Far-focused pixel-based imaging of internal defects in multi-layered media based on attenuation compensation and circular coherence factor

The multi-layered media composed of layers with different sound velocities exhibit anisotropy, strong attenuation, and interface reflection in terms of sound propagation, posing challenges for conventional ultrasound imaging methods, especially in detecting deep-seated and near-interface defects. In this study, an improved far-focused pixel-based (FPB) imaging method for detecting internal defects in multi-layered media is proposed. First, the time delay calculation in the FPB method is corrected using the shortest path searching method to determine the acoustic time-of-flight. Then, phase information is extracted from the echo signal to construct a circular coherence factor (CCF) that dynamically weights the time-corrected FPB images, addressing the issue of ineffective detection of near-interface defects caused by interface reflection. Finally, considering the sound attenuation in multi-layered media, the directivity coefficient, transmission coefficient, and divergence coefficient are determined through theoretical derivation to compensate for the echo amplitude. Experimental results demonstrate that the improved FPB method significantly enhances the reflection echo from deep-seated defects, reduces the maximum relative localisation error to 0.9%, and the quantisation error to 6.4%. The proposed method also greatly improves the lateral resolution and signal-to-noise ratio (SNR) of internal defect imaging compared to the total focusing method (TFM) and traditional FPB method.