# Anisotropy Corrected FMC/TFM Based Phased Array Ultrasonic Imaging in an Austenitic Buttering Layer
## 4 Results and Discussion
### FMC-TFM Imaging  
To study the response of the defects, side drill holes (SDHs) of 2 mm diameter are used as reflectors, as shown in Figure 3. FMC data were acquired with 64-element aperture in 2.25 MHz, 1 mm pitch PA transducer at 33.3 MHz sampling rate. The FMC data were processed using the TFM algorithm developed in Python. Prior to implementing the velocity correction method to the TFM process, the acquired FMC data were processed at different isotropic velocity values. The isotropic velocity values are chosen from the anisotropic velocity curve, as shown in Figure 5b. Those are 5660 m/s, 5960 m/s and 6260 m/s. The velocity values of 5660 m/s and 6260 m/s correspond to the minimum and the maximum in the anisotropic velocity curve, respectively. The 5960 m/s is the average of the two extreme velocities. The TFM images for velocities 5660 m/s, 5960 m/s, and 6260 m/s are shown in Figure 6c,e,g, respectively. The photograph and a schematic sketch of the block with SDHs are shown in Figure 6a,b, respectively, for ready comparison with the FMC-TFM images. All three isotropic velocity cases could image the SDHs at 7 mm and 15 mm depths without any ambiguity. However, the third SDH placed at 26 mm depth exhibited large distortion and splitting. Further, even though only 6 SDHs are present at 26 mm depth, seven indications are observed in Figure 6g, and no indication is observed at the location of the leftmost (8 th) SDH in Figure 6c,e,g. This is attributed to the fact that with the isotropic ultrasonic velocities used in these cases in an anisotropic material, TFMreconstructions at different angles do not superimpose at the same point for a given SDH, leading to distorted imaging. In order to improve the quality of images, TFM images are generated using angle dependent ultrasonic velocities as per Equation (1). The anisotropic velocity corrected TFM images using the sixth order polynomial fit (Equation (3)) and the sine fit (Equation (4)) are shown in Figure 6d,f, respectively. All the SDHs could be effectively reproduced at the corresponding locations in both TFM images with about 6-20 dB improvements in the amplitude for different SDHs as compared to those shown in Figure 6c,e,g. The resolutions obtained at 26 mm depth in these TFM images generated with anisotropic velocity in the buttering layer are observed to be similar to those obtained in isotropic materials at similar depths using similar wavelength and aperture size [29]. Even though TFM images in the anisotropic buttering layer could be obtained with high sensitivity and good resolution by using direction-dependent ultrasonic velocities, this approach cannot be implemented for online inspection using commercial PAUT equipment which provides an option only for a single isotropic ultrasonic velocity to be used for TFM imaging. To enable online inspection with improved FMC/TFM imaging in the anisotropic  
Figure 6: (**a**) Photograph and (**b**) schematic sketch of the reference block showing locations of side drill holes (SDHs). (**c**,**e**,**g**) are TFM images processed using isotropic ultrasonic longitudinal wave velocity values of 5660 m/s, 5960 m/s, and 6260 m/s, respectively. (**d**,**f**) provide TFM images generated using angle dependent ultrasonic velocities as per the sixth-order polynomial fit (Equation (3)) and the sine fit (Equation (4)), respectively. (**h**) TFM image generated using the alternate approach with an isotropic ultrasonic velocity of 6900 m/s. The amplitude values in dB scale for all the TFM images are calculated with respect to the maximum amplitude observed in (**d**). buttering layer, an alternate approach is proposed. It can be seen in Figure 6c,e,g that the two split indications (marked with arrows) corresponding to the third SDH come closer with an increase in the isotropic ultrasonic velocity used for TFM processing. It is felt intuitively that with a further increase in ultrasonic velocity, the two split indications may overlap to produce a high-amplitude image.