# Spatial DIC Errors due to Pattern-Induced Bias and Grey Level Discretization

- 125 Downloads

## Abstract

Digital image correlation (DIC) is an optical metrology method widely used in experimental mechanics for full-field shape, displacement and strain measurements. The required strain resolution for engineering applications of interest mandates DIC to have a high image displacement matching accuracy, on the order of 1/100th of a pixel, which necessitates an understanding of DIC errors. In this paper, we examine two spatial bias terms that have been almost completely overlooked. They cause a persistent offset in the matching of image intensities and thus corrupt DIC results. We name them pattern-induced bias (PIB), and intensity discretization bias (IDB). We show that the PIB error occurs in the presence of an undermatched shape function and is primarily dictated by the underlying intensity pattern for a fixed displacement field and DIC settings. The IDB error is due to the quantization of the gray level intensity values in the digital camera. In this paper we demonstrate these errors and quantify their magnitudes both experimentally and with synthetic images.

## Keywords

Digital image correlation Pattern induced bias Intensity discretization bias Pattern induced errors Uncertainty quantification## Notes

### Acknowledgements

Thank you to Mr. Paul Farias for his assistance during the experimental work, Dr. Daniel Turner for his assistance during internal writing review, and Dr. Elizabeth Jones for advising and review in the writing process. This work was supported by the Laboratory Directed Research and Development program at Sandia National Laboratories, a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

## References

- 1.Jones E, Reu P (2017) Distortion of Digital Image Correlation (DIC) Displacements and Strains from Heat Waves. Exp Mech:1–24Google Scholar
- 2.Sutton MA et al (2008) The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. 46(10):746–757Google Scholar
- 3.Schreier HW, Braasch JR, Sutton MA (2000) Systematic errors in digital image correlation caused by intensity interpolation. Opt Eng 39(11):2915–2921CrossRefGoogle Scholar
- 4.Wang YQ et al (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
- 5.Lehoucq R, Reu P, Turner D (2017) The effect of the ill-posed problem on quantitative error assessment in digital image correlation. Exp Mech:1–13Google Scholar
- 6.Schreier HW, Sutton MAJEM (2002) Systematic errors in digital image correlation due to undermatched subset shape functions. 42(3):303–310Google Scholar
- 7.Yu L, Bing P (2015) The errors in digital image correlation due to overmatched shape functions. Meas Sci Technol 26(4):045202CrossRefGoogle Scholar
- 8.Grediac M, Blaysat B, Sur F (2017) A Critical Comparison of Some Metrological Parameters Characterizing Local Digital Image Correlation and Grid Method. Exp Mech 57(6):871–903CrossRefGoogle Scholar
- 9.Reu, P.L., et al., DIC challenge: developing images and guidelines for evaluating accuracy and resolution of 2D analyses. 2017: p. 1–33CrossRefGoogle Scholar
- 10.Reu PL et al (2017) DIC Challenge: Developing Images and Guidelines for Evaluating Accuracy and Resolution of 2D Analyses. Exp MechGoogle Scholar
- 11.Grédiac M, Sur F (2013) Effect of Sensor Noise on the Resolution and Spatial Resolution of Displacement and Strain Maps Estimated with the Grid Method. StrainGoogle Scholar
- 12.Lucas, B.D. and T. Kanade, An iterative image registration technique with an application to stereo vision. 1981Google Scholar
- 13.Sur F, Blaysat B, Grédiac M (2017) Rendering Deformed Speckle Images with a Boolean Model. Journal of Mathematical Imaging and VisionGoogle Scholar
- 14.Yuan Y et al (2014) Accurate displacement measurement via a self-adaptive digital image correlation method based on a weighted ZNSSD criterion. 52:75–85Google Scholar
- 15.Wang D et al (2016) Bias reduction in sub-pixel image registration based on the anti-symmetric feature. 27(3):035206Google Scholar
- 16.MATLAB. LOWESS Smoothing. https://www.mathworks.com/help/curvefit/lowess-smoothing.html. Accessed 18 Feb 2019
- 17.Cleveland WSJAS (1981) LOWESS: A program for smoothing scatterplots by robust locally weighted regression. 35(1):54CrossRefGoogle Scholar
- 18.Patterson EA (2007) et al, Calibration and evaluation of optical systems for full-field strain measurement. 45(5):550–564Google Scholar
- 19.Balcaen R (2017) et al, Stereo-DIC uncertainty quantification based on simulated images. 57(6):939–951Google Scholar
- 20.A Good Practices Guide for Digital Image Correlation (2018) M.A.I. E.M.C. Jones, Editor. International Digital Image Correlation SocietyGoogle Scholar