Uncertainty on fringe projection technique: A Monte-Carlo-based approach

Molimard, Jérôme; Navarro, Laurent

doi:10.1016/j.optlaseng.2013.01.023

Cited by 16 publications

(11 citation statements)

References 25 publications

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“…Even though it is possible to perform Monte‐Carlo‐based approaches to assess the measurement resolution in displacement and strain maps (see for instance), it is of prime importance to have closed‐form expressions for this measurement resolution to conveniently study the influence of various parameters. These expressions are obtained assuming that a Gaussian white noise affects the grid images (the standard deviation of this noise is a constant denoted σ image ).…”

Section: Metrological Performancementioning

confidence: 99%

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: Metrological Performancementioning

confidence: 99%

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 number of pixels per grid period is equal to five. • A Gaussian white noise n, whose standard deviation image lies between 2 7 and 2 10 , is added to the simulated grid image. image linearly decreases along the vertical axis of the synthetic grid images, from the top to the bottom.…”

Section: Image Featuring Spatially Changing Contrast and Noisementioning

confidence: 99%

50^th Anniversary Article: Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method

Grédiac

Sur

2013

Strain

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This paper deals with noise propagation from camera sensor to displacement and strain maps when the grid method is employed to estimate these quantities. It is shown that closed‐form equations can be employed to predict the link between metrological characteristics such as resolution and spatial resolution in displacement and strain maps on the one hand and various quantities characterising grid images such as brightness, contrast and standard deviation of noise on the other hand. Various numerical simulations confirm first the relevance of this approach in the case of an idealised camera sensor impaired by a homoscedastic Gaussian white noise. Actual CCD or CMOS sensors exhibit, however, a heteroscedastic noise. A pre‐processing step is therefore proposed to first stabilise noise variance prior to employing the predictive equations, which provide the resolution in strain and displacement maps due to sensor noise. This step is based on both a modelling of sensor noise and the use of the generalised Anscombe transform to stabilise noise variance. Applying this procedure in the case of a translation test confirms that it is possible to model correctly noise propagation from sensor to displacement and strain maps, and thus also to predict the actual link between resolution, spatial resolution and standard deviation of noise in grid images.

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“…Here, we propose a definition corresponding to a flat surface submitted to in-plane or out-ofplane motions. Then the confidence in the results may be estimated from previous works [17,16]. Resolution is estimated using a repeatability test at 5 µm in x and y, and 50 µm in z.…”

Section: Metrological Performancesmentioning

confidence: 99%

Characterisation of Knee Brace Migration and Associated Skin Deformation During Flexion by Full-Field Measurements

et al. 2014

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Fabric-based knee braces are widely used as orthotic devices to support and align the joint. Despite significant prescription, compliance with the treatment is often negatively affected by discomfort issues, in particular brace slippage and migration. Full-field measurements associated with digital image correlation were performed on 11 subjects to determine if the brace was able to follow skin deformation during knee flexion, which was suspected to be a primary slippage mechanism. This technique allowed measurement of relatively small slippage magnitudes, which proved to be mostly reversible on re-extension of the leg. Strain fields derived from these measurements indicated a strong influence of gender on skin deformations, and showed that slippage may be due to the inability of the brace fabric to match the non-linear mechanical behaviour of the skin. Consequently, compliance to knee braces may be improved by differentiating their design between genders and judiciously selecting fabrics based on their mechanical behaviour.

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Uncertainty on fringe projection technique: A Monte-Carlo-based approach

Cited by 16 publications

References 25 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

50^th Anniversary Article: Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method

Characterisation of Knee Brace Migration and Associated Skin Deformation During Flexion by Full-Field Measurements

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Uncertainty on fringe projection technique: A Monte-Carlo-based approach

Cited by 16 publications

References 25 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

50th Anniversary Article: Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method

Characterisation of Knee Brace Migration and Associated Skin Deformation During Flexion by Full-Field Measurements

Contact Info

Product

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50^th Anniversary Article: Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method