Phase velocity estimation technique based on adaptive beamforming for ultrasonic guided waves propagating along cortical long bones

The axial transmission technique, which is used to estimate the phase velocity of an ultrasonic guided wave propagating along cortical bone is a promising tool for bone quality assessment. Lamb waves are ultrasonic guided waves that consist of multiple modes. The number of existing modes and the signal-to-noise ratio required for phase velocity estimation depend on the frequency of the signal. Hence, we employ an adaptive beamforming technique with spatial averaging to control signal-to-noise ratio and resolution by situating subarrays within the full array. Because the determination of the optimal size for spatial averaging is difficult, we propose a new algorithm that does not require a specific size with a new falsephasevelocity rejection technique. Using a 2.0-mm-thick copper plate, the proposed method accurately estimates phase velocity with fitting errors of 0.26 and 1.3%, as shown by simulation and experimental results, respectively. The measurement frequency ranges are more than twice wider than those measured by the conventional method.