The past theoretical contributions in Doppler ultrasonic imaging have borrowed heavily from the electromagnetic case. In these contributions, most points of departure between the ultrasonic and electromagnetic cases were taken care of by heuristic incorporation of factors in the derived formulas. A theory is presented that is more complete in the sense that it specifically accounts for the diffracted fields of the transducer aperture (assumed to be a source of a Gaussian focussed beam), the interaction of these fields with the scattering sites, and the interaction of the transducer aperture with the back scattered fields. The theoretical formulation was used to perform a series of computer simulation studies on Doppler ultrasound. The control afforded by the theory over different parameters of the system has allowed us to study the effect of the different signal bandwidths, tissue attenuation constants, and the role of transducer design in the ultrasound Doppler systems.
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