Correction of ultrasonic wavefront distortion using backpropagation and a reference waveform method for time-shift compensation

Abstract

A model is introduced to describe ultrasonic pulse amplitude and shape distortion as well as arrival time fluctuation produced by propagation through specimens of human abdominal wall. In the model, amplitude and shape distortion develops as the wavefront propagates in a uniform medium after passing through a phase screen that only causes time shifts. This distortion is compensated by a backpropagation of the wavefront using the angular spectrum method. The compensation employed waveforms emitted by a pointlike source and measured after propagation through the tissue. The waveforms were first corrected for geometric path and then were backpropagated over a sequence of increasing distances. At each distance, a waveform similarity factor was calculated to find the backpropagation distance at which the waveforms were most similar. A new method was devised to estimate pulse arrival time for geometric correction as well as to perform time-shift compensation. The method adaptively derives a reference waveform that is then cross correlated with all the waveforms in the aperture to obtain a surface of arrival times. The surface was smoothed iteratively to remove outlying points due to waveform distortion. The mean (+/- s.d.) of the waveform similarity factor for 14 specimens was found to be 0.938 (+/- 0.025) initially. After backpropagation of waveforms to the distance of maximum waveform similarity for each specimen, the waveform similarity factor improved to 0.967 (+/- 0.015). The corresponding energy level fluctuation in the wavefront was 4.2 (+/- 0.4) dB initially and became 3.3 (+/- 0.3) dB after backpropagation. For wavefronts focused at 180 mm, the -30 dB mean (+/- s.d.) effective radius of the focus was 4.2 (+/- 1.2) mm with time-shift compensation in the aperture and became 2.5 (+/- 0.5) mm with backpropagation followed by time-shift compensation. These results indicate that a phase screen placed some distance away from the aperture is an improved model for the description of wavefront distortion produced by human abdominal wall and that wavefront backpropagation followed by time-shift estimation and compensation is an effective method to compensate for such distortion.