Ultrasonic reflection mode imaging of the nonlinear parameter B/A: I. A theoretical basis

Abstract

The theoretical basis of a new method for obtaining both reflection and transmission mode images of the nonlinear parameter B/A is given. An expression for the instantaneous (not cumulative) phase shift in a sinusoidal probe waveform due to nonlinear interaction with an arbitrary pump waveform propagating in the opposite direction is derived. This instantaneous phase shift is proportional to the convolution of the pump waveform with the spatial distribution of the nonlinear parameter B/A along the propagation path of the pump and interacting probe. The instantaneous phase of the probe can be obtained in real time giving a measure of the variation of B/A along an image line.