fourier domain, a set of frequencies close to the nominal grid frequency [42,43], or picking only the nominal frequency of the grid and performing phase extraction with this sole frequency [44,39,17]. We propose to consider here only the last case for two main reasons (besides the computation time which is much shorter in this case):…”

Section: Localized Spectrum Analysismentioning

confidence: 99%

A Critical Comparison of Some Metrological Parameters Characterizing Local Digital Image Correlation and Grid Method

2017

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International audienceThe main metrological performance of two full-field measurement techniques, namely local digital image correlation (DIC) and grid method (GM), are compared in this paper. The fundamentals of these techniques are first briefly recalled. The formal link which exists between them is then given (the details of the calculation are in Appendix 1). Under mild assumptions, it is shown that GM theoretically gives the same result as DIC, since the formula providing the displacement with GM is the solution of the minimization of the cost function used in DIC in the particular case of a regular marking. In practice however, the way the solution is found being totally different from one technique to another, they feature different metrological performance. Some of the metrological characteristics of DIC and GM are studied in this paper. Since neither guideline nor precise standard is available to perform a fair comparison between them, a methodology must first be defined. It is proposed here to rely on three metrological parameters, namely the displacement resolution, the bias and the spatial resolution, to assess the metrological performance of each technique. These three parameters are thoroughly defined in the paper. Some of these quantities depend on external parameters such as the pattern of the surface of interest, so the same set of grid images is processed with both techniques. Only the contribution of the camera sensor noise to the displacement resolution is considered in this study. The displacement resolution, the bias and the spatial resolution are not independent but linked. These links are therefore studied in depth for DIC and GM and compared. In particular, it is shown that the product between the displacement resolution and the spatial resolution can be considered as a metric to perform this comparison. The extension to speckled patterns of the lessons drawn from grids is finally addressed in the last part of the paper. As a general conclusion, it can be said that for the value of the bias fixed in this study, the additional cost due to grid depositing offers GM to feature a better compromise than subset-based local DIC between displacement resolution and spatial resolution

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“…These patterns are those of crystal structures observed at the atomic scale. GPA being a purely geometric technique, it has also been used at the macroscopic level to process grid images, [17,13] for instance. In the present paper, the idea is to use it to retrieve phase maps (and thus subsequent displacement and strain maps) from checkerboard images.…”

Section: Geometric Phase Analysismentioning

confidence: 99%

Comparing several spectral methods used to extract displacement fields from checkerboard images

Grédiac

Blaysat

Sur

2020

Optics and Lasers in Engineering

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Checkerboard represents the best pattern for in-plane displacement measurement in terms of sensor noise propagation because this pattern maximizes image gradient. It also exhibits other interesting properties in terms of pattern-induced bias for instance. Digital Image Correlation (DIC) is not the best option to extract displacement fields from such periodic patterns, and spectral methods should be used instead. In this paper, it is shown that three different spectral techniques initially developed for classic bidimensional grids can be adapted to process checkerboard images. These three techniques are the Geometric Phase Analysis (GPA), the windowed version of the Geometric Phase Analysis (WGPA), and the Localized Spectrum Analysis (LSA), which can be regarded as the ultimate version of WGPA. The main features of these three techniques as well as the link between them are given in this paper. Their metrological performance are compared in terms of displacement resolution, spatial resolution and bias. Synthetic checkerboard images deformed with a suitable reference displacement field are considered for this purpose. It is shown that GPA is the fastest method. According to the metric used in this paper, the best metrological performance is obtained with WGPA with suitable settings. LSA followed by a deconvolution algorithm is just behind, but the calculation time is approximately 10 times lower than that of WGPA for the examples considered in this paper, which makes it a reasonable choice for the determination of in-plane displacement fields from checkerboard images.

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The geometric phase analysis method based on the local high resolution discrete Fourier transform for deformation measurement

Cited by 23 publications

References 30 publications

The Grid Method for In‐plane Displacement and Strain Measurement: A Review and Analysis

The Grid Method for In‐plane Displacement and Strain Measurement: A Review and Analysis

A Critical Comparison of Some Metrological Parameters Characterizing Local Digital Image Correlation and Grid Method

Comparing several spectral methods used to extract displacement fields from checkerboard images

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