PSI - Issue 5

H. Lopes et al. / Procedia Structural Integrity 5 (2017) 1205–1212

1206

H. Lopes et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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interferometry techniques used today. Static or dynamic measurements of the surface displacement and their spatial derivatives up to the second order can be obtained (Schnars and Jueptner (2005), Steinchen and Yang (2003), Kreis (2005)). Since optical techniques allow full-field, real time, non-contact and high resolution measurements, they have become popular within the experimentalists community. In the last decades, these techniques have received a great impulse with the introduction of the temporal and spatial phase modulation techniques, thus increasing the resolution of the measurements. However, these speckle interferometry techniques suffer from several inconvenient effects, which may lead to high levels of noise and errors in the experimental measurements. Noise is intrinsic to any experimental measurement and mainly due to its random nature it is difficult to characterize its source and control it. On the other hand, errors are usually systematic and may be controlled and quantified, as they can be related to a single measurement parameter, such as, for instance, the numerical aperture, the sensitivity vector, the phase step, and the deformation and loading ranges. The time and space low coherency of the light source, the non-uniform illumination of the object, the superposition of high frequency speckle noise, the presence of dust particles in the optical path, the reflectivity variation of the object surface, the electronic recording system and the external perturbations are common examples of noise sources in speckle interferometry (Schnars and Jueptner (2005), Steinchen and Yang (2003), Kreis (2005)). Typical examples of errors sources in speckle interferometry are misalignment of the optical setup and miscalibration of the phase step (Creath and Schmit (1996), Steinchen et al. (1998), Picart et al. (2001), Abdullah and Petzing (2005), Kreis (2005)). In this work, we are only interested in the analysis and evaluation of the noise, being the errors considered in other studies. A particular application of speckle interferometry is structural damage identification using dynamic responses and modal parameters (Lopes et al. (2014), Mininni et al. (2016), Araújo dos Santos and Lopes (2017)). Shearography possesses several advantages in relation to others experimental modal analysis techniques, since it allows the direct measurement of modal rotation fields with high spatial resolution. Nevertheless, since most damage identification methods require the post-processing of these modal rotation fields, namely the application of finite differences to obtain the modal curvatures (Pandey et al. (1991)), the control and quantification of noise is of paramount importance to obtain reliable results. The evaluation of noise in measurements with shearography is one of the most important steps in finding its accuracy. However, a detailed analysis of noise in shearography has not been reported yet, mainly because for its evaluation it is necessary to know the continuous full-fields, which are obtained from the discontinuous measured phase maps. Thus, the procedure to quantify the noise is not straightforward, since it is necessary to resolve simultaneously the discontinuities and the ambiguities in the phase maps. A recent method has been proposed to overcome these problems and is applied here (Lopes et al. (2017)). The present paper reports the analysis of noise on experimental measurements produced by several setup parameters. With this purpose in mind, the first four modal rotation fields of a free-free beam were measured using a digital shearography technique, in which we varied the shearing amount and the vibration amplitude. A signal coming from an experimental measurement, i.e. an experimental signal, is composed by a true signal and by a noise signal. The true signal presents a smooth variation, while the noise signal presents random fluctuations. For the accuracy assessment of a given measure quantity it is necessary to evaluate the contribution of noise. The noise can be estimated by computing its root mean square (RMS) or its signal-to-noise ratio (SNR). However, this evaluation requires the knowledge of the true signal in a given measurement in order to identify the random fluctuations in the signal associated with the noise. The true signal is usually obtained by post-processing the experimental signal, such as by applying low-pass filters. Therefore, the noise signal can be estimated by subtracting the true signal to the experimental signal. Speckle interferometry involves the measurement of phase maps, which are discontinuous signals. The corresponding continuous true signal must be obtained by filtering and unwrapping these phase maps (Steinchen and Yang (2003), Kreis (2005), Ghiglia and Pritt (1998)). However, this is not a straightforward procedure when we want to obtain the continuous experimental signal, since we must deal simultaneously with phase discontinuities and phase ambiguities due to the noise. It has been shown that it is possible to obtain the continuous experimental signal starting from the measured phase map (Lopes et al. (2017)). The method proposed by Lopes et al. (2017) can resolve the phase 2. Method for the evaluation of noise