Speckle motions induced by rigid-body movements in freespace geometry: an explicit investigation and extension to new cases.

In line with the current interest in speckle motion in free-space propagation, it is proposed to investigate new aspects of the induced speckle motion due to rigid-body movements of a model using as a starting point the well-known concept of homology, first stated in holographic interferometry, the importance of which has only recently been realized in speckle metrology. At the outset, stating the homology conditions leads to a general expression relating the speckle shift to the geometrical parameters at the recording and to the six degrees of movement of the object surface. The expression presented in this explicit form is found to be true for both opaque and thin transparent diffusing models and for different conditions of illumination and observation. The study is then extended to (1) when the object is at rest, subjecting the illuminating source to a small displacement and (2) when the wavelength of the illuminating beam is changed between the two exposures. The case of the rigid-body displacement of the object is experimentally verified and the results are found to be in good agreement with theory. The viability of the method to make measurements is assessed, several applications are envisaged, and some advantages are pointed out.