Digital Image Correlation - Overview

Overview

Digital image correlation (DIC) techniques have been increasing in popularity, especially in micro- and nano-scale mechanical testing applications due to its relative ease of implementation and use. Advances in computer technology and digital cameras have been the enabling technologies for this method and while white-light optics has been the predominant approach, DIC can be and has been extended to almost any imaging technology.

The concept of using correlation to measure shifts in datasets has been known for a long time, and it was applied to digital images at least as early as 1975. The present day applications are almost innumerable and include image analysis, image compression, velocimetry, and strain estimation. Much early work in DIC in the field of mechanics was led by researchers at the University of South Carolina in the early 1980s and has been optimized and improved in recent years. Commonly, DIC relies on the maximization of a correlation coefficient that is determined by examining pixel intensity array subsets on two or more corresponding images and extracting the deformation mapping function that relates the images (Figure 1). However, there are other methods that do not directly analyze the correlation coefficient, as is common in phase correlation. An iterative approach can be used to maximize the correlation coefficient by using nonlinear optimization techniques. The nonlinear optimization approach tends to be conceptually simpler, but as with most nonlinear optimization techniques, it is quite slow, and the problem can sometimes be reduced to a much faster and more stable linear optimization in phase space.

The cross correlation coefficient is defined as


r_{ij}(u,v,\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},\frac{\partial v}{\partial x},\frac{\partial v}{\partial y}) = 1 - \frac{\sum_i \sum_j }{\sqrt{\sum_i \sum_j {^2} \sum_i \sum_j {^2}}}

Here F(xi ,yj) is the pixel intensity or the gray scale value at a point (xi ,yj) in the undeformed image. G(xi* ,yj*) is the gray scale value at a point (xi* ,yj*) in the deformed image. and are mean values of the intensity matrices F and G, respectively. The coordinates or grid points (xi ,yj) and (xi* ,yj*) are related by the deformation that occurs between the two images. If the motion is perpendicular to the optical axis of the camera, then the relation between (xi ,yj) and (xi* ,yj*) can be approximated by a 2D affine transformation such as:

Here u and v are translations of the center of the sub-image in the X and Y directions, respectively. The distances from the center of the sub-image to the point (x, y) are denoted by and . Thus, the correlation coefficient rij is a function of displacement components (u, v) and displacement gradients

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DIC has proven to be very effective at mapping deformation in macroscopic mechanical testing, where the application of specular markers (e.g. paint, toner powder) or surface finishes from machining and polishing provide the needed contrast to correlate images well. However, these methods for applying surface contrast do not extend to the application of freestanding thin films for several reasons. First, vapor deposition at normal temperatures on semiconductor grade substrates results in mirror-finish quality films with RMS roughnesses that are typically on the order of several nanometers. No subsequent polishing or finishing steps are required, and unless electron imaging techniques are employed that can resolve microstructural features, the films do not possess enough useful surface contrast to adequately correlate images. Typically this challenge can be circumvented by applying paint that results in a random speckle pattern on the surface, although the large and turbulent forces resulting from either spraying or applying paint to the surface of a freestanding thin film are too high and would break the specimens. In addition, the sizes of individual paint particles are on the order of μms, while the film thickness is only several hundred nms, which would be analogous to supporting a large boulder on a thin sheet of paper.

Very recently, advances in pattern application and deposition at reduced length scales have exploited small-scale synthesis methods including nano-scale chemical surface restructuring and photolithography of computer-generated random specular patterns to produce suitable surface contrast for DIC. The application of very fine powder particles that electrostatically adhere to the surface of the specimen and can be digitally tracked is one approach. For Al thin films, fine alumina abrasive polishing powder was initially used since the particle sizes are relatively well controlled, although the adhesion to Al films was not very good and the particles tended to agglomerate excessively. The candidate that worked most effectively was a silica powder designed for a high temperature adhesive compound (Aremco, inc.), which was applied through a plastic syringe. A light blanket of powder would coat the gage section of the tensile sample and the larger particles could be blown away gently. The remaining particles would be those with the best adhesion to the surface, and under low-angle grazing illumination conditions, the specimen gage section would appear as shown in Figure 2. While the surface contrast present is not ideal for DIC, the high intensity ratio between the particles and the background provide a unique opportunity to track the particles between consecutive digital images taken during deformation. This can be achieved quite straightforwardly using digital image processing techniques, although the resolution is always limited to a single pixel. To attain tracking with subpixel resolution, a novel image-based tracking algorithm using MATLAB was developed, dubbed Digital Differential Image Tracking (DDIT), and will be discussed here briefly.

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