Frequency-difference beamforming in inhomogeneous media

Abstract

Frequency-difference beamforming (Abadi et al., 2012, JASA, 132, 3018-3029) is an array signal processing technique that overcomes the limitations of the spatial Nyquist criterion by lowering the processing to out-of-band frequencies. This is accomplished using a quadratic product of complex signal amplitudes at different frequencies, resulting in wave propagation information at the out-of-band difference-frequency. Acoustic waves are susceptible to strong scattering in inhomogeneous media when the sizes of the inhomogeneities are comparable to or larger than the signal wavelength. Thus, conventional beamforming in random media at high frequencies with sparse arrays may be impossible, even in the presence of small inhomogeneities. However, at lower frequencies, acoustic propagation and beamforming in the same environment might not be significantly impacted. Thus, frequency-difference beamforming in the presence of high-frequency scattering is expected to maintain robustness similar to that of a low-frequency field. In this presentation, we present a theoretical framework that supports this hypothesis using the Born approximation. The theory is tested using experiments in a 1.07-m-diameter, 0.8-m-deep cylindrical water tank with an array of up to 16 receivers and 100 kHz to 200 kHz signal pulses that propagate through an inhomogeneous medium. [Sponsored by NAVSEA through the NEEC, and by ONR.]