# High-Precision Noncontact Guided Wave Tomographic Imaging of Plate Structures Using a DHB Algorithm
## 4 Results and Discussion  
In this work, the test specimen is an aluminum plate with a thickness of 1 mm. The wavelength was designed as 6 mm. Both the A\({}_{0}\) and S\({}_{0}\) modes of a Lamb wave can be excited based on the laser ultrasonic technique. Because the air-coupled transducer is more sensitive to the antisymmetric modes than the symmetric modes, the detection range of the air-coupled transducer was chosen as 0.2 to 0.5 MHz to detect the A\({}_{0}\) mode Lamb wave. An experiment was done to see the appearance of a defect, as shown in Figure 20. There is a penetrating hole in the center of the specimen. The diameter of this through hole is 20 mm. The signal of both the defect-free and with the defect areas have been obtained in both time and frequency domains. As shown in Figure 21, the signal attenuates clearly due to the appearance of the defect. Only an A\({}_{0}\) mode Lamb wave can be detected, as mentioned above. The generated S\({}_{0}\) mode was filtered by the air-coupled transducer due to its detection range. Only one mode of the Lamb wave was needed for the tomography once the new DHB method was used. This is also another advantage of the new algorithm. For example, the probabilistic algorithm requires at least two modes of Lamb waves for comparison. The tomographic imaging technique used in this work is based on the wave attenuation. The attenuation law of a Lamb wave is subject to Equation (12), and the equation for data projection is given in Equation (13). The parameter \(\alpha\) in those two equations is the attenuation coefficient, \(A\) is the signal amplitude, and \(x\) is the propagation distance. \[A\ =\ A_{0}e^{-\alpha x} \tag{12}\]  
\[\int\limits_{-\infty}^{\infty}\alpha(x)dx\ =\ \ln\frac{A_{0}}{A} \tag{13}\]  
Figure 19: The actual experimental platform. Figure 20: The schematic of the defect-detecting experiment. The attenuation curve and the corresponding scanning sketch based on the fan-beam iterative method are shown in Figure 22a,b. The signal attenuation becomes evident within the scanning range of 83\({}^{\circ}\) to 90\({}^{\circ}\) in the area where a defect starts to appear. Particularly, the illumination area can cause a \"dead zone\" due to the geometrical features (the diameter of the slit mask used in this work is 60 mm). In other words, the detection cannot be achieved effectively along a full circle arc when the line laser source is used. As shown in Figure 22, the signal within the scanning range of 0\({}^{\circ}\) to 13\({}^{\circ}\) was invalid data. It is unnecessary to test the \"dead zone\" when the DHB algorithm is used because the short-scan condition can be relaxed to a great extent. The real data shown in Figure 22 also supports the advantage of this new DHB algorithm compared with FBP or other algorithms. Figure 23a,b is a sample drawing and specimen of the initial single defect. The imaging of the penetrating hole is given in Figure 24. There are 36 emitter and receive points. If there are 19 receiving points from a single emitter point to a semicircle, and inspection is performed up to the 20 th emitter point, 361 data points can be collected. Figure 21: The signals of the defect detecting experiment. Figure 22: The attenuation curve of Lamb wave obtained from the experiment: (**a**) Attenuation curve; (**b**) Schematic of scanning direction. Complex shapes or multiple defects should be inspected up to the 36 th emitter point, but a single circular defect, as shown in Figure 24, was able to quantitatively represent the defect. The imaging of the defect is displayed clearly compared with the defect-free area. Another experiment was conducted to further verify the effectiveness of the new DHB algorithm in the aspect of detection precision. Different types of defects were made in different positions of specimen #2.