Theory of ultrasound Doppler-spectra velocimetry for arbitrary beam and flow configurations

In conventional ultrasound Doppler systems, the velocity component along the beam axis is derived from the observed frequency shift. Recently, it was verified that by using a pulsed-Doppler system with the beam transversely oriented with respect to the flow, the velocity component transverse to the beam can be derived from the edges of the spectrum. These results are generalized to take into account arbitrary angles of incidence, effects of velocity gradients, arbitrary apertures, and arbitrary source pulses. For uniform apertures and transverse flow, it has been previously shown that the Doppler output spectrum is symmetrical about zero frequency, with its width depending on the Doppler effect due to the transverse velocity and the geometry of the problem. For a beam direction oblique to the velocity, it is shown that the spectrum is now shifted, and is centered about the classical Doppler frequency. For velocity gradients and transverse flows the spectrum remains symmetrical, with the edges corresponding to the maximal velocity; however, the profile becomes peaked at the center. For oblique incidence, an asymmetrical spectrum is obtained and its edges are related to the maximal and minimal velocities within the sampling volume.