Parallel Multi-Focusing Using Plane Wave Decomposition

In conventional phased-array imaging, identical short single-carrier pulses are emitted from the entire aperture, and focusing is done in one direction at a time by applying simple geometric delays. This is a sequential and not optimal transmission scheme, which limits the frame rate and makes 3D imaging in real-time impossible. By using a transmit matrix with frequency and apodization variations across the aperture, it is possible to focus in several directions simultaneously (5 or more), significantly increasing the frame rate to 170 frames/s or more. The algorithm used for the determination of the transmitted pulses is based on the directivity spectrum method, a generalization of the angular spectrum method, a generalization of the angular spectrum method, containing no evanescent waves. The underlying theory is based on the Fourier slice theorem, and field reconstruction from projections. First a set of desired 2-D sensitivity functions is specified, for multi-focusing in a number of directions. The field along these directions is decomposed to a sufficiently large (for accurate specification) number of plane waves, which are then back-propagated to all transducer elements. The contributions of all plane waves result in one time function per element. The numerical solution is presented and discussed. It contains pulses with a variation in central frequency and time-varying apodization across the aperture (dynamic apodization). The RMS difference between the transmitted field using the calculated pulse-excitation and a designed multi-focused field in 3 focal directions at a depth corresponding to an F-number of 1.5 is 4%, and in increases with depth. These results demonstrate the close agreement between specified and actual acoustic fields. It is, then, shown how specification of long frequency-modulated desired field functions can yield more strongly focused fields or higher number of multi-focused beams, with the additional advantage of higher SNR.