Douglass Alexander S, Song H C, Dowling David R
Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
Marine Physical Laboratory, Scripps Institute of Oceanography, University of California, San Diego, La Jolla, California, 92093, USA.
J Acoust Soc Am. 2017 Sep;142(3):1663. doi: 10.1121/1.5003787.
Frequency-difference beamforming [Abadi, Song, and Dowling (2012b). J. Acoust. Soc. Am. 132, 3018-3029] is an unconventional beamforming method for use with sparse receiver arrays. It involves beamforming a quadratic product of complex field amplitudes, P(ω)P(ω), at the difference frequency, ω-ω, instead of beamforming the complex field amplitude P(ω) at frequencies ω within the signal bandwidth. Frequency-difference beamforming is readily implemented with ordinary transducer array recordings of non-zero bandwidth signals. Results for, and comparisons of, frequency-difference beamforming from simulations and experiments are reported herein. In particular, spherical-wave beamforming is investigated using 15 and 165 kHz pulse signals in a 1.07-m-diameter water tank with a linear array having 14 elements spaced 5.08 cm apart. Here, frequency-difference beamforming using the high-frequency pulses provides comparable results to conventional beamforming at 15 kHz. Plane-wave beamforming is investigated using 11.2-32.8 kHz frequency-sweep signals broadcast 3 km through a 106-m-deep ocean sound channel to a vertical array having 16 elements spaced 3.75 m apart. Here, frequency difference beamforming in the 1.7-2.3 kHz difference frequency band provides results comparable to conventional beamforming in this band.
频差波束形成法[阿巴迪、宋和道林（2012b）。《美国声学学会杂志》132, 3018 - 3029]是一种用于稀疏接收器阵列的非常规波束形成方法。它涉及在差频ω - ω处对复场幅度的二次乘积P(ω)P(ω)进行波束形成，而不是在信号带宽内的频率ω处对复场幅度P(ω)进行波束形成。频差波束形成法可以很容易地用非零带宽信号的普通换能器阵列记录来实现。本文报告了频差波束形成法的模拟和实验结果以及比较情况。具体而言，在直径为1.07米的水箱中，使用15千赫和165千赫的脉冲信号，对具有14个元件、间距为5.08厘米的线性阵列进行球面波波束形成研究。在此，使用高频脉冲的频差波束形成法提供了与15千赫时的传统波束形成法相当的结果。使用11.2 - 32.8千赫扫频信号通过106米深的海洋声道传播3千米到具有16个元件、间距为3.75米的垂直阵列，对平面波波束形成进行研究。在此，在1.7 - 2.3千赫差频带内的频差波束形成法提供了与该频带内传统波束形成法相当的结果。
