1. A processing system for a Doppler ultrasound system having a transmit circuit configured to independently drive transducer elements of a multi-element transducer to deliver ultrasound to different positions relative to a normal axis extending from the multi-element transducer and further having a receive circuit configured to generate respective receive echo signals resulting from the ultrasound delivered to the different positions in response to each of the transducer elements detecting echo signals, the processing system comprising: an analog-to-digital converter (ADC) circuit operably coupled to the receive circuit and configured to digitize the receive echo signals into data representing the respective receive echo signals; a memory for storing data; and a processor operably coupled to the ADC and transmit circuit and configured to generate control signals to control the transmit circuit to steer ultrasound beams from the transducer and along respective beam axes to respective sample locations, the sample locations arranged spatially across a virtual surface having a lateral extent, wherein each beam axis intersects the virtual surface at only the respective sample location, the processor further configured to process the data from the receive circuit to extract Doppler shift signals and generate Doppler shift data therefrom for each of the sample locations, and configured to store the Doppler shift data for the sample locations in the memory.