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An accurate frequency-domain synthetic aperture focusing technology (F-SAFT) based on 2-D equivalent velocity mapping is proposed for laser ultrasonic testing (LUT) to detect and image internal defects in specimens. The equivalent velocity mapping varies with depth and spatial frequency to match the characteristics of the separated excitation and detection commonly used in LUT. Bulk acoustic waves are non-destructively excited by a line-shaped laser source and are detected by a laser Doppler Vibrometer. By compensating for the distance shift arising from the separation of the laser spots, the imaging defect location is corrected. Several optimisations of the algorithm are carried out: the calculation time of the equivalent velocity is reduced by simplifying its expression, and the imaging quality, especially for defects with a shallow depth, is improved by the 2-D equivalent velocity mapping. The results show that compared with traditional F-SAFT, the optimised F-SAFT algorithm can not only improve the imaging quality but also locate the defect more accurately with separated excitation and detection. • F-SAFT with various velocity mappings for separated excitation and detection. • 2-D velocity mapping with high calculation efficiency. • Improved imaging quality of shallow defects by optimising equivalent velocity. • Corrected defect's horizontal location by compensating imaging shift. [ABSTRACT FROM AUTHOR]

The Synthetic Aperture Focusing Technique (SAFT) is employed in laser ultrasonic non-destructive testing to image defects. However, during the laser ultrasonic imaging process, the influence of multi-mode waves often introduces various artifacts in the imaging results. We investigated a multi-iteration frequency-domain SAFT (MIF-SAFT) algorithm to tackle this challenge. Initially, a single low-precision F-SAFT imaging result is performed to identify potential defect locations. Subsequently, a back-projection method is applied to determine defect positions and separates acoustic waves of different modes in the B-scan. After that, a multi-mode F-SAFT imaging is performed for evaluation, and the above process is repeated until the imaging outcome stabilizes. The result shows that artifacts are removed when the image remains unchanged after multiple iterations, and the imaging quality is effectively improved by MIF-SAFT. Furthermore, including directivity patterns of laser ultrasound also enhances defect imaging capabilities within MIF-SAFT. Additionally, we examined the MIF-SAFT's capacity to detect multiple defects, which can image them simultaneously. • Multi-iteration in F-SAFT for artifact removal. • Different ultrasonic signals are separated by using the algorithm. • Directivity patterns are performed to enhance the imaging result. • Applied for multiple defects imaging simultaneously. [ABSTRACT FROM AUTHOR]