“…Thus, the mathematical model of UT can be referred to the geometrical optics or ray optics model, and the most commonly considered modes of the ultrasonic wave propagation are transmission and reflection modes, as shown in Figure 1. In addition, the piston transducer is used in the paper, where the energy of the ultrasonic wave is mainly concentrated in a narrow main lobe area [42]. The power of the transmission and reflection wave is mainly affected by the acoustic impedance of the media where the ultrasonic wave pass through, and it can be described as follows:αR=(PrPi)2=(Z2−Z1Z2+Z1)2, αT=(PtPi)2=(2Z2Z2+Z1)2, where Pi, Pr, Pt represent incident, reflection, and transmission sound pressures, respectively.…”