Khosla S R, Dowling D R
Department of Mechanical Engineering, University of Michigan, Ann Arbor 48109-2121, USA.
J Acoust Soc Am. 2001 Feb;109(2):538-46. doi: 10.1121/1.1338560.
Acoustic time reversal is a robust means of retrofocusing acoustic energy, in both time and space, to the original sound-source location. However, noise may limit the performance of a time-reversing array (TRA) at long source-array ranges, or when the original-source or TRA-element power levels are low. The operation of a TRA requires two steps (reception and transmission) so both TRA-broadcast noise and ambient noise must be taken into account. In this paper, predictions are made for how a simple omnidirectional noise field influences the probability that the signal amplitude from a narrow-band TRA will exceed the noise at the TRA's retrofocus. A general formulation for the probability of TRA retrofocusing, which can be used for TRA design, is developed that includes: the variance of the noise field, the original source strength, the TRA's element output power, the number of TRA elements (N), and the propagation characteristics of the environment. This formulation predicts that a TRA's array gain (in dB) at the retrofocus may be as high as + 10log10(N) to + 20 log10(N) depending on the relative strengths of the original source and the TRA's elements. Monte Carlo simulations in both a free-space environment and a shallow-ocean sound-channel environment compare well to this probability formulation even when simple approximate parametric relationships for the appropriate Green's functions are used. The dominant deviation between theory and simulation in the sound channel is caused by acoustic absorption.
声学时间反演是一种在时间和空间上都能将声能反向聚焦到原始声源位置的稳健方法。然而，在声源与阵列距离较远时，或者当原始声源或时间反演阵列（TRA）元件的功率水平较低时，噪声可能会限制TRA的性能。TRA的运行需要两个步骤（接收和发射），因此必须同时考虑TRA广播噪声和环境噪声。本文预测了一个简单的全向噪声场如何影响窄带TRA的信号幅度超过TRA反向聚焦处噪声的概率。开发了一种可用于TRA设计的TRA反向聚焦概率的通用公式，该公式包括：噪声场的方差、原始声源强度、TRA元件的输出功率、TRA元件的数量（N）以及环境的传播特性。该公式预测，TRA在反向聚焦处的阵列增益（以分贝为单位）可能高达 + 10log10(N) 至 + 20 log10(N)，具体取决于原始声源和TRA元件的相对强度。即使使用适当格林函数的简单近似参数关系，在自由空间环境和浅海声道环境中的蒙特卡罗模拟与该概率公式的比较结果也很好。声道中理论与模拟之间的主要偏差是由声吸收引起的。
