# Anisotropy Corrected FMC/TFM Based Phased Array Ultrasonic Imaging in an Austenitic Buttering Layer
## 4 Results and Discussion
### FMC-TFM Imaging
Accordingly, TFM images were generated at different ultrasonic velocities above 6260 m/s, even though it is clear that the material does not exhibit ultrasonic velocity above 6260 m/s in any direction in the inspection plane. The TFM image with the highest amplitude of indications for isotropic ultrasonic velocity is obtained at the ultrasonic velocity of 6900 m/s, as shown in Figure 6h. The amplitudes of the first three SDHs in Figure 6h are almost similar to that obtained in Figure 6d,f using angle dependent ultrasonic velocities. However, the amplitudes of the closely spaced SDHs are lower as compared to those in Figure 6d,f. Further, as a higher ultrasonic velocity is used, all the indications are moved at larger depths (29.6 mm) with slight shifts in the lateral positions also. The effects of isotropic and angle-dependent ultrasonic velocity values on the amplitude and signal-to-noise ratio (SNR), for the third SDH, as observed in Figure 6c-h, are shown in Figure 7. The amplitude values are normalized with respect to that for the same SDH in the TFM image processed with angle dependent velocity obtained using sixth-order polynomial fit. For SNR calculation, the maximum noise amplitude was within 20 mm before the corresponding SDH signal was considered. As seen in Figure 8, the amplitudes and SNRs are similar for the TFM images processed with angle-dependent velocity. Compared to the TFM images processed with the velocity of 5960 m/s (velocity in the isotropic alloy 617), the SNR values for the anisotropy corrected images exhibit about 18 dB higher amplitude and about 25 dB better SNR. Similarly, the alternate approach of using 6900 m/s velocity provided about 18 dB higher amplitude and SNR as compared to that processed with the isotropic velocity of 5960 m/s, exhibiting the efficacy of the methodology. The reason for obtaining improved imaging at the velocity value of 6900 m/s can be understood from Figure 8. A small reflector is considered at a depth of 26 mm in a buttering layer material. The time of flight (TOF) values calculated for pulse-echo signals received in all elements of a 64-element PAUT transducer of 1 mm pitch kept above the reflector are shown in Figure 8. The TOF values calculated for the angle dependent ultrasonic velocities as per sixth order polynomial fit (Equation (3)) and sine fit (Equation (4)) are shown as solid and dashed black lines. This may be considered as the true TOF values as obtained for the third SDH shown in Figure 6a,b. If a velocity value of 5660 m/s is used, the TOF value matches only at 0\({}^{\circ}\), and a large deviation is observed from the actual values at other  
Figure 7: Amplitude and signal-to-noise ratio (SNR) obtained for third SDH in the TFM images processed with isotropic and angle dependent ultrasonic velocity values as shown in Figure 6. The amplitude values are normalized with respect to that of the same SDH in the TFM image processed with angle dependent velocity obtained using sixth-order polynomial fit. angles. In TFM reconstruction, it means that the experimental signals corresponding to most of the elements will not be considered constructively. However, if we use a higher velocity of 6900 m/s and assume the reflector to be at 31 mm depth in an isotropic material, the TOF values (as shown by the orange curve in Figure 8) for most of the elements match closely with that corresponding to the reflector at 26 mm depth in the anisotropic buttering layer. Hence, when the FMC signals obtained from a reflector at a depth of 26 mm in the anisotropic buttering layer are processed using an isotropic velocity of 6900 m/s, a high amplitude well-focused image is observed for the same at \(\sim\)31 mm depth. As a single isotropic ultrasonic velocity value is used for generating the TFM image shown in Figure 6h, this can be directly implemented in any commercial PAUT equipment with FMC/TFM facility for obtaining improved imaging in an anisotropic material.