Optimized auto-focusing method for 3D ultrasound imaging in NDT

In this work, we propose an optimized auto-focusing algorithm to be used with ultrasound matrix arrays for three-dimensional imaging in the presence of interfaces. Its main application is for non-destructive-testing (NDT), where usually two mediums with different propagation velocities are present. The refraction at the interface between those mediums complicates the calculation and the application of the focusing delays, which requires iterative processes that are usually the main bottleneck for high-speed inspections. 

We tackle this problem by generalizing the virtual array concept previously proposed for linear arrays and plane images to the case of matrix-arrays and three-dimensional (3D) beamforming. Furthermore, we propose a two-dimensional iterative algorithm for exact time-of-flight calculation to the two foci per scan line required by the virtual array. The mathematical formulation for the 3D case is obtained and the time-delay errors are analyzed by simulation. Finally, image quality with the proposed method is compared with that obtained with conventional Total Focusing Method (TFM) and exact delay calculation. The principal conclusion is that the virtual array approach generates images with equivalent quality to those obtained by exact calculation, while it reduces more than two orders of magnitude the computation load.