Iterative reconstruction of the transducer surface velocity

Ultrasound arrays used for medical imaging consist of many elements placed closely together. Ideally, each element vibrates independently. However, because of mechanical coupling, crosstalk between neighboring elements may occur. To quantify the amount of crosstalk, the transducer velocity distribution should be measured. In this work, a method is presented to reconstruct the velocity distribution from far-field pressure field measurements acquired over an arbitrary surface. The distribution is retrieved from the measurements by solving an integral equation, derived from the Rayleigh integral of the first kind, using a conjugate gradient inversion scheme. This approach has the advantages that it allows for arbitrary transducer and pressure field measurement geometries, as well as the application of regularization techniques. Numerical experiments show that measuring the pressure field along a hemisphere enclosing the transducer yields significantly more accurate reconstructions than measuring along a parallel plane. In addition, it is shown that an increase in accuracy is achieved when the assumption is made that all points on the transducer surface vibrate in phase. Finally, the method has been tested on an actual transducer with an active element of 700 × 200 μm which operates at a center frequency of 12.2 MHz. For this transducer, the velocity distribution has been reconstructed accurately to within 50 μm precision from pressure measurements at a distance of 1.98 mm (=16λ₀) using a 200-μm-diameter needle hydrophone.