Experimental Mechanics

, Volume 59, Issue 2, pp 207–218 | Cite as

Extracting Displacement and Strain Fields from Checkerboard Images with the Localized Spectrum Analysis

  • M. GrédiacEmail author
  • B. Blaysat
  • F. Sur


The performance of white-light full-field measurement methods strongly depends on the nature of the pattern used to mark the surface on which displacements and strains are measured. Finding optimized patterns is therefore a topical question. The aim of this study is to examine the case of the checkerboard pattern. It is first shown that this periodic pattern can be processed with a Fourier-based technique such as LSA. Experiments are then carried out to compare the noise level in displacement and strain maps obtained by processing classic 2D grid and checkerboard images. The conclusion is that the noise level observed in displacement and strain maps is significantly lower with a checkerboard than with a classic 2D grid. A notched specimen is finally tested to illustrate that very low strain levels can be measured with checkerboard patterns.


Checkerboard Digital image correlation Grid method Heteroscedastic noise Localized spectrum analysis Metrology Optimal pattern Pattern optimization Windowed Fourier transform 


  1. 1.
    Bomarito GF, Hochhalter JD, Ruggles TJ, Cannon AH (2017) Increasing accuracy and precision of digital image correlation through pattern optimization. Opt Lasers Eng 91:73–85CrossRefGoogle Scholar
  2. 2.
    Pan B, Xie H, Wang Z, Qian K, Wang Z (2008) Study on subset size selection in digital image correlation for speckle patterns. Opt Express 16(10):703–7048CrossRefGoogle Scholar
  3. 3.
    Sutton M, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements. Basic concepts, theory and applications. Springer, BerlinGoogle Scholar
  4. 4.
    Wang YQ, Sutton M, Bruck H, Schreier HW (2009) Quantitative error assessment in pattern matching: effects of intensity pattern noise, interpolation, strain and image contrast on motion measurements. Strain 45(2):16–178CrossRefGoogle Scholar
  5. 5.
    Réthoré J (2010) A fully integrated noise robust strategy for the identification of constitutive laws from digital images. Int J Numer Methods Eng 84(6):63–660CrossRefzbMATHGoogle Scholar
  6. 6.
    Grédiac M, Blaysat B, Sur F (2017) A critical comparison of some metrological parameters characterizing local digital image correlation and grid method. Exp Mech 57(3):871–903CrossRefGoogle Scholar
  7. 7.
    Sur F, Grédiac M (2016) Influence of the analysis window on the metrological performance of the grid method. J Math Imaging Vision 56(3):472–498MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Grafarend EW (2006) Linear and nonlinear models: fixed effects, random effects, and mixed models. Walter de GruyterGoogle Scholar
  9. 9.
    Surrel Y (1994) Moiré and grid methods: a signal-processing approach. In: Stupnicki J, Pryputniewicz RJ (eds) Interferometry’94: photomechanics, vol 2342. SPIEGoogle Scholar
  10. 10.
    Surrel Y (1997) Design of phase-detection algorithms insensitive to bias modulation. Appl Opt 36(4):805–807CrossRefGoogle Scholar
  11. 11.
    Grédiac M, Sur F, Blaysat B (2016) The grid method for in-plane displacement and strain measurement: a review and analysis. Strain 52(3):205–243CrossRefGoogle Scholar
  12. 12.
    Sur F, Grédiac M (2014) Towards deconvolution to enhance the grid method for in-plane strain measurement. Inverse Problems and Imaging 8(1):259–291. American Institute of Mathematical SciencesMathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Piro JL, Grédiac M (2004) Producing and transferring low-spatial-frequency grids for measuring displacement fields with moiré and grid methods. Exp Tech 28(4):23–26CrossRefGoogle Scholar
  14. 14.
    Sur F, Blaysat B, Grédiac M (2016) Determining displacement and strain maps immune from aliasing effect with the grid method. Opt Lasers Eng 86:317–328CrossRefGoogle Scholar
  15. 15.
    Dai X, Xie H, Wang H, Li C, Liu Z, Wu L (2014) The geometric phase analysis method based on the local high resolution discrete fourier transform for deformation measurement. Meas Sci Technol 25(2):025402CrossRefGoogle Scholar
  16. 16.
    Dai X, Xie H, Wang H (2014) Geometric phase analysis based on the windowed fourier transform for the deformation field measurement. Opt Laser Technol 58(6):119–127CrossRefGoogle Scholar
  17. 17.
    Avril S, Ferrier E, Vautrin A, Hamelin P, Surrel Y (2004) A full-field optical method for the experimental analysis of reinforced concrete beams repaired with composites. Composites Part A 35(7-8):873–884CrossRefGoogle Scholar
  18. 18.
    Pierron F, Zhu H, Siviour C (2014) Beyond Hopkinson’s bar. Philos Trans R Soc A Math Phys Eng Sci 372(2023):20130195CrossRefGoogle Scholar
  19. 19.
    Rossi M, Pierron F, Forquin P (2014) Assessment of the metrological performance of an in situ storage image sensor ultra-high speed camera for full-field deformation measurements. Meas Sci Technol 25(2):025401CrossRefGoogle Scholar
  20. 20.
    Le Louedec G, Pierron F, Sutton MA, Siviour C, Reynolds AP (2015) Identification of the dynamic properties of Al 5456 FSW welds using the virtual fields method. Journal of Dynamic Behavior of Materials.
  21. 21.
    Lukic B, Saletti D, Forquin P (2017) Use of simulated experiments for material characterization of brittle materials subjected to high strain rate dynamic tension. Philos Trans R Soc A Math Phys Eng Sci 28(2085):375. pii: 20160168Google Scholar
  22. 22.
    Haddadi H, Belhabib S (2008) Use of a rigid-body motion for the investigation and estimation of the measurement errors related to digital image correlation technique. Opt Lasers Eng 46(2):185– 96CrossRefGoogle Scholar
  23. 23.
    Reu P (2014) All about speckles: aliasing. Exp Tech 38(5):1–3CrossRefGoogle Scholar
  24. 24.
    Healey GE, Kondepudy R (1994) Radiometric ccd camera calibration and noise estimation. IEEE Trans Pattern Anal Mach Intell 16(3):267–276CrossRefGoogle Scholar
  25. 25.
    Boulanger J, Kervrann C, Bouthemy P, Elbau P, Sibarita J-B , Salamero J (2010) Patch-based nonlocal functional for denoising fluorescence microscopy image sequences. IEEE Trans Med Imaging 29(2):442–454CrossRefGoogle Scholar
  26. 26.
    Foi A, Trimeche M, Katkovnik V, Egiazarian K (2008) Practical Poissonian-Gaussian noise modeling and fitting for single-image raw-data. IEEE Trans Image Process 17(10):1737– 1754MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Ramani S, Vonesch C, Unser M (2008) Deconvolution of 3D fluorescence micrographs with automatic risk minimization. In: Proceedings of the IEEE international symposium on biomedical imaging (ISBI), pp 732–735Google Scholar
  28. 28.
    Sur F, Grédiac M (2015) On noise reduction in strain maps obtained with the grid method by averaging images affected by vibrations. Opt Lasers Eng 66:210–222CrossRefGoogle Scholar

Copyright information

© Society for Experimental Mechanics 2018

Authors and Affiliations

  1. 1.SIGMA, Institut Pascal, UMR CNRS 6602Université Clermont AuvergneClermont-FerrandFrance
  2. 2.Laboratoire Lorrain de Recherche en Informatique et ses Applications, UMR CNRS 7503Université de Lorraine, CNRS, INRIA projet MagritVandoeuvre-les-Nancy CedexFrance

Personalised recommendations