Reconstructing transducer surface motion by inverse extrapolation of measured pressure wavefields

Optimising the design of medical ultrasound transducers requires precise knowledge of the motion of the transmitting elements, especially if cross-talk between neighboring elements plays a significant role. Direct measurement of the motion of the elements is complicated. Therefore we propose to compute these velocity profiles from a pressure field measured in a plane parallel to the surface of the transducer. The method employs an inverse extrapolation of the measurements using an analytical deconvolution based on Weyl´s representation of the Green´s function. The method is tested for transducers operating in the MHz-range and with spatial dimensions in the order of 100 μm. Both measured and simulated pressure fields are used to investigate its performance. It is shown that relevant results, in terms of energy localisation and temporal behaviour, can be obtained for realistic distances between the transducer and measurement planes and for coarse sampling grids. In addition, the results show that sharp reconstructions of the velocity profiles are only possible if fine measurement grids are used and if the measurement distance is less than a wavelength of the ultrasound wave field.