Pulsed Doppler flow-line spectrum for focused transducers with apodized apertures

The properties of the single flow-line Doppler spectrum using pulsed wave (PW) ultrasound is studied on the basis of previously developed spectral theory for transducers with apodized apertures. It has been shown previously that the spectral width of Doppler signals from a sample volume in low velocity-shear flow is independent of the sample volume depth but that is not true for the spectra from the individual streamlines. The work presented here on the Doppler flow-line spectrum shows that its width should be invariant with flow-line location, if the sample volume depth is fixed. At the same time, for a transducer operating in PW mode not only the Doppler spectral width depends on the sample volume depth, but also the modal Doppler frequency shift changes with flow-line displacement in the illuminating field except if the sample volume centre and the beam focus coincide. The variation of modal Doppler frequency shift is the more explicit manifestation of the effect of wavefront curvature increasing for lines and sounding depths distant from the focal point. The values of the Doppler shift and spectral bandwidth are reported taking account of beam diffraction and variations in its geometry due to focusing.