Processing of non-stationary interference patterns: adapted phase-shifting algorithms and wavelet analysis. Application to dynamic deformation measurements by holographic and speckle interferometry

A new technique is presented, dynamic phase-shifting, which is based on a dedicated phase-shifting algorithm and a wavelet-transform analysis. This technique allows to perform measurements on non-static objects, using whole-field optical methods. These methods include classical, holographic and speckle interferometry as well as fringe projection and moiré. They cover a large domain of resolutions and dynamic ranges for the measurement of shape and deformation of rough and smooth objects. However, the lack of efficient solutions to process the fringe patterns obtained in dynamic conditions has hindered the development of high-potential methods such as speckle interferometry outside of the laboratory. The main goal of this thesis work is to find new answers to this problem. The solutions we propose are based on the exploitation of the fringe movement produced by the deformation or displacement of the object. We observe that the corresponding phase variations of the interferogram can be used as a natural phase-shift to perform a quantitative phase evaluation. Moreover, it is shown that by adding a known phase step during image acquisition the sign of the displacement can be known without ambiguity. We demonstrate two particular techniques to process the image series recorded during dynamic phenomena. The first one is a 5-image phase-shifting algorithm, adapted to the problem of phase determination with unknown phase increments. The second solution is based on a wavelet-transform processing of the temporal signal recorded at each pixel of the camera. The goal is to estimate the phase of this sinusoidal signal as a function of time. We demonstrate that it can be obtained directly from the phase of the wavelet transform. The resulting method is highly immune to large signal noise. Moreover, we show that phase errors can be eliminated by combining the estimated phase evolution of neighboring pixels or by combining the corresponding real signals to create complex signals. This last approach is also used to extend the dynamic range of the technique. Application examples in the case of holographic and speckle interferometry are presented and both processing methods compared. Their complementarity and robustness brings forth the possibility to apply optical interferometric techniques in situ, our goal being the development of such methods for civil engineering applications.

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