# High-Precision Noncontact Guided Wave Tomographic Imaging of Plate Structures Using a DHB Algorithm
## 1 Introduction  
It is well known that Lamb waves can propagate long distances with little energy loss. Lamb waves have been shown to be sensitive to most types of defects. They are also efficient for detecting tiny subsurface damages and inspecting large areas. Such noncontact nondestructive testing (NDT) methods have great advantages for online inspection because high temperature or other negative factors can restrict the application of contact methods. In earlier research, ultrasonic Rayleigh and Lamb waves were used to reconstruct images in metal plates using water immersion techniques [1]. Other studies have used electromagnetic acoustic transducer (EMAT)-based methods [2; 3; 4] and contact techniques [5; 6; 7; 8; 9]. Air-coupled transducers have been used for tomography imaging since the end of the last century [10]. The application of purely air-coupled transducers has always been limited for the detection of nonmetallic materials [11; 12] due to the high acoustic impedance between air and solid materials. Other methods, such as disc sensors, have also been widely used for the detection ofmetallic materials [13], but those methods are not truly noncontact methods. The research team of [PERSON] developed PMN-PT synthesized with lead magnesium niobate-lead titanate crystals, and applied PMN-PT, which has a strong piezoelectric effect, to an air-coupled transducer to improve performance [14; 15]. Therefore, it is believed that the hybrid application of a pulse laser and air-coupled transducer will have good performance as a fully noncontact detection system [16; 17]. Most of the works mentioned above are based on the traditional filtered back projection (FBP) algorithm. The FBP algorithm is mainly used for radiographic inspection using X-ray [18; 19]. Although high resolution is shown in the radiographic inspection, there is a disadvantage that image artifacts are generated when ultrasonic tests are applied. Other works have been based on the reconstruction algorithm for the probabilistic inspection of damage (RAPID) [20; 21; 22; 23]. The RAPID algorithm is actively used in ultrasonic tomographic techniques as a technique for imaging defects using a signal difference coefficient. However, the RAPID algorithm has the advantage of being able to visualize faults with small transmission and reception points, but due to some negative influences such as shape factor (factor of influence), there is a limit to quantifying the defects. It is also not suitable for multidefect imaging. In this study, in order to overcome the limitations of the resolution of the RAPID algorithm, which is typical of the existing ultrasonic tomographic algorithm, the FBP algorithm, an imaging technique used in the radiography technique, was applied to the ultrasonic technique. We confirmed the problem with the image artifacts generated in the FPB algorithm using ultrasonic waves. Difference of the projection data, Hilbert transform of the difference data, distance weight, and back projection were applied to the FBP algorithm to reconstruct the Difference Hilbert Back Projection (DHB) algorithm. The radiographic imaging techniques require many data points and reliable data for high-resolution imaging. However, manual operation is still being widely used for data acquisition. The work efficiency of manual operation is very low, and the precision of signal acquisition cannot be guaranteed. Although automatic control was used in some studies, many of the devices can only be used in some special circumstances. In this work, a laser switch has been adopted in an automatic detection system to improve the precision of signal acquisition. The automatic detection system was developed based on the hybrid application of a pulse laser and an air-coupled transducer. This is one of the best combinations among many different kinds of noncontact NDT methods. The detection system consists of two main parts. One part is an automatic scanning robot arm for the air-coupled transducer.