Diffuse ultrasonic backscatter at normal incidence through a curved interface

Diffuse ultrasonic backscatter techniques are useful for probing heterogeneous materials to extract microstructural parameters and detect flaws which cannot be detected by conventional ultrasonic techniques. Such experiments, usually done using a modified pulse-echo technique, utilize the spatial variance of the signals as a primary measure of microstructure. Quantitative ultrasonic scattering models include components of both transducer beams as well as microstructural scattering information. Of particular interest for interpretation of many experiments is the propagation through a liquid-solid interface. Here, a recent single-scattering model is expanded to include components needed for comparison with experiments. In particular, the Wigner distribution of the displacement profile is derived to model the beam pattern of an ultrasonic transducer through a curved liquid-solid interface. A simple Gaussian beam is used to model the transducer beam pattern. This expression is then used in conjunction with an appropriate scattering operator to complete the derivation. The theory developed is then compared with experimental results for a fine-grained steel using both a planar and a cylindrical interface. These results are anticipated to impact ultrasonic nondestructive evaluation and characterization of heterogeneous media with arbitrary curvatures.