Fig. 1. Sound speed and thickness model of multilayer dielectric structures

Fig. 2. Principle of exploding reflecting model (ERM). (a) Equivalent route path for ERM; (b) scenes of multi-points exciting waves together, amplitude proportional reflection coefficient, and sound field synthesis and all probes receiving simultaneously

Fig. 3. Coordinate transformation and wave paths for oblique incidence algorithm

Fig. 4. Flow chart and relative computational complexity of proposed algorithm

Fig. 5. Comparison of imaging for longitudinal and transverse waves at same refraction angle of 45°. (a), (d), (g) Respectively represent test specimen setups for side-drilled holes (SDHs), vertical cracks (cracks), and semi-spherical flat-bottomed holes (FBHs); (b), (e), (h) respectively represent images for longitudinal wave upon SDHs, cracks, and FBHs; (c), (f), (i) respectively represent images for transverse wave upon SDHs, cracks, and FBHs

Fig. 6. Multi-angle transverse wave imaging for vertical SDHs; (a) Test specimen setup for multi-angle transverse wave vertical SDHs; vertical SDHs imaging with refraction angles of (b) 20°, (c) 30°, (d) 40°, (e) 50°, and (f) 60°, respectively

Fig. 7. API rectangle imaging area for top and bottom SDHs with each transverse wave refraction angle. (a), (c), (e), (g), (f) Respectively represent imaging for top SDHs at refraction angles of 20°, 30°, 40°, 50°, and 60°; (b), (d), (f), (h), (j) respectively represent imaging for bottom SDHs at refraction angles of 20°, 30°, 40°, 50°, and 60°

Fig. 8. Effect comparison of proposed method and conventional time-domain method under 40° transverse wave refraction. (a) Whole image and API images for first and fourth SDHs respectively using proposed method; (b) whole image and API images for first and fourth SDHs respectively using conventional time-domain method

Fig. 9. Equipment setup for experiment

Fig. 10. Defects distribution for experimental specimens. (a) Test specimens contain right side oblique placed SDHs with diameter of 1 mm; (b) test specimens contain a series of 3-mm spacing FBHs with diameters of 1, 2, 3, 4, and 6 mm respectively

Fig. 11. Experimental SDH imaging with refraction angles of (a) 30°, (b) 45°, and (c) 60°, respectively when refracting into aluminum block

Fig. 12. Transverse wave imaging for FBHs with refraction angle of 30°

Table 1. Refractive angles of longitudinal and transverse waves at different incidence angles

Table 2. API values for ultrasonic testing imaging of SDHs using transverse waves

Table 3. Incidence and refraction angles used for experiments