PSI - Issue 37

Pedro J. Sousa et al. / Procedia Structural Integrity 37 (2022) 730–737 Sousa et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 1. Representation of the developed testing machine and the different beam sources for ESPI. The represented situation corresponds to the Z sensitivity out-of-plane setup. The arrow indicates the sensitivity direction, midway between the camera and the right beam.

In order to obtain phase maps in this setup, it is necessary to obtain a set of intensity images in different phases. That is, one of the laser beams in each setup has to be phase stepped. This set of images is then processed using the Carré method algorithms (Carre, 1966; Creath, 1985) to create the necessary phase maps. These phase maps have to be further processed before use, namely through filtering and unwrapping, for which Kemao’s methods were used (Kemao, 2007, 2004; Kemao et al., 2008). Thus, there are mirror and piezo assemblies in the path of two of those five beams that are used to produce these precise phase steps, controlled by a commercial piezo controller from Thorlabs each, in this case, one model MDT694A, and another model MDT694B. To measure displacement in the X direction, two beams on both sides of the camera, aligned with the measurement axis, are used. The u displacement can then be obtained from the phase measurement ( ), the wavelength ( ), and the angle between the camera and the beams ( ), as shown in Eq. 1 (Yang et al., 2014): = 4 sin (1) To measure in the Y direction, another pair of beams is used, now aligned along that axis, and also on both sides of the camera. The displacement is then obtained applying the same type of expression, as shown in Eq. 2 (Yang et al., 2014): = 4 sin (2) In this setup, the out-of-plane portion uses an object beam from the X direction, the one with phase stepping, and a reference beam shining directly onto the camera. Therefore, the Z sensitivity is not perfectly aligned with the camera, but, if necessary, can be corrected by knowing the u displacement along the X direction, as shown in Eq. 3 (Yang et al., 2014): = − (1 + cos ) sin 2 (1 + cos ) (3)