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

Abstract

Focus degradation produced by abdominal wall has been compensated using a least-mean-square error estimate of arrival time. The compensation was performed on data from 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 14 different specimens of human abdominal wall. Time histories of the virtual point source were reconstructed by removing the time delays produced by geometric path differences and also removing time shifts produced by propagation inhomogeneities in the case of compensation, finding the complex 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 delay expressed in terms of the arrival time differences between neighboring points and included an algorithm to determine arrival time differences when correlation based estimates were unsatisfactory due to dissimilarity of neighboring waveforms. Comparisons of reconstructed time histories in the image plane show that the -10-dB effective radius of the focus for reception through abdominal wall without compensation for inhomogeneities averaged 48% greater than the corresponding average effective radius for ideal waveforms, while time-shift compensation reduced the average -10-dB effective radius to a value that is only 4% greater than for reception of ideal waveforms. The comparisons also indicate that the average ratio of energy outside an ellipsoid defined by the -10-dB effective widths to the energy inside that ellipsoid is 1.81 for uncompensated tissue path data and that time-shift compensation reduced this average to 0.93, while the corresponding average for ideal waveforms was found to be 0.35. These results show that time-shift compensation yields a significant improvement over the uncompensated case although other factors must be considered to achieve an ideal diffraction limited focus.