Imaging of the Nonlinear Acoustic Parameter B/A

Abstract

The nonlinear acoustic interaction between a single frequency sinusoid and a broadband pump waveform propagating in the opposite direction produces phase changes in the probe proportional to the nonlinear parameter B/A in the spatial region of interaction. The instantaneous phase change along the received probe can be expressed as the convolution of the pump waveform with the spatial distribution of B/A along the propagation path over which the pump and reflected probe interact. In theory, the phase modulated sinusoidal probe can be processed (phase detection and deconvolution) to produce an “A-mode” representation of B/A. If the pump is an intense impulse and the probe a swept-frequency sinusoid, then the pump interacts with the probe at each spatial position along the propagation path at a unique frequency. Thus, the phase modulation, proportional to $[\frac{B}{A}\left( x \right)$ along the propagation path, can be extracted directly from the phase spectrum obtained from the Fourier transform of the swept-frequency probe. This is somewhat analogous to the mapping of space to frequency which forms the basis for magnetic resonance imaging.

If the impulsive pump is replaced by another swept-frequency sinusoid, then the phase change in the probe due to B/A at a particular point along the propagation path will be spread out for the duration of the pump along the probe. Passage of the received signal through an appropriate matched filter restores spatial coherence to the phase information in the probe so that it can be processed as if the pump were a broadbanded impulse. This approach suggests a means of approaching the design of effective pump waveforms which can resolve a wide range of spatial frequencies in $\frac{B}{A}\left( x \right)$.