Time Difference Measurement of Ultrasonic Pulses Using Cross-Correlation Function between Analytic Signals

Many methods have been developed in order to measure precisely the velocities of elastic waves in materials. However, most of them assume that elastic waves are not distorted when propagating through a medium. In real materials, such a case is rare or only approximately valid. As a result, it is difficult to obtain sound velocities precisely. In this study, in order to solve this problem, we attempt to improve the cross-correlation method, that is, we first extend ultrasonic pulses into analytic signals and then develop the theory of the cross-correlation function between those analytic signals. Consequently, we found a method to measure the precise time difference between pulses. This method is applicable to the following cases: 1) no dispersion exists in medium; 2) not dispersion but constant phase shift exists; 3) not dispersion but frequency-dependent attenuation ratio exists; 4) there exists dispersion whose group velocity is constant; and finally 5) includes all cases from 2) to 4).