Parametric array signal in confocal vibro-acoustography

In vibro-acoustography imaging systems, two ultrasound beams of distinct frequencies are employed to form an image of biological tissue at the difference-frequency. Three mechanisms contribute to the difference-frequency pressure, namely induced acoustic emission by a time-modulated radiation force, parametric array signal due to the superposition the beams along the propagation direction, and interaction of sound-with-sound effects. We analyze the strength of parametric array signal generated by a vibro-acoustography system composed of a two-element confocal transducer driven by two sinusoidal signals with center frequency 3.2 MHz. A 1-mm diameter tungsten sphere, placed at the transducer's focus, is used as the target object. We measure the difference-frequency pressure in water at room temperature with a calibrated hydrophone. The measurements are taken along the beam's axis in the farfield. In this configuration, the difference-frequency signal is mostly due to the parametric array phenomenon. Additionally, the acoustic emission and interaction of sound-with-sound signal levels are theoretically estimated. They are, respectively, 33 and 20 dB below the parametric array signal.