# American Institute of Mathematical Sciences

February  2014, 8(1): 259-291. doi: 10.3934/ipi.2014.8.259

## Towards deconvolution to enhance the grid method for in-plane strain measurement

 1 LORIA - projet Magrit, Université de Lorraine, Cnrs, Inria, Umr 7503, Campus Scientifique BP 239, 54506 Vanduvre-lès-Nancy cedex, France 2 Institut Pascal, Clermont Université, Cnrs Umr 6602, Université Blaise Pascal BP 10448, 63000 Clermont-Ferrand, France

Received  November 2012 Revised  June 2013 Published  March 2014

The grid method is one of the techniques available to measure in-plane displacement and strain components on a deformed material. A periodic grid is first transferred on the specimen surface, and images of the grid are compared before and after deformation. Windowed Fourier analysis-based techniques permit to estimate the in-plane displacement and strain maps. The aim of this article is to give a precise analysis of this estimation process. It is shown that the retrieved displacement and strain maps are actually a tight approximation of the convolution of the actual displacements and strains with the analysis window. The effect of digital image noise on the retrieved quantities is also characterized and it is proved that the resulting noise can be approximated by a stationary spatially correlated noise. These results are of utmost importance to enhance the metrological performance of the grid method, as shown in a separate article.
Citation: Frédéric Sur, Michel Grédiac. Towards deconvolution to enhance the grid method for in-plane strain measurement. Inverse Problems & Imaging, 2014, 8 (1) : 259-291. doi: 10.3934/ipi.2014.8.259
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