Objective speckle displacement resulting from the deformation of shaped objects

This paper describes an extended theory of the displacement of the objective speckle pattern resulting from displacement and/or deformation of a coherently illuminated diffuse object where the influence of the surface shape is included via the linear surface gradients. An experimental system capable of measuring the translational scaling factors, the ratios of speckle shift to object translations, to an accuracy of ± 0.02 and a repeatability of approximately ± 0.008 is described which was used to experimentally measure the speckle shift for a range of detector positions and surface gradients. The original expressions developed by Yamaguchi1 and the new extended expressions2 are then compared with experimental results for measurements on zero surface gradients, i.e. the mean surface lying in the x-y plane. The divergence of Yamaguchi’s expressions from experimental results for off-axis detector positions that was first observed by Světlík3 was confirmed, and the new expressions shown to successfully predict translational scaling factors for off-axis positions. The new expressions are then compared to the experimental results for a range of surface gradient magnitudes and directions, as well as detector positions both on and off-axis, and shown to successfully predict the observed speckle shift.