1 A New Method for Improving Measurement Accuracy of Digital Image Correlation 3 Fig. 1.2 Schematic of system error reduction strategy using quasi odd function feature strategy, the deformed speckle image with the symmetric displacement is obtained by Fourier Shift theorem. Due to the fact that the true displacement of the sampled point is unknown in practical application, the symmetric displacement is estimated by the traditional DIC calculation. Here it should be noted that the updated deformed speckle image with the symmetric displacement is generated from the original deformed image (not the reference image), since the noises of the original deformed and reference images are different. So the amplitude of the final translated displacement is double of that of the symmetric displacement estimated by DIC calculation. As displayed in Fig. 1.2, the first step of the developed strategy is implementing the traditional DIC calculation between the original reference image and original deformed image. The calculated displacement is assumed as uc. Subsequently, the updated deformed image is generated by translating the original deformed image with -2uc displacement. Then DIC calculation is carried out again between the original reference image and the updated deformed image. And the second calculated displacement is assumed as uc2. Next the updated displacement uu can be obtained by the following formula: uu D uc Cuc2 . 2uc/ 2 D 3uc Cuc2 2 : (1.1) The sampled points are judged whether calculated or not in the final step of the proposed strategy. Mathematically, the system error of the proposed strategy can be derived. The true displacement of the sampled point is assumed as u. and the corresponding system error is denoted bye(u). As displayed in Fig. 1.1, the quasi odd function feature can be written as e.u/ De. u/ : (1.2) In addition, the first calculated displacement uc can be written as uc DuCe.u/: (1.3) Similarly, the second calculated displacement uc2 can be written as uc2 Du 2uc Ce.u 2uc/ : (1.4)
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