The use of the Born approximation for microstructural imaging with ultrasonic phased arrays

The applicability of the Born approximation for modeling ultrasonic wave propagation in polycrystalline materials is commonly assumed to require weak-scattering conditions. However, the quantitative criteria for its validity in ultrasonic array imaging have not yet been fully established. In this paper, an analytical model based on the Born approximation is developed to simulate ultrasonic array signals for arbitrary polycrystalline structures. Total Focusing Method (TFM) images reconstructed from these simulations are quantitatively compared with reference images obtained from finite element (FE) simulations, which account for all physical effects of ultrasonic wave scattering. Analysis of image similarity metrics across a wide range of materials and grain sizes shows that the accuracy of TFM images produced by the analytical model is directly correlated with the single-scattering rate (SSR). The SSR is defined as the fraction of the single-scattering contribution to the total image intensity and can be directly measured from phased-array images generated by FE simulations. These results demonstrate that the SSR can serve as a practical quantitative indicator of the validity of ultrasonic array imaging models based on the Born approximation.