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

## Abstract

The 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.

## Keywords

Digital image correlation Displacement Full-field measurement Grid method Metrology Strain## Notes

### Acknowledgments

The GDR CNRS ISIS is gratefully acknowledged for its partial financial support of this study (TIMEX project).

## References

- 1.Wang Z Y, Li H Q, Tonga J W, Ruan J T (2007) Statistical analysis of the effect of intensity pattern noise on the displacement measurement precision of digital image correlation using self-correlated images. Exp Mech 47(5):701–707CrossRefGoogle Scholar
- 2.Bornert M, Brémand F, Doumalin P, Dupré J -C, Fazzini M, Grédiac M, Hild F, Mistou S, Molimard J, Orteu J -J, Robert L, Surrel Y, Vacher P, Wattrisse B (2009) Assessment of digital image correlation measurement errors: methodology and results. Exp Mech 49(3):353–370CrossRefGoogle Scholar
- 3.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
- 4.Lava P, Cooreman S, Coppieters S, DeStrycker M, Debruyne D (2009) Assessment of measuring errors in DIC using deformation fields generated by plastic FEA. Opt Lasers Eng 47(7):747–753CrossRefGoogle Scholar
- 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):631–660CrossRefMATHGoogle Scholar
- 6.Reu P (2013) Calibration: a good calibration image. Exp Tech 37(6):1–3CrossRefGoogle Scholar
- 7.Reu P (2014) Speckles and their relationship to the digital camera. Exp Tech 38(4):1–2MathSciNetCrossRefGoogle Scholar
- 8.Badaloni M, Rossi M, Chiappini G, Lava P, Debruyne D (2015) Impact of experimental uncertainties on the identification of mechanical material properties using DIC. Exp Mech 55(8):1411–1426CrossRefGoogle Scholar
- 9.Reu P (2015) All about speckles: contrast. Exp Tech 39(1):1–2CrossRefGoogle Scholar
- 10.Gras R, Leclerc H, Hild F, Roux S, Schneider J (2015) Identification of a set of macroscopic elastic parameters in a 3d woven composite Uncertainty analysis and regularization. Int J Solids Struct 55:2–16CrossRefGoogle Scholar
- 11.Wittevrongel L, Lava P, Lomov S V, Debruyne D (2015) A self adaptive global digital image correlation algorithm. Exp Mech 55(2):361–378CrossRefGoogle Scholar
- 12.Wang Y, Lava P, Reu P, Debruyne D (2016) Theoretical analysis on the measurement errors of local 2D DIC Part I part i temporal and spatial uncertainty quantification of displacement measurements. Strain 52 (2):110–128CrossRefGoogle Scholar
- 13.Blaysat B, Grédiac M, Sur F (2016) Effect of interpolation on noise propagation from images to DIC displacement maps. Int J Numer Methods Eng 108(3):213–232MathSciNetCrossRefGoogle Scholar
- 14.Blaysat B, Grédiac M, Sur F (2016) On the propagation of camera sensor noise to displacement maps obtained by DIC. Exp Mech 56(6):919–944CrossRefGoogle Scholar
- 15.Sur F, Grédiac M (2014) Towards deconvolution to enhance the grid method for in-plane strain measurement. Inverse Probl Imag 8(1):259–291. American Institute of Mathematical SciencesMathSciNetCrossRefMATHGoogle Scholar
- 16.Grédiac M, Sur F (2014) Effect of sensor noise on the resolution and spatial resolution of the displacement and strain maps obtained with the grid method. Strain 50(1):1–27. Paper invited for the 50th anniversary of the journalCrossRefGoogle Scholar
- 17.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
- 18.Sur F, Grédiac M (2016) Influence of the analysis window on the metrological performance of the grid method. J Math Imag Vis 56(3):472–498MathSciNetCrossRefMATHGoogle Scholar
- 19.Patterson E A, Hack E, Brailly P, Burguete R L, Saleeme Q, Siebert T, Tomlinsone R A, Whelan M P (2007) Calibration and evaluation of optical systems for full-field strain measurement. Opt Lasers Eng 45(5):550–564CrossRefGoogle Scholar
- 20.Hack E, Lampeas G, Mottershead J E, Patterson E A, Siebert T, Whelan M P (2011) Progress in developing a standard for dynamic strain analysis. In: Experimental and applied mechanics, volume 6 of conference proceedings of the society for experimental mechanics series, pp 425–429Google Scholar
- 21.Sebastian C, Lin X, Hack E, Patterson E (2015) A reference material for establishing uncertainty for static and dynamic displacements. In: Proceedings of the SEM conference. Costa Mesa, to appearGoogle Scholar
- 22.Hack E, Lin X, Patterson EA, Sebastian CM (2015) A reference material for establishing uncertainties in full-field displacement measurements. Measur Sci Technol 26(7):075004CrossRefGoogle Scholar
- 23.Standard guide for evaluating non-contacting optical strain measurement systems, ASTM standard E2208-02 (2010)Google Scholar
- 24.JCGM 200 (2008) International vocabulary of metrology basic and general concepts and associated termsGoogle Scholar
- 25.Doumalin P, Bornert M, Caldemaison D (1999) Microextensometry by image correlation applied to micromechanical studies using the scanning electron microscopy. In: Japanese Society for Experimental Mechanics (ed) Proceedings of the international conference on advanced technology in experimental mechanics. Ube City, pp 81–86Google Scholar
- 26.Schreier H W, Sutton M A (2002) Systematic errors in digital image correlation due to undermatched subset shape functions. Exp Mech 42(3):303–310CrossRefGoogle Scholar
- 27.Sutton M, Orteu J J, Schreier H (2009) Image correlation for shape, motion and deformation measurements. Basic concepts, theory and applications. SpringerGoogle Scholar
- 28.Fedele R, Galantucci L, Ciani A (2013) Global 2d digital image correlation for motion estimation in a finite element framework: a variational formulation and a regularized, pyramidal, multi-grid implementation. Int J Numer Methods Eng 96(12):739– 762CrossRefMATHGoogle Scholar
- 29.Besnard G, Hild F, Roux S (2006) Finite-element displacement fields analysis from digital images: application to Portevin-Le Chatelier bands. Exp Mech 46(6):1–15CrossRefGoogle Scholar
- 30.Sun Y, Pang J H L, Wong C K, Su F (2005) Finite element formulation for a digital image correlation method. Appl Opt 44(34):7357–7363CrossRefGoogle Scholar
- 31.Hild F, Roux S (2012) Comparison of local and global approaches to digital image correlation. Exp Mech 52(9):1503–1519CrossRefGoogle Scholar
- 32.Pan B, Wang B, Lubineau G, Moussawi A (2015) Comparison of subset-based local and finite element-based global digital image correlation. Exp Mech 55(5):887–901CrossRefGoogle Scholar
- 33.Wang B, Pan B (2016) Subset-based local vs. finite element-based global digital image correlation: a comparison study. Theor Appl Mech Lett 6(5):200–208CrossRefGoogle Scholar
- 34.Neggers J, Blaysat B, Hoefnagels J P M, Geers M G D (2016) On image gradients in digital image correlation. Int J Numer Methods Eng 105(4):243–260MathSciNetCrossRefGoogle Scholar
- 35.Badulescu C, Grédiac M, Mathias J-D (2009) Investigation of the grid method for accurate in-plane strain measurement. Measur Sci Technol 20(9):20:095102. doi: 10.1088/0957--0233/20/9/095102. IOP
- 36.Ri S, Fujigaki M, Morimoto Y (2010) Sampling moiré method for accurate small deformation distribution measurement. Exp Mech 50(4):501–508CrossRefGoogle Scholar
- 37.Hïtch M J, Snoeck E, Kilaas R (1998) Quantitative measurement of displacement and strain fields from HREM micrographs. Ultramicroscopy 74:131–146CrossRefGoogle Scholar
- 38.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. Measur Sci Technol 25(2):025402CrossRefGoogle Scholar
- 39.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
- 40.Surrel Y (2000) Photomechanics, topics in applied physic, vol 77, chapter Fringe Analysis, pp 55–102Google Scholar
- 41.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
- 42.Huntley J M (1989) Noise-immune phase unwrapping algorithm. Appl Opt 28(16):3268–3270CrossRefGoogle Scholar
- 43.Arevallilo Herraez M A, Boticario J G, Lalor M J, Burton D R (2002) Agglomerative clustering-based approach for two-dimensional phase unwrapping. Appl Opt 41(35):7437–7444CrossRefGoogle Scholar
- 44.ISO 5725. Accuracy (trueness and precision) of measurement methods and results, 1994. the International Organization for StandardizationGoogle Scholar
- 45.Schreier H, Hubert W, Braasch J R, Sutton M (2000) Systematic errors in digital image correlation caused by intensity interpolation. Opt Eng 39(11):2915–2921CrossRefGoogle Scholar
- 46.Reu P L (2011) Experimental and numerical methods for exact subpixel shifting. Exp Mech 51(4):443–452CrossRefGoogle Scholar
- 47.Su Y, Zhang Q, Gao Z, Xu X, Wu X (2015) Fourier-based interpolation bias prediction in digital image correlation. Opt Express 23(15):19242–19260CrossRefGoogle Scholar
- 48.Tong W (2013) Formulation of Lucas-Kanade digital image correlation algorithms for non-contact deformation measurements: a review. Strain 49(4):313–334CrossRefGoogle Scholar
- 49.Badulescu C, Grédiac M, Mathias J -D, Roux D (2009) A procedure for accurate one-dimensional strain measurement using the grid method. Exp Mech 49(6):841–854CrossRefGoogle Scholar
- 50.Wang Y Q, Sutton M, Bruck H, Schreier H W (2009) Quantitative error assessment in pattern matching: effects of intensity pattern noise, interpolation, strain and image contrast on motion measurements. Strain 45(2):160–178CrossRefGoogle Scholar
- 51.Savitzky A, Golay M J E (1964) Smoothing and differentiation of data by simplified least-squares procedures. Anal Chem 36(3):1627–1639CrossRefGoogle Scholar
- 52.Grafarend E W (2006) Linear and nonlinear models: fixed effects, random effects, and mixed models. Walter de GruyterGoogle Scholar
- 53.Grédiac M, Sur F, Badulescu C, Mathias J -D (2013) Using deconvolution to improve the metrological performance of the grid method. Opt Lasers Eng 51(6):716–734CrossRefGoogle Scholar
- 54.Yu L, Pan B (2015) The errors in digital image correlation due to overmatched shape functions. Measur Sci Technol 26(4): 045202CrossRefGoogle Scholar
- 55.Badulescu C, Grédiac M, Haddadi H, Mathias J -D, Balandraud X, Tran H -S (2011) Applying the grid method and infrared thermography to investigate plastic deformation in aluminium multicrystal. Mech Mater 43(11):36–53CrossRefGoogle Scholar
- 56.Chrysochoos A, Surrel Y (2012) Chapter 1. Basics of metrology and introduction to techniques. In: Grédiac M, Hild F (eds) Full-field measurements and identification in solid mechanics. Wiley, pp 1–29Google Scholar
- 57.Zhao B, Surrel Y (1997) Effect of quantization error on the computed phase of phase-shifting measurements. Appl Opt 36(12):2070–2075CrossRefGoogle Scholar
- 58.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– 1754MathSciNetCrossRefGoogle Scholar
- 59.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):7037–7048CrossRefGoogle Scholar
- 60.Badulescu C, Bornert M, Duprè J -C, Equis S, Grédiac M, Molimard J, Picart P, Rotinat R, Valle V (2013) Demodulation of spatial carrier images: performance analysis of several algorithms. Exp Mech 53(8):1357–1370CrossRefGoogle Scholar
- 61.Buades A, Le T M, Morel J M, Vese L A (2010) Fast cartoon + texture image filters. IEEE Trans Image Process 19(8):1978– 1986MathSciNetCrossRefGoogle Scholar
- 62.Foroosh H, Zerubia J B, Berthod M (2002) Extension of phase correlation to subpixel registration. IEEE Trans Image Process 11(3):188–200CrossRefGoogle Scholar
- 63.Chen D J, Chiang F P, Tan Y S, Don H S (1993) Digital speckle-displacement measurement using a complex spectrum method. Appl Opt 32(11):1839–1849CrossRefGoogle Scholar