Ultrasonic Frequency-Domain Reverse-Time Migration Imaging Incorporating Element Directivity Correction

The finite width of ultrasonic array elements results in a non-uniform angular radiation pattern of elastic waves in solids, deviating from the ideal point-source assumption commonly adopted in reverse-time migration (RTM). This angular radiation non-uniformity produces a crack tip-dominated imaging amplitude with weak crack flank representation, manifesting as a pronounced depth-dependent amplitude imbalance along vertically oriented defects. As a result, cracks may be misinterpreted as point reflectors, which compromises the reliability of characterization in ultrasonic nondestructive testing (NDT). This study proposes an ultrasonic frequency-domain reverse-time migration (FDRTM) imaging method incorporating element directivity correction. A longitudinal-wave directivity model in solids is formulated in the frequency domain and normalized at each frequency to ensure consistent scaling during multi-frequency stacking. During backward wavefield reconstruction using full matrix capture (FMC) data, the angular-dependent energy distribution associated with the receiving direction is explicitly corrected, rebalancing the angular energy distribution in the reconstructed wavefield. Defect imaging is then performed using a frequency-domain cross-correlation imaging condition, followed by stacking over frequency and normalization. Validation experiments were conducted on an artificially manufactured vertical crack in a 7075 aluminum alloy specimen. The results indicate that, relative to conventional RTM, the proposed method reduces crack tip dominance and enhances the relative visibility and continuity of crack flanks. Compared with conventional RTM, the peak imaging amplitude increases by 22.44%, and the amplitude at a depth of 6.8 mm is enhanced by 24.39%. In addition, the proposed method outperforms the total focusing method (TFM) in crack profile continuity and the relative visibility of crack flanks. The results confirm that incorporating element directivity correction into frequency-domain RTM mitigates depth-dependent amplitude imbalance and restores crack flank visibility, thereby improving the reliability of crack defect characterization in ultrasonic NDT.