Quantifying the breakdown of single scattering for ultrasonic backscatter measurements

Diffuse ultrasonic backscatter, which results from the interaction of elastic waves with material heterogeneity, can be used to characterize microstructural information. The scattering that occurs within the material can be complex and accurate models are needed to interpret measurements quantitatively, particularly for higher-scattering materials. Recently, a double scattering model was derived in which it was assumed that the energy scatters at most twice within the microstructure prior to detection. The significance of this model, with a focus on valid ranges of applicability, has not been thoroughly explored. In this article, theoretical and experimental results are examined to compare the single and double scattering models. The theoretical results show that single scattering models are appropriate for weakly scattering materials for a wide range of experimental setups while stronger scattering materials predict significant second-order scattering for certain measurement parameters, including transducer frequency and material path. Experimental results for steel, a strongly scattering material, are presented for frequencies of 5, 7.5, 10, and 15 MHz and show the domain for which the doubly scattered response becomes significant, as well as model limitations, due to selected experimental parameters. Finally, guidelines are provided for experiment design in order for measurements to remain within the desired scattering regime.