Transverse-to-transverse diffuse ultrasonic double scattering.

Previously, a transverse-to-transverse single scattering model (T-T SSR) was developed for a pulse echo configuration, which may have limitations for strongly scattering materials. In this work, a transverse-to-transverse double scattering model (T-T DSR) is presented to model the transverse ultrasonic backscatter more accurately. First, the Wigner distribution of the transducer beam pattern is extended to a transverse wave. Next, the multiple scattering framework is followed to derive the transverse and longitudinal components of the second-order scattering. Then, a quasi-Monte Carlo (QMC) method is used with Graphics Processing Unit (GPU) acceleration to calculate numerical results of the final expression which contains a five-dimensional integral. The correlation length, the focal length of the transducer, and incident angle are used to investigate differences between the T-T DSR model and the T-T SSR model. Finally, a backscatter experiment is performed on two stainless steel specimens with different grain sizes to determine the respective correlation lengths. The results show that the T-T DSR model has better performance over the T-T SSR model for evaluating the grain size of these relatively strongly-scattering specimens.