Modeling of Doppler signal considering sample volume and field distribution

The ultrasound Doppler amplitude spectrum for a single scatterer and the power spectrum for multiple scatterers were calculated in terms of the echo signal from scatterers crossing the sample volume, defined by the transmitted pulse and the diffracted field distribution for cw. The observation time for the Doppler signal is also considered. Statistical parameters such as mean and variance of the Doppler power spectrum are studied as continuous functions of the intersection angle between the beam axis and the flow direction, the pulse length and the viewing position. The derived equations are valid whether the transit time is governed by the pulse length, or beam geometry, or both. It is shown that the Doppler power spectra calculated by the proposed model and by the Doppler signal obtained from field theory are in good agreement. It is also shown that, when the Doppler signal broadening due to the transmitted pulse and beam geometry is constant without regard to the intersection angle, the degree of spread of the velocity distribution can be estimated from the variance of the Doppler power spectrum measured by the Doppler system once the intersection angle is known.