Back-propagation of ultrasound pulses via directivity spectrum method

Abstract

The directivity spectrum encodes information about the three dimensional field and its magnitude is independent of the distance from the transducer face in a lossless medium. The shape of the ultrasound pulse is determined by the phase of the directivity spectrum, and its phase is related to the position of the pulse in the space-time domain. This feature of the directivity spectrum can be used to predict the shape of the ultrasound pulse at any position by changing the phase of its directivity spectrum. The method for measuring the directivity spectrum proposed here depends on the utilization of a Large Aperture Hydrophone (LAH) which has the unique feature that its output is independent of the distance from the transducer face, in a lossless medium, and it is also diffraction-insensitive. The Fourier transform of the field is related to the directivity spectrum of the transducer and the LAH can measure its angular components. We confirmed these arguments by measurements in a water tank, with pulsed fields, for several orientations of the LAH. Once the directivity spectrum of the pulsed field was known, its phase could be shifted by a specific shift factor, and the spatial distribution of the field at a new position could be obtained by the inverse Fourier transform of the shifted directivity spectrum. We present images corresponding to the predicted (back-propagated) spatial distribution of the ultrasound field of a planar transducer, obtained from the directivity spectrum measured at 6 cm from the transducer face.