34 High-Speed Digital Image Correlation for Endoscopy: A Feasibility Study 253 Fig. 34.1 The camera, image, and world coordinates in a pinhole model [10] Fig. 34.2 Experiment setup. (a) Aluminum plate mounted on a manual x-y translation stage used for discrete displacement measurement; (b) piezoelectric tilt stage is observed by the endoscope; (c) experiment setup showing the sample, endoscope and camera assembly and the illumination lamps 34.3 Representative Results A discrete translational displacement in the x-direction of 1 mm is measured by the endoscopic HS-DIC. The x-direction displacement error (eU) and y −direction displacement error (eV) without applying the calibration process and those of the same data set calibrated for optical distortions are shown in Fig. 34.3. The results demonstrate that through the calibration, the errors inx and y-directions are reduced from±24 to±8%, and±12 to±2.5%, respectively. In addition, a series of single direction translational displacements are measured by the same DIC configuration, and the measurement results after calibration are depicted in Fig. 34.4. Figure 34.4a shows the calibrated DIC measurements of xdirection translational displacement of 1 mm at different step size. Blue line is the actual displacement applied by the stage, and orange and yellow lines are the averaged DIC results of x-direction displacement (U) and y-direction displacement (V), respectively. Similar translational displacement along y-direction is also measured shown in Fig. 34.4b with green line being the actual displacement.
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