The angular spectrum method is a powerful technique for modeling the propagation of acoustic fields. The technique can predict an acoustic pressure field distribution over a plane, based upon knowledge of the pressure field distribution at a parallel plane. Predictions in both the forward and backward propagation directions are possible. In addition to predicting the effects of diffraction, the model also includes the effects of attenuation, refraction, dispersion, phase distortion, and the effects of finite amplitude acoustic propagation. No other model currently exists which can predict the propagation of wideband acoustic fields produced by sources of arbitrary geometry including all of the above propagation effects. Prior investigations have focused on using backward propagation predictions to analyze the surface vibration patterns of acoustic radiators. In contrast, the current effort has placed particular emphasis on verifying the model in the forward propagation case. In this paper, both forward and backward predictions are presented which demonstrate the ability of the model to characterize a three-dimensional acoustic field based upon measurements at a single plane. Results are also presented which examine the ability of the extended model to predict acoustic propagation through media composed of stacked homogeneous layers. The model has immediate applications in the study of acoustic phenomena and in the field of acoustic transducer design. Additionally, significant progress has been made toward the ultimate goal of predicting the degradation of acoustic transducer performance due to propagation through inhomogeneous, nonlinear, tissue-like media.

Prediction of ultrasonic field propagation through layered media using the extended angular spectrum method.

To be successful, correlation-based, phase-aberration correction requires a high correlation among backscattered signals. For harmonic imaging, the spatial coherence of backscatter for the second harmonic component is different than the spatial coherence of backscatter for the fundamental component. The purpose of this work was to determine the effect of changing the transmit apodization on the spatial coherence of backscatter for the nonlinearly generated second harmonic. Our approach was to determine the effective apodizations for the fundamental and second harmonic using both experimental measurements and simulations. Two-dimensional measurements of the transverse cross sections of the finite-amplitude ultrasonic fields generated by rectangular and circular apertures were acquired with a hydrophone. Three different one-dimensional transmit apodization functions were investigated: uniform, Riesz, and trapezoidal. An effective apodization was obtained for each transmit apodization by backpropagating the values measured from within the transmit focal zone using a linear angular spectrum approach. Predictions of the spatial coherence of backscatter were obtained using the pulse-echo Van Cittert-Zernike theorem. In all cases the effective apodization at 2f was narrower than the transmit apodization. We demonstrate that certain transmit apodizations result in a greater spatial coherence of backscatter at the second harmonic than at the fundamental.

Spatial coherence of backscatter for the nonlinearly produced second harmonic for specific transmit apodizations

The present work measures the effective apodizations for the fundamental and second harmonic and uses the Van Cittert-Zernike theorem to predict the spatial coherence of the second harmonic portion of backscatter. Two-dimensional pseudo-array scans of a transverse cross section of the finite amplitude ultrasonic fields generated by rectangular and circular apertures were performed with a hydrophone. Three transmit apodization functions were investigated: rectangular, Riesz, and trapezoidal. An effective apodization was obtained by backpropagating the values measured from within the transmit focal zone using a linear angular spectrum approach. In all cases the effective apodization at 2f was narrower than the transmit apodization. Our results demonstrate that choices of apodization can be identified that yield better spatial coherence at the second harmonic than at the fundamental.

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Papers

Finite amplitude acoustic propagation modeling using the extended angular spectrum method