Theory of true-velocity duplex imaging using a single transducer

We study the B-mode/Doppler duplex imaging problem. We begin by looking at the problem of determining the true velocity vector only. We develop a model for the power spectrum of a signal reflected by a line of point scatterers with a Poisson distribution. We show that with circularly symmetric apertures it is possible to use the expression of that power spectrum to determine the true velocity vector from a single excitation and two measurements. We also describe an illumination configuration that guarantees that the velocity estimation process is range-invariant. We conclude the paper by studying the problem of simultaneously estimating the range and true velocity of a flow. In particular, we show that this problem is completely characterized by a generalized range-2-D Doppler ambiguity function that depends on the excitation signal and the transducer geometry.