# A Robust-to-Noise Deconvolution Algorithm to Enhance Displacement and Strain Maps Obtained with Local DIC and LSA

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## Abstract

Digital Image Correlation (DIC) and Localized Spectrum Analysis (LSA) are two techniques available to extract displacement fields from images of deformed surfaces marked with contrasted patterns. Both techniques consist in minimizing the optical residual. DIC performs this minimization iteratively in the real domain on random patterns such as speckles. LSA performs this minimization nearly straightforwardly in the Fourier domain on periodic patterns such as grids or checkerboards. The particular case of local DIC performed pixelwise is considered here. In this case and regardless of noise, local DIC and LSA both provide displacement fields equal to the actual one convolved by a kernel known a priori. The kernel corresponds indeed to the Savitzky-Golay filter in local DIC, and to the analysis window of the windowed Fourier transform used in LSA. Convolution reduces the noise level, but it also causes actual details in displacement and strain maps to be returned with a damped amplitude, thus with a systematic error. In this paper, a deconvolution method is proposed to retrieve the actual displacement and strain fields from their counterparts given by local DIC or LSA. The proposed algorithm can be considered as an extension of Van Cittert deconvolution, based on the small strain assumption. It is demonstrated that it allows enhancing fine details in displacement and strain maps, while improving the spatial resolution. Even though noise is amplified after deconvolution, the present procedure can be considered as robust to noise, in the sense that off-the-shelf deconvolution algorithms do not converge in the presence of classic levels of noise observed in strain maps. The sum of the random and systematic errors is also lower after deconvolution, which means that the proposed procedure improves the compromise between spatial resolution and measurement resolution. Numerical and real examples considering deformed speckle images (for DIC) and checkerboard images (for LSA) illustrate the efficiency of the proposed approach.

## Keywords

Checkerboard Digital image correlation Displacement Deconvolution Full-field measurement Grid method Localized spectrum analysis Metrology Periodic pattern Speckle Strain## References

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