Frequency Domain Method for Resolution of Two Overlapping Ultrasonic Echoe

The ability to identify and resolve overlapping echoes is crucial to the enhancement of axial scan resolution in ultrasonic testing. Overlapping echoes are frequently encountered in the inspection of shallow and/or short cracks in Time-of-Flight Diffraction and normal incidence reflection inspection of near surface flaws. Dictionary-based parametric representation (DBPR) has been proposed as a powerful framework to separate overlapping echoes of different shapes. However, the large solution space in DBPR renders the optimization process difficult. We propose a new echo separation method named Trigonometric Echo Identification (TEI) that exploits the consistent frequency domain amplitude and phase relationships of two overlapping ultrasonic echoes to reduce the number of optimization parameters.;In TEI, frequency amplitude profiles are entered as inputs and the corresponding set of frequency phase profiles are reconstructed as outputs. The optimality of the output phase profiles is then used as a metric to determine the accuracy of the trial amplitude inputs. By reconstructing the phase information instead of explicitly specifying the phase profiles, we can reduce the number of unknowns in the problem of identifying two overlapping ultrasonic echoes. Compared to DBPR, TEI can describe more complex ultrasonic echoes using the same number of optimization parameters. In addition, since the phase profiles are reconstructed using the acquired data, TEI would perform more reliably in the presence of noise.;Simulation tests were conducted to assess the relative performance of TEI and DBPR. Echo parameters including center frequency, phase shift and relative amplitudes were systematically varied to yield different test configurations. The standard deviation of timing errors obtained from TEI were 50% lower compared to DBPR. The difference in algorithm performance is especially evident in low SNR signals and signals containing echoes of complex shapes. The TEI algorithm was also verified on experimental ultrasound testing data containing overlapping echoes. The echo arrival times extracted using TEI agree with the values obtained using geometric calculations.