Effects of transducer beam geometry and flow velocity profile on the Doppler power spectrum: a theoretical study

A theoretical model is used to show how the Doppler spectrum for various axisymmetric velocity profiles is affected by beam misalignment and incomplete insonation. Results are presented for both circular and square beam geometries. Moreover, a closed-form expression is derived for the power spectral density received by an on-axis transducer with a Gaussian beam profile. It is shown that the error incurred in measuring the mean Doppler frequency with such a profile will generally be bounded by the results for the circular and square beam geometries. The effects of an ideal high-pass filter on the mean Doppler frequency and the backscattered Doppler power are examined. It is shown that such a filter can introduce large differences in the measured systolic to diastolic power ratios. Finally, theoretical expressions and results are presented for the spectral broadening index (SBI), normalized spectral variance (NSV), coefficient of kurtosis (CK), the coefficient of skewness (CS) as functions of the axisymmetric velocity profile shape assuming complete uniform insonation.