Chapter 4 A Digital Laser Speckle Technique for Generating Slope, Curvature, and Deflection Contours of Bent Plates Austin Giordano and Fu-Pen Chiang Abstract A digital method is proposed whereby spatial speckles created when an optically rough surface is illuminated by a diffuse coherent laser beam are used to generate slope contour fringes. This is done by photographing the speckles contained in a parallel plane in front of the plate before and after deformation. The resulting photographs are then fast Fourier transformed twice and numerically compared with the digital image correlation (DIC) software computer-aided speckle interferometry (CASI) to produce slope contours of the plate. The slope contour data is then stored in an array. The curvature contours are generated by numeric differentiation of the slope data; similarly the deflection contour is generated by numeric integration of the slope data. The curvature data can then be further used in conjunction with plate theory to obtain the bending and twisting moments, the plate’s experiences, as well as the fiber stress on the surface of the plate. Keywords Laser speckle · Digital speckle photography · Digital image correlation · Stress analysis · Plate bending 4.1 Introduction When a coherent laser beam impinges upon an optically rough surface of a specimen, the reflected wavelets from every point of the surface mutually interfere into a volumetric speckle pattern. These speckles move when the surface of the specimen move, and they tilt when the surface of the specimen tilts in much the same way as a mirror tilts an impinging light beam. These speckles can be used to measure the deformation of the specimen. If a camera is focused at the surface of the specimen, the speckles act as if they are in-plane displacement gages; but when the camera focuses at a plane away from the surface of the specimen, the movement of the speckles can be used to measure the slope of the surface. A detailed description of using laser speckle for deformation measurement is given by Chiang [1]. Laser speckle has been used for metrology and experimental mechanics for some time, but most of the work has been done before digitization. In this paper, we propose a digital technique for slope measurement. Defocused speckles have been used by Juang and Chiang [2] to generate slope contours and by Keene and Chiang [3] to measure vibrational modes. Many experimental methods for solving plate bending problems are methods of deflection measurement [4, 5]; however, in the case of thin plate bending, the more advantageous approach is to generate the slope contour thus eliminating the need to differentiate twice to obtain the curvature of the plate. This would reduce the errors associated with numerical differentiation. Techniques for obtaining the curvature of a plate were presented by Kao and Chiang [6], these approaches required the use of a fine grating to produce the curvatures. Additionally Kao and Chiang’s method was incapable of producing the twisting curvature without capturing the curvature of the plate in a rotated coordinate system; no such requirement exists with the digital technique proposed. In this paper, a full-field technique of slope measurement is described in which the specimen surface can be of almost any texture. Using the slope measurement curvature can simply be obtained via numeric differentiation, and deflection can be obtained by numeric integration. This technique is based on the usage of speckles that are created by a beam of coherent light from a laser that is passed through a microscope objective and a pinhole aperture. With this method, no surface preparation is necessary if sufficient light is reflected back from the surface. Otherwise, a thin coating of white paint sprayed onto the surface is all that is needed. A. Giordano ( ) · F.-P. Chiang Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY, USA e-mail: austin.giordano@stonybrook.edu; fu-pen.chiang@stonybrook.edu © The Society for Experimental Mechanics, Inc. 2021 M.-T. Lin et al. (eds.), Advancement of Optical Methods & Digital Image Correlation in Experimental Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59773-3_4 43
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