Image-based Continuous Displacement Measurements Using an Improved Spectral Approach

• Published in: Strain 2013-06, Vol.49 (3), p.233-248
• Main Authors: Mortazavi, F., Lévesque, M., Villemure, I.
• Format: Article
• Language: English
• Subjects: continuous displacements; Digital Image Correlation; fast Fourier transform; inverse problem; noise sensitivity
• ISSN: 0039-2103; 1475-1305
• DOI: 10.1111/str.12031

ABSTRACT Digital Image Correlation algorithms capable of determining continuous displacement fields are receiving growing attention in the field of mechanical properties identification. In this paper, we develop an Improved Spectral Approach (ISA) to reconstruct continuous displacements based on their Fourier decomposition. This approach leads to a time and memory‐efficient algorithm, thanks to the fast Fourier transform. Moreover, the Fourier‐based decomposition enables accurate heterogeneous measurements. Improvements consist in increasing the accuracy and convergence rate as well as dealing with non‐periodic displacements and images. Furthermore, a theoretical framework is presented to quantify the noise sensitivity of the ISA from which useful information is retrieved. The approach is evaluated using synthetic images deformed by heterogeneous displacement fields. Comparisons show that the introduced modifications lead to lower uncertainties by one order of magnitude in the case of non‐periodic images and displacement field studied. Moreover, first‐order (SO1) and second‐order (SO2) subset‐based Digital Image Correlation algorithms are compared with the ISA. The comparisons herein reveal that the uncertainties of the ISA are 6–9 times smaller than those of the SO1 due to insufficiency of the first‐order shape function for the estimation of heterogeneous displacements, while being slightly smaller than those of the SO2. Moreover, as the image smoothness decreases, the uncertainties of the SO2 deviate from those of the ISA and the exact displacements. The presented approach shows great potentials for challenging applications such as strain measurements at microstructural levels.