Digital speckle-displacement measurement using a complex spectrum method

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Abstract
An alternative approach to fully automatic speckle-displacement measurement is described. Two speckle patterns of a specimen, one before and one after deformation, are captured by a CCD camera and registered by a frame grabber. Two series of small subimages are obtained by segmenting the two speckle patterns. The corresponding subimage pairs extracted from both series are analyzed pointwise. The interrogation of each subimage pair involves a two-step fast-Fourier transform. While the first-step fast-Fourier transform achieves a complex spectrum characterized by the local displacement information, the second-step one generates a signal peak in the second spectral domain that resolves the local displacement vector. A rough estimate of the displacement vector is achieved by detecting the maximum pixel of the discrete spectrum. A more accurate determination is attained by a subpixel-maximum determination through a biparabolic fitting near the signal peak. The u- and v-displacement fields are deduced by analyzing all subimage pairs. A large rigid-body displacement can be overcome by introducing an artificial rigid shift of the two speckle patterns toward each other before the numerical process. The technique retains all the advantages of optical speckle photography and provides an extended range of measurement. Dynamic incremental deformations can be inspected by registering more speckle patterns at many consecutive deformation stages by using a high-speed CCD camera. The system was applied successfully to the study of crack-tip deformation fields.