EXAMPLE OF SPECKLE METROLOGY

Use a mechanical loading frame to apply a compressive force of 240 newtons along the long dimension of a square cross-section plastic rod of dimensions 1 cm x 1 cm x 5 cm. Set a lens of diameter 8 cm and focal length of 25 cm 60 cm away from the loading stage and image the speckle pattern onto a photographic glass plate. Produce a double exposure specklegram by taking a photograph of the rod surface before and after applying the compression. When interrogating a small region of the resulting specklegram with a HeNe laser and viewing Young’s fringes on a screen 25 cm from the specklegram, the fringes are found to be 7.9 mm apart with horizontally oriented grating lines. What was the in-plane displacement of the rod surface at the point of interrogation? To obtain a Fourier transform of the specklegram an expanded HeNe laser beam is projected normally through the specklegram and a transform lens of diameter 8 cm and focal length 25 cm is placed right after it. When the specklegram is analyzed by Fourier filtering with a small aperture located 1.5 cm from the optic axis, on the vertical axis, and placed in the Fourier plane, evenly spaced horizontal fringes divide the specklegram image into four equal parts. What is Young’s modulus for this plastic material? What would happen if the filtering aperture was located 0.75 cm from the optic axis, still on the vertical axis? What if the aperture was placed 1.5 cm from the optic axis but at 45 degrees clockwise from the horizontal axis?

Email comments or questions to: matthysd@vms.csd.mu.edu

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