Application of the factorisation method to limited aperture ultrasonic phased array data

This paper puts forward a methodology for applying the frequency domain Factorisation Method to time domain experimental data arising from ultrasonic phased array inspections in a limited aperture setting. Application to both synthetic and experimental data is undertaken and a multi-frequency approach is explored to address the difficulty encountered in empirically choosing the optimum frequency at which to operate. Additionally, a truncated singular value decomposition (TSVD) approach is implemented in the case where the flaw is embedded in a highly scattering medium, to regularise the scattering matrix and minimise the contribution of microstructural noise to the final image. It is shown that when the Factorisation Method is applied to multi-frequency scattering matrices, it can better characterise crack-like scatterers than in the case where the data arises from a single frequency. Finally, a volumetric defect and a lack-of-fusion crack are both successfully reconstructed from experimental data, where the resulting images exhibit only 3\% and 10\% errors respectively in their measurement.