Ultrasonic Reflection Mode Imaging of the Nonlinear Parameter B/A: A Theoretical Basis

The theoretical basis of a new method for obtaining reflection mode images of the nonlinear parameter B/A is given. An expression for the instantaneous phase shift in a reflected sinusoidal probe due to nonlinear interaction with an arbitrary pump waveform propagating in the opposite direction is derived. This i nstantaneous phase shift is proportional to the convolution of the pump waveform with the spatial d istribution of the nonlinear parameter B/A along the propagation path of the pump and interacting probe. If a linear frequency modulated (LFM) sinusoid is used for t he probe, then the pump interacts with the reflected probe at each point in space at a unique frequency . This u seful property simplifies signal processing and leads to algorithms for separation of the desired from undesired reflections in a r ever be rant env i r onmen t .