Modification of Spectra of Pulses from Ultrasonic Transducers by Scatterers in Non-Attenuating and in Attenuating Media

When an ultrasonic pulse is scattered off a particle, the spectrum of the scattered pulse differs from that which was transmitted. A mathematical analysis is presented to show that the center frequency of the backscattered pulse is greater than that of the transmitted pulse and that the bandwidth decreases slightly when the spectrum of the pulse is Gaussian in shape. The results of measurements designed to test the theory are presented. The magnitude of the shift in center frequency for pulses backscattered off subwavelength-diameter wires is found to be similar to that predicted by the analysis. It is shown that characteristics of the spectra of the backscattered pulses can differ from those predicted if the shape of the spectrum is not truly Gaussian (as is assumed in most published analyses, including that introduced here). In medical ultrasonic imaging, the pulses are modified by scattering and absorption. The analysis is extended to account for the effects of both interactions. This allows the bandwidth and center frequency of pulses backscattered from tissues and received by medical ultrasonic scanners to be predicted.