# High-Precision Noncontact Guided Wave Tomographic Imaging of Plate Structures Using a DHB Algorithm
## 3 Experimental Set-Up and Specim  
The hybrid application of an air-coupled transducer and pulse laser is used in this work. Air-coupled sensors can have increased sensitivities compared to optical transducers. Well-designed capacitive air transducers can be expected to be as sensitive as laser interferometric sensors [25; 26]. In addition, the air-coupled transducers can receive a specific mode of guided waves. This can be realized by changing the receiving angle to a leak direction of the selected modes. It is well-known that a static scanning process of the receiver is very important for high-precision acquisition of the signals. The application of air-coupled transducers is one of the most appropriate choices to realize high-precision acquisition. However, the mismatch of acoustic impedances between solid materials and air is a huge weakness of a purely air-coupled transducer detection system. Consider the scenario shown in Figure 8. The ultrasound passes through the interface between the solid specimen and air two times. Only a tiny fraction (\(10^{-8}\)) of the original acoustic energy is transmitted through both solid-air interfaces to reach the receiver. Consider the second scenario shown in Figure 9. The ultrasound is generated directly in the solid using a pulsed laser. The solid-air interface on the generation part has effectively been removed. The energy reaching the receiver could increase by a factor of \(10^{4}\)[27]. As a receiver, the air-coupled transducer can also have good performance if the proper parameters are set [28]. The hybrid application of an air-coupled transducer and pulse laser can make material characterization more feasible. It can also be used where the air-coupled transducer and pulse laser are put on the opposite sides of the specimen [29; 30]. The laser ultrasonic technique can also be used in the detection of a curved surface specimen [31; 32]. A line laser source is much better than a point source for long-range detection [33; 34]. Many researchers used spatial array illumination sources produced by several means. Those methods include slit masks, lenticular arrays, optical diffraction gratings, multiple lasers, and interference patterns. The linear slit array mask was used in this study, as shown in Figure 10. A Lamb wave of specific modes can be generated selectively by adjusting the line spacing. The distance between two adjacent line laser sources is defined as the line spacing or element gap marked as \(\Delta S\). The value of the line spacing is equal to the wavelength of the generated Lamb wave. The difference between it and the element width equals the width of the single line laser source. The width of the single line light source is also known as the line width marked as w. The value of \(w/\Delta s\) is known as the duty ratio. It is found that an A0 mode Lamb wave has the optimum signal-noise ratio when the value of \(w/\Delta s\) is 0.5 [35]. Figure 8: Transmission in air using two air-coupled transducers. Values shown are approximate fractions of the original energy. As shown in Figure 10b, the generated wave should be analyzed by using a Gaussian model. Specifically, the spatial energy profile of each line beam is assumed as Gaussian. A Gaussian model is also suitable for the focused laser beams. However, the diffraction effect is negligible when the slit mask is very close to the target surface. Then, the spatial energy profile of each line beam is closer to a square pulse than Gaussian in the line-arrayed slit mask shown in Figure 10a. The energy of each line laser beam can be assumed to have a uniform distribution, and the temporal profile is a delta function. The spatial energy profile of each line beam can be taken as a simple one-dimensional square pulse. For an array of N equally spaced identical laser sources, the final displacement can be taken as a summation of N single-source surface waves displaced in time by the surface wave propagation interval between two adjacent sources, as shown in Equation (5).