## 2 Ultrasonic Computerized Tomography  
Ultrasonic computerized tomography, which combines ultrasonic waves and X-ray computerized tomography, is an imaging technique pursuing the internal condition of the structures. The aim of using ultrasonic CT is to reconstruct the internal spatial distribution of wave velocities, acoustical impedances, or wave attenuation from the measurements of the structure [15]. The reconstruction algorithm of the ultrasonic CT requires various densely spaced sets of transmitter and receiver positions, which is shown in Figure 1. Before the experimental process, the cross-section of the detected structure is divided into discrete microstructures. Then, the transmitter and receiver are arranged at each position of the specimen to excite and receive the ultrasonic waves. The interaction of ultrasonic waves and the damaged microstructures will alter the acoustic parameters of the ultrasonic wave and cause wave diffraction. On the one hand, the ultrasonic wave will propagate rather quickly in the compact part of the object. On the other hand, the travel time will be longer by diffraction when the ultrasonic wave confronts the defects such as holes and flaws, which is caused by the wave traveling to the observer by crossing the edge in a longer path. Multiple ultrasonic measurements carry the parametric information of the microstructures, including the healthy parts and damaged ones. Then the inverse scattering problem will be solved, and the acoustic parameters of each microstructure will be determined by the reconstructed algorithms. That is to say, by obtaining the travel time of the ultrasonic waves via the external measurements, the internal situation of the detected specimen or structure could be able to be imaged. Ultrasonic CT represents an improvement in the acoustic transmission testing method, which not only performs the direct mode but also stands for the traveling path of the ultrasonic waves affected by the damage in the structures. By creating a dense net of the measured paths, each of which relates to a particular travel time between the ultrasonic actuator and sensor, the section of the structure is crossed and measured multiple times. The values of the travel time of the ultrasonic waves are used to compute a reconstruction of the velocity distribution across the selected section. The local variations in velocity, which indicate the zones of weakness or flaws in the internal fabric of the structure, are identified. The basic ultrasonic CT formulas are shown as follows. The variation from the expected travel time is attributed to inhomogeneity in the structure or damage occurred. In order to obtain an accurately reconstructed result, the section of the structure has to be adequately covered by the measurement paths, as shown in Figure 1.  
The value of travel time in one selected measuring path is determined by the travel path and the microstructures in the section of the structure, which can be expressed as the following relationship:  
\[T_{i}=\int_{L_{i}}\frac{1}{V(x,y)}dL=\int_{L_{i}}s(x,y)dL \tag{1}\]  
Figure 1: Schematic of ultrasonic computerized tomography (CT): (**a**) Densely measurement net; (**b**) Measurement path and the meshed microstructures of the specimen. where, \(T_{i}\) is the travel time of \(i^{th}\) path, \(L_{i}\) is the distance of the \(i^{th}\) measurement path from the actuator to the sensor, \(V(x,y)\) is the velocity of ultrasonic waves in the location of \((x,y)\), and \(s(x,y)\) is the slowness function of the microstructure, which is the reciprocal of the velocity function, \(V(x,y)\). In order to reconstruct the value of the velocity distribution in the structure, the section is divided into numbers of microstructures.