PSI - Issue 17

Pedro J. Sousa et al. / Procedia Structural Integrity 17 (2019) 835–842 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 1. Developed 3D ESPI setup

Here, the laser beam is divided into five beams in two stages. From the first stage results the reference beam, which goes into the camera through a beam splitter, and from the second stage result the other four, which are object beams that provide illumination. The reference beam requires a considerably lower power than the other beams and, thus, the first stage sends the majority of the power to the second one, while a small portion is used for the reference beam. Among the object beams, two (1 and 3 in Fig. 1) include a phase modulator comprised of a mirror and a piezoelectric actuator. When performing an acquisition, the beams that are not necessary should be blocked. For this, shutters were created using small servomotors using custom microcontroller-based hardware. As a reference, the measurement directions for the developed setup are shown in Fig. 2.

Fig. 2. Measurement directions

Results are obtained by comparing two situations: the reference and deformed states. For obtaining quantitative data, phase stepping was employed using Carré Method. That method [3], [11] is applied to a particular state of the object and involves the acquisition of four interferograms ( I 1 , I 2 , I 3 and I 4 ) with an unknown phase step between them. Therefore, for a complete measurement, it is necessary to acquire a minimum of eight interferograms: four for the reference state and four for the deformed state. [12] In this setup, each sensitivity direction is treated independently from the remaining. Thus, when using 4-frame phase stepping, it is necessary to acquire 4×3 interferograms in each state (at least 4×3×2 total). This is so because each sensitivity direction requires one set of four frames for the reference state and another for the deformed state, which are then processed to yield 3 phase difference maps, one per direction. Having obtained a wrapped phase map, it is then filtered and unwrapped using a method developed by Kemao [13] – [16]. The displacements u (X axis) and v (Y axis) can be calculated from these phase maps as [1]: