The feasibility of two-beam speckle interferometry for the study of time-varying mechanical deformation of diffusely reflecting bodies is demonstrated. A sequence of speckle patterns produced by a vibrating cantilever beam was recorded photographically by means of a high-speed camera. These speckle photographs were subsequently digitized using a CCD camera for input into an image processing computer. By gray-level subtraction of carefully registered pairs of speckle images, fringes corresponding to the relative surface displacements were obtained. A sequence of these fringe patterns was reconstructed to obtain the time-history of deformation. These are compared with time-frozen (strobed) patterns for the same body.
When a coherent light beam is scattered by a diffuse surface, a random speckle pattern is observed. If the surface is now deformed, the resulting speckle pattern could be correlated with the original pattern to obtain a fringe pattern representing the relative displacement of the surface1. Many types of speckle interferometers have been configured to provide either out-of-plane or in-plane displacement-sensitive devices2. These interferometers have been so successful that many systems are commercially available today. However, speckle interferometry has been thus far confined to the study of static deformation, or at most, periodic deformation in a time-average or time-frozen sense. It has been stated as recently as 1989 that"dynamic speckle pattern interferometry is not possible"3. While there are in principle no physical limitations that would necessarily preclude the use of dynamic speckle techniques, a number of technical difficulties had to be overcome before dynamic speckle interferometry could be established as a viable technique. Among these were insufficient light intensity for the extant photographic recording media, resolution of typical high-speed camera systems, and perhaps most importantly, image registration.
In this paper, we present preliminary results demonstrating that dynamic two-beam ("holographic") speckle interferometry can be successfully used to study dynamic, mechanical deformation of diffusely reflecting bodies. This work was motivated in part to remove the misconception that speckle interferometry is unsuitable for dynamic studies, but more importantly because there is a pressing need for such a technique. Currently available full-field optical techniques can be used to study dynamic deformation in only certain classes of materials. For instance, the method of photoelasticity4 works only with transparent materials that are birefringent. In moire techniques,5,6 typically a grating has to be ruled or etched on to the specimen surface. Michelson and grating shearing interferometry7 require that the material be either transparent or opaque but highly polishable. However, most of the advanced materials that are being actively pursued by the technological community today are either composites or ceramics, and it is expected that time-varying deformation in such materials may be more amenable to high-resolution optical scrutiny through the dynamic two-beam speckle interferometer described in this paper.
The details of dynamic holographic speckle interferometry are given in a forthcoming report8. Here, only the basic principles are described. As shown in Figure 1, the diffuse surface of a test object is in the xy plane, and two collimated laser beams W1 and W2 are incident on it along the xz plane making angles 2θ1 and 2θ2 to the normal respectively.
Figure 1: Schematic representation of double illumination of the test object, and the corresponding propagation vectors.
The diffusely scattered light from the test object is then collected by a lens system and the resulting speckle pattern is imaged in a camera. As in conventional speckle correlation interferometry, the electric field at the film plane of the camera can be expressed as the sum of the fields E1 and E2 due to the two illuminations, where:
E1 (x,y,t) = A(x,y)ei ψ T 1 (x,y,t), (1)
E1 (x,y,t) = B(x,y)ei ψ T 2 (x,y,t), (2)
Here A(x,y) and B(x,y) are possibly spatially varying amplitudes, and the phases are:
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