## 1 Introduction  
When ultrasonic waves propagating through a material encounter a discontinuity, reflected waves are generated at the surface of the discontinuity. The conventional ultrasonic non-destructive testing (NDT) techniques, pulse-echo testing techniques, exploit this reflex phenomenon to detect flaws inside materials, and have been widely used in the inspection of industrial structures and parts. Although pulse-echo techniques show excellent performance in defect characterization, such as location and quantification of defects, the particular directionality of echo, which can only be received by the transducer at a specific position, limits the defect detection rate. In the late 1970s, an innovative ultrasonic testing technique based on diffracted waves from acute ends of the crack was first invented by [PERSON] at the Harwell Laboratory [1; 2]. The advantage of diffracted waves is that they travel in any direction and can therefore be received by the transducers at many positions. Additionally, defect assessment for the ultrasonic diffraction method only depends on the arrival times of diffracted waves rather than their amplitudes [3]. Hence, the ultrasonic diffraction method is sensitive to defects, especially cracks [4; 5]. The defect detection rate of the ultrasonic diffraction method is comparable to or exceeds that of radiographic detection [6]. In this technology, two angle probes, one for the transmitter and the other for the receiver, are separated by a certain distance, called the probe center separation (PCS), fixed with a scanning device and step-by-step moved along the direction to be detected. Figure 1a illustrates the ultrasonic diffraction inspection schematic at a cross-section of a weld, where the scanning direction is parallel to the center line of the weld, that is, perpendicular to the screen. At each position or cross-section, an A-scan signal is obtained. Each A-scan always has two typical waves, one that propagates along the surface of the weld (surface wave), and another that is reflected on the backwall (backward wave), as shown in Figure 1b. When the ultrasonic beam encounters an internal defect, diffracted waves from top and bottom tip of the defect are generated between the surface wave and backwall wave. The presence of a defect can be established by the detection of diffracted waves. Measuring the arrival time of the waves, the depth and height of the defect can be calculated by corresponding geometric relation. All A-scans in the scanning path will constitute ultrasonic diffraction image where every pixel is the sample amplitude in the A-scan and a column of pixels corresponds to an A-scan, as shown in Figure 2. The length of the defect can be determined by identifying the region where the defect occurs in the ultrasonic diffraction image. The sizing accuracy for the ultrasonic diffraction method includes two aspects, length measurement and height measurement. The length measurement accuracy is related to accurate identification of the region where the defect occurs in the ultrasonic diffraction image. In the image, the defect usually appears as a flat parabola, as shown in Figure 3. This results from the large angle range of the ultrasonic beam in the ultrasonic diffraction method. At present, the standard measurement method is to manually fit two small parabolas with the two cambered ends of the defect, and the resulting distance between the vertex of the  
Figure 1: Schematic diagram of the ultrasonic diffraction technique. (**a**) is the formation of diffracted waves generated by the defect and the two inherent waves generated by the interfaces of the tested specimen, respectively, called surface wave and backwall wave; (**b**) is the representation of the typical ultrasonic diffraction A-scan. two parabolas is the length of the defect (Figure 3). However, the measurement results depend on and vary with the experience of the inspector. Different results are obtained even by the same inspector at different times.