Mechanical Systems and Signal Processing , 20 : — Moreover, we developed a specific phase evaluation technique that renders quantitative data of transient SAW, namely the instantaneous out-of-plane acoustic displacement field and the out-of-plane acoustic displacement amplitude and phase fields, with a minimum measurable displacement of the order of one nanometer Trillo et al.
One of the most popular variants of TVH for industrial NDT is speckle-shearing interferometry, also named shearography, which employs common-path illumination-detection geometry where the role of the reference beam is played by a duplicate of the object beam displaced laterally.
This offers a certain degree of immunity although not as complete as with pulsed techniques to environmental perturbations even with long exposure times. Shearography has been successfully employed for measuring instantaneous SAW displacement fields Bard et al. Gordon , and Shudong Wu. Laser-modulated phase-stepping digital shearography for quantitative full-field imaging of ultrasonic waves. Shearographic visualization of Lamb waves in carbon epoxy plates interaction with delaminations. European Physical Journal Applied Physics , 9 : 69 — A systematic approach to TV-holography.
Measurement Science and Technology 11 : R1 — R Even in the simplest case of small shear, in which the displacement difference can be approximated by its spatial derivative, the relationship between the measured data and the material structure and flaws is more complex than in HI and TVH Mast and Gordon Mast , T. For fields propagating in other directions, sensitivity decreases with the angle between the shearing vector and the wavevector.
For example, for the standard linear shear, cylindrical waves scattered from defects would be detected predominantly in the shearing direction.
Hence, optimum shearing vector selection requires a previous knowledge of the acoustic wavevector. From the former considerations it seems that, among all the holographic techniques, the pulsed TVH ones hold possibly the greatest potential for probing of ultrasound in industrial NDT tasks. In this section, we briefly describe the VUPTVH technique and the associated self-developed prototype to apply this technique.
As stated in the introduction, it has been developed by our research group over the last decade, with successive improvements in the optical and electronic hardware and, especially, in the information processing scheme. Some parts of the current system have been incorporated from former prototypes already described elsewhere Trillo et al. Spatiotemporal Fourier Transform method for the measurement of narrowband ultrasonic surface acoustic waves with TV holography.
Slangen and C. Cerruti , M-1 to M SPIE Enhanced measurement of ultrasonic surface acoustic waves with TV holography by correction of phase mismatch between laser cavities. Cerruti , Proc. Bellingham , Washington : X-1 to X The use of VUPTVH for NDT is based on the same three-step working principle explained in the introduction: 1 generation of ultrasound in the part to inspect, 2 interaction ultrasound-flaws, and 3 probing by TVH of the ultrasonic displacement field at the part surface. In our case, we have used Lamb waves, including the particular case of quasi-Rayleigh waves, in aluminium plates a few millimeters thick as depicted in Figure 2 , generated by the wedge method.
Our generating system Figure 3 consists of a piezoelectric element PZT attached to a wedge of plastic material and the corresponding driver, that produces high-voltage tone-bursts with the possibility of selecting both the number of cycles and the central frequency in the range of a few MHz.
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In the near future, we expect to implement generation by laser. A flaw consisting of a flat bottom bore is also depicted. Figure 2 Notation for the incident surface acoustic wave, u 1 x , t , in a plate. From the illumination-observation geometry Figure 3 it can be seen that the sensitivity vector of our TVH system is approximately parallel to the observation direction. This means that we only measure the out-of-plane component of the surface displacement vector. Therefore, in the current configuration, the interesting Lamb modes are those with an appreciable out-of-plane component at the object surface.
It is also possible to make the system sensitive to the in-plane components by changing the illumination-observation geometry or by tilting the inspected part a large angle for instance, 45 degrees ; these variants will be explored in future developments. With respect to the temporal behavior, we classify the fields into two categories:.
The fields are intrinsically transient and there is not a clear temporal periodicity but, instead, the time waveforms at each point consist of isolated pulses with very few cycles or, when dispersive effects appear, chirped or similar waveforms formed by an oscillatory signal of variable period and amplitude. Apart from the components of the guided ultrasonic waves i. Into this scheme, we can differentiate two basic behaviors:.
In most cases, the coexistence of several travelling waves of the same central frequency gives rise to spatial variations of the amplitude, i.
Similarly to the broadband case, quasi-stationary patterns may appear due to evanescent waves or to eigenmodes. To enhance the capability of VUPTVH to detect isolated flaws like cracks and voids, a single-mode narrowband incident plane wavetrain in the form of a tone-burst of constant amplitude and a number of cycles between 5 and 30 is quite adequate.
In a first approximation, ignoring diffraction and dispersive effects, Eq. In our case, for solving the inverse problem we have at our disposal, as the directly measured data, a set of 2-D instantaneous acoustic displacement maps of the plate surface, recorded in successive instants of the ultrasound propagation. The development of a model that relates this information of the scattered field to the flaw localization and characteristics is out of the scope of this article.
Nevertheless, we will denote here generic equations of the different classes of possible ultrasonic fields for a better understanding of the obtained maps.
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Also, we will consider in these equations Figure 4 the existence of scattering centers at the specimen surface that are point sources of the scattered waves. The distribution of scattering centers is intimately related to the positions of the flaws embedded in the plate material. Specifically, for surface-breaking and near-surface flaws of size comparable to or smaller than the SAW wavelength, a cylindrical scattered SAW seems to emanate from a scattering center located approximately at the projection of the flaw on the specimen surface.
This fact provides an easy procedure to get a first indication of the existence and location of flaws without solving the inverse problem. Following the same classification as seen in 3. Figure 4 Notation for the acoustic incident and scattered fields. If the material works in the linear regime, the resultant field can be regarded as a superposition of the incident and scattered fields, including traveling and evanescent waves and transient vibration patterns. The total out-of-plane instantaneous acoustic displacement at the plate surface can be written, from Eq.
Presuming that the material works in the linear regime, the resultant field can be regarded as a superposition of the incident and scattered fields, including traveling waves and quasi-stationary patterns, all excited by the incident wave and, in consequence, with the same central frequency.
Fundamentals and applications of ultrasonic waves
The total out-of-plane instantaneous acoustic displacement at the plate surface can be written, from Eqs. The optical probing system is depicted in Figure 3. It is a self-developed double-pulsed TVH system with specific phase evaluation techniques. Fourier-transform evaluation of phase data in spatially phase-biased TV holograms. Applied Optics 35 2 : — 6. In these conditions, the output of the system is a 2-D map that renders, at each point of the field of view, the difference between the out-of-plane displacements corresponding to the two mechanical states defined by the illuminating laser pulses see Figure 5.
Details of the practical implementation and some examples of the system output can be found in Trillo et al.
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This measurement scheme can be particularized to the ultrasonic temporal behavior as follows. The incident acoustic wave is a narrowband, practically pure single-mode wavetrain 90 cycles in length propagating from right to left. Row a : incident quasi-Rayleigh mode of central frequency 1. Row b : incident A1 mode of central frequency 1.
Row c : incident S2 mode of central frequency 2. This is the most general case. Taking into account Eq. Firing the first laser pulse with the object at rest, it results a field called instantaneous optical phase-change. Taking into account Eqs. In these points, Eq. Whenever an incident narrowband traveling wave is employed, a second evaluation stage that takes advantage of the periodicity of the signal can be applied to the output of the first stage, Eq.
We have devised two variants. This variant Trillo et al. For its practical realization, we have used a single-mode incident plane wavetrain in the form of a tone-burst of smooth envelope. Once obtained the optical phase-change map, Eq. Therefore, a second application of the SFTM see Figure 6 allows recovering the complex optical phase-change field at the instant t : which is, apart from the noise, proportional to the complex acoustic field incident plus scattered at the instant t.
The box in b indicates the filtering window. Figure 6 Sketch of the second evaluation stage, spatial version, applied to the field of Figure 5 a , i. However, care must be taken to select an appropriate filtering window to avoid eliminating useful information and to avoid introducing artifacts that can be mistaken for acoustic signals.
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The time interval between two consecutive maps is selected short enough compared to the acoustic period to ensure the Nyquist sampling condition. We have then spatial periodicity at a given instant across each map and temporal periodicity at a given point across the series of maps. Then a three-dimensional 3-D Fourier transform, followed by a filtering and an inverse 3-D Fourier transform, renders a set of N complex amplitude maps of the acoustic field incident plus scattered , corresponding to successive instants t n of the acquisition procedure. This technique allows a noise filtering even better than the spatial evaluation variant because the temporal narrowband character of the acoustic fields is taken into account in the filtering process, although it requires a larger data acquisition time and a more powerful data processing equipment.
Another advantage of the spatio-temporal evaluation, in opposition to the spatial evaluation, is that quasi-stationary patterns as those described by Eq. The data are acquired in successive experiments under repeatability conditions. In addition, for obtaining the other three maps, two alternatives can be followed:.
Afterwards, the maps are arranged with a video editor like the frames of a standard movie. By applying the spatio-temporal evaluation described in 3. Afterwards, like in the method given in 3.
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This procedure renders better results than the alternative method 3. Taking into account that the acoustic displacements to measure are of the order of a few nanometers, different sources of noise need to be controlled, which imposes severe requirements to the whole system, especially to the laser and image acquisition hardware. An estimation of the main contributions to the system noise was made in Cernadas et al.
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