Time-shift compensation of ultrasonic pulse focus degradation using least-mean-square error estimates of time delay

Abstract

Focus degradation produced by abdominal wall has been compensated using least-mean-square error estimates of time shifts in measurements of ultrasonic pulses from a curved transducer that emits a hemispheric wave and simulates a point source. The pulse waveforms were measured in a two-dimensional aperture after propagation through a water path and after propagation through different specimens of human abdominal wall. Time histories of the virtual point source were reconstructed by removing the time delay produced by geometric path differences and including time shift produced by propagation inhomogeneities in the case of compensation, finding the amplitudes of the Fourier harmonics across the aperture, calculating the Fraunhofer diffraction pattern of each harmonic, and summing the patterns. This process used a least-mean-square error solution for the relative arrival time expressed in terms of the arrival time differences between neighboring points. Comparisons of the time histories in the source plane show that the −30 dB effective radius of the focus can be 90% greater for propagation through abdominal wall than through a water path and that this percentage is reduced to 37% by time-shift compensation.