Journal of Mathematical Imaging and Vision

, Volume 56, Issue 3, pp 472–498 | Cite as

Influence of the Analysis Window on the Metrological Performance of the Grid Method

  • Frédéric SurEmail author
  • Michel Grédiac


This paper deals with the grid method in experimental mechanics. It is one of the full-field methods available for estimating in-plane displacement and strain components of a specimen submitted to a load producing slight local deformation. This method consists in, first, depositing a regular grid on the surface of a specimen, and, second, comparing images of the grid before and after deformation. A possibility is to perform windowed Fourier analysis to measure these deformations as changes of the local grid aspect. The aim of the present study is to investigate the choice of the analysis window and its influence on the metrological performances of the grid method. Two aspects are taken into account, namely the reduction of the harmonics of the grid line profile, which are not pure sine because of manufacturing constraints, and the transfer of the digital noise from the imaged grid to the mechanical measurements. A theoretical study and a numerical assessment are presented. In addition, the interested reader can find in this paper a calculation of the Wigner–Ville transform of a triangular function which, to the best of the present authors’ knowledge, is not available in the existing literature.


Image-based contactless measurement Displacement and strain maps Grid method Windowed Fourier analysis Spatially correlated noise Derivative of a random process Wigner–Ville transform 



This work is partially funded by GdR CNRS ISIS (Timex project).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Université de LorraineVandoeuvre-lès-Nancy CedexFrance
  2. 2.Clermont Université, Université Blaise Pascal. Institut PascalClermont-FerrandFrance

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