Wideband time-reversal imaging of an elastic target in an acoustic waveguide

Time-reversal is addressed for imaging elastic targets situated in an acoustic waveguide. It is assumed that the target-sensor range is large relative to the channel depth. We investigate the theory of wideband time-reversal imaging of an extended elastic target, for which the target dimensions are large relative to the principal wavelengths. When performing time-reversal imaging one requires a forward model for propagation through the channel, and the quality of the resulting image may be used as a measure of the match between the modeled and actual (measured) channel parameters. It is demonstrated that the channel parameters associated with a given measurement may be determined via a genetic-algorithm (GA) search in parameter space, employing a cost function based on the time-reversal image quality. Example GA channel-parameter-inversion results and imagery are presented for measured at-sea data.     

Transmission mode time-reversal super-resolution imaging

The theory of time-reversal super-resolution imaging of point targets embedded in a reciprocal background medium [A. J. Devaney, "Super-resolution imaging using time-reversal and MUSIC," J. Acoust. Soc. Am. (to be published)] is generalized to the case where the transmitter and receiver sensor arrays need not be coincident and for cases where the background medium can be nonreciprocal. The new theory developed herein is based on the singular value decomposition of the generalized multistatic data matrix of the sensor system rather than the standard eigenvector/eigenvalue decomposition of the time-reversal matrix as was employed in the above-mentioned work and other treatments of time-reversal imaging [Prada, Thomas, and Fink, "The iterative time reversal process: Analysis of the convergence," J. Acoust. Soc. Am. 97, 62 (1995); Prada et al., "Decomposition of the time reversal operator: Detection and selective focusing on two scatterers," J. Acoust. Soc. Am. 99, 2067 (1996)]. A generalized multiple signal classification (MUSIC) algorithm is derived that allows super-resolution imaging of both well-resolved and non-well-resolved point targets from arbitrary sensor array geometries. MUSIC exploits the orthogonal nature of the scatterer and noise subspaces defined by the singular vectors of the multistatic data matrix to form scatterer images. The time-reversal/MUSIC algorithm is tested and validated in two computer simulations of offset vertical seismic profiling where the sensor sources are aligned along the earth's surface and the receiver array is aligned along a subsurface borehole. All results demonstrate the high contrast, high resolution imaging capabilities of this new algorithm combination when compared with "classical" backpropagation or field focusing. Above and beyond the application of seismo-acoustic imaging, the time-reversal super-resolution theory has applications in ocean acoustics for target location, and ultrasonic nondestructive evaluation of parts.     

Time-reversal simulations for detection in randomly layered media

A time-reversal mirror is, roughly speaking, a device which is capable of receiving an acoustic signal in time, keeping it in memory and sending it back into the medium in the reversed direction of time. In this paper, we employ an accurate numerical method for simulating waves propagating in complex one-dimensional media. We use numerical simulations to reproduce the time-reversal self-averaging effect which takes place in randomly layered media. This is done in the regime where the inhomogeneities are smaller than the pulse, which propagates over long distances compared to its width. We show numerical evidence for possible use of an expanding window time-reversal technique for detecting anomalies buried in the medium.     

Time-reversal simulations for detection in randomly layered media

Abstract

A time-reversal mirror is, roughly speaking, a device which is capable of receiving an acoustic signal in time, keeping it in memory and sending it back into the medium in the reversed direction of time. In this paper, we employ an accurate numerical method for simulating waves propagating in complex one-dimensional media. We use numerical simulations to reproduce the time-reversal self-averaging effect which takes place in randomly layered media. This is done in the regime where the inhomogeneities are smaller than the pulse, which propagates over long distances compared to its width. We show numerical evidence for possible use of an expanding window time-reversal technique for detecting anomalies buried in the medium.     

Time reversal of light with linear optics and modulators

We introduce a new physical process that can perform a complete time-reversal operation on any electromagnetic pulse. The process uses only small refractive index modulations of linear optical elements. No nonlinear multiphoton effects such as four-wave mixing are required. The introduced process can be implemented on chip with standard semiconductor materials. Furthermore, the same process can be used to compress or expand the spectrum of electromagnetic waves while completely preserving the coherent information. We exhibit the time-reversal process by first-principles simulations of microcavity complexes in photonic crystals.     

Intersymbol interference in underwater acoustic communications using time-reversal signal processing

Coherent underwater communication is hampered by the time spread inherent to acoustic propagation in the ocean. Because time-reversal signal processing produces pulse compression, communications has been suggested as a natural application of the technique. Passive versions of time-reversal processing use a receive-only array to do combined temporal and spatial matched filtering. It can be shown, however, that the pulse compression it achieves is not perfect and that an equalizer that relies solely on time-reversal processing will have an error floor caused by uncompensated intersymbol interference (ISI). In the present paper, a physics-based model is developed for the uncompensated ISI in a passive time-reversal equalizer. The model makes use of a normal-mode expansion for the acoustic field. The matched-filtering integral is approximated and the intermediate result interpreted using the waveguide invariant. After combining across the array and sampling, formal statistical averages of the soft demodulation output are calculated. The results show how performance scales with bandwidth, with the number and position of array elements, and with the length of the finite impulse response matched filters. Good agreement is obtained between the predicted scaling and that observed in field experiments.     

Time reversal of electromagnetic waves

We report the first experimental demonstration of time-reversal focusing with electromagnetic waves. An antenna transmits a 1-micros electromagnetic pulse at a central frequency of 2.45 GHz in a high-Q cavity. Another antenna records the strongly reverberated signal. The time-reversed wave is built and transmitted back by the same antenna acting now as a time-reversal mirror. The wave is found to converge to its initial source and is compressed in time. The quality of focusing is determined by the frequency bandwidth and the spectral correlations of the field within the cavity.     

时间反演脉冲电磁波在双负材料中传播特性研究

利用全时域电磁仿真技术, 对比研究了时间反演脉冲电磁波和脉冲电磁波透过Smith结构双负材料后的时域波形、脉宽压缩以及材料内部空间电场峰值强度分布等时域传播特性. 结果表明：时间反演脉冲电磁波在透过双负材料后, 在初始源激励处表现出良好的时间和空间聚焦特性. 更重要的是, 在双负材料内部, 观测到了电场峰值强度减弱、截面电场峰值强度趋向均衡分布等新型的物理现象. 这些物理现象对发展能够承受大功率新型的双负材料电子器件及其应用系统很有参考研究价值.     

强混响背景下悬浮目标的时反成像

提出了一种加权宽带全信号子空间时反成像方法,将扩展性目标建模为有限数量个、相互独立的点散射体构成,实现了时反成像在可疑目标区域的全信号子空间和整个宽带的累加。在实验室波导水池中,底部放置圆柱筒制造混响背景,共进行了两个实验,一是扩展性的悬浮目标位于圆柱筒附近,其回波与圆柱筒反射的混响不在同一个时间窗内,二是弱点目标回波与圆柱筒反射的混响重叠于同一个时间窗内,对所提出的方法进行强混响背景下弱悬浮目标的成像能力验证。结果表明,此方法对强混响背景下的弱悬浮目标的成像质量明显优于传统的时反成像方法。      

Time reversal imaging of suspended target in strong reverberation

The weighted wideband time-reversal imaging approach of full signal subspaces was proposed.The extended target is modeled as an infinite number of independent point-like scatterers,and the imaging is constructed by accumulating all time-reversal images over all signal subspaces and the entire bandwidth in the region of suspected targets.On the bottom of a laboratory water waveguide,a cylindrical shell was used to produce reverberation.Two experiments were carried out.The first experiment is that an extended target was suspended near the cylindrical shell,whose echo and the reverberation reflected by the cylindrical shell were in different time windows.The second experiment is that a point-like target was suspended above the cylindrical shell,thus the echo and the reverberation were in the same time window.The experimental results show that the imaging quality of the proposed method is better than that of the conventional time reversal imaging methods for weak suspended targets in a strong reverberation background.     

Multiple focusing with adaptive time-reversal mirror

Recently, adaptivity was introduced to time-reversal mirror to steer the nulls, and referred to as an adaptive time-reversal mirror (ATRM) [J. S. Kim, H. C. Song, and W. A. Kuperman, J. Acoust. Soc. Am. 109, 1817-1825 (2001)]. In this study, ATRM is extended to simultaneous multiple focusing in an ocean waveguide. The multiple focusing is achieved by imposing a set of constraints in the formulation to find the weight vectors. The algorithm is applied to the long-range underwater acoustic communication to show, via simulation, that the simultaneous pulse compression at multiple receiving locations is achieved.     

Amplitude degradation of time-reversed pulses in nonlinear absorbing thermoviscous fluids

The linear wave equation in a lossless medium is time reversible, i.e., every solution p(x, t) has a temporal mirror solution p(x, -t). Analysis shows that time reversal also holds for the lossless nonlinear wave equation. In both cases, time-reversal invariance is violated when losses are present. For nonlinear propagation loses cannot normally be ignored; they are necessary to prevent the occurrence of multivalued waveforms. Further analysis of the nonlinear wave equation shows that amplification of a time-reversed pulse at the array elements also leads to a violation of time reversal even for lossless nonlinear acoustics. Numerical simulations are used to illustrate the effect of nonlinearity on the ability of a time-reversal system to effectively focus on a target in an absorbing fluid medium. We consider both the amplitude and arrival time of retrodirected pulses. The numerical results confirm that both shock generation (with the accompanying absorption) and amplification at the array, adversely affect the ability of a time-reversal system to form strong retrodirective sound fields.     

Optimal control of light pulse storage and retrieval

We demonstrate experimentally a procedure to obtain the maximum efficiency for the storage and retrieval of light pulses in atomic media. The procedure uses time-reversal to obtain optimal input signal pulse shapes. Experimental results in warm Rb vapor are in good agreement with theoretical predictions and demonstrate a substantial improvement of efficiency. This optimization procedure is applicable to a wide range of systems.     

Time-reversal imaging of objects near rough surfaces based on surface flattening transform

This paper considers the imaging of objects located close to rough surfaces such as ocean or terrain. If transmitters and receivers are also located close to rough surfaces, incident wave is no longer a plane wave nor a spherical wave in free space and it is necessary to consider Green’s functions with the point source located close to the surface, similar to the Sommerfeld dipole problem. This paper considers the near-surface imaging by making use of time-reversal imaging and surface flattening transform. Surface flattening transform converts the rough surface problem into flat surface with inhomogeneous random medium. Mutual coherence function is obtained and used to obtain imaging of point target near rough surface, making use of the multi-static data matrix, time-reversal matrix, the eigenvectors, and the steering matrix. Numerical examples are given. An important point is that integration of stochastic wave propagation and signal processing is necessary to obtain imaging through complex clutter environment. Surface flattening transform is related to the transformation electromagnetics which attracted much interest because of cloaking possibilities. This paper includes some discussions on the relations between surface flattening and transformation electromagnetics.     

基于时间反转理论的聚焦Lamb波结构损伤成像

从理论和实验上研究了时间反转法在频散和多模式的Lamb波结构健康检测方面的应用.当Lamb波在包含有损伤的板类结构中传播时,损伤的存在表现为一个被动波源.采用分布式传感器网络,基于传递函数的观点,通过推导由损伤这个被动波源产生的时间反转波场幅值的表达式,证实了当观察点位于损伤位置时,时间反转波场的幅值最大.为验证时间反转方法的聚焦效应,提出了一种适合于分布的激励/接收传感器网络的成像方法,该方法可以对损伤定位并近似确定损伤尺寸.结合有限元的实验结果显示了Lamb波检测信号的能量可在损伤处聚焦,表明时间反转     

Selection rules for multiple quantum NMR excitation in solids: derivation from time-reversal symmetry and comparison with simulations and (13)C NMR experiments.

New derivations of selection rules for excitation and detection of multiple quantum coherences in coupled spin-1/2 systems are presented. The selection rules apply to experiments in which the effective coupling Hamiltonian used for multiple quantum excitation is both time-reversal invariant and time-reversible by a phase shift of the radiofrequency pulse sequence that generates the effective couplings. The selection rules are shown to be consequences of time-reversal invariance and time-reversibility and otherwise independent of the specific form of the effective coupling Hamiltonian. Numerical simulations of multiple quantum NMR signal amplitudes and experimental multiple quantum excitation spectra are presented for the case of a multiply (13)C-labeled helical polypeptide. The simulations and experiments confirm the selection rules and demonstrate their impact on multiple quantum (13)C NMR spectra in this biochemically relevant case.     

A comparison between ultrasonic array beamforming and super resolution imaging algorithms for non-destructive evaluation

In this paper the total focusing method, the so called gold standard in classical beamforming, is compared with the widely used time-reversal MUSIC super resolution technique in terms of its ability to resolve closely spaced scatterers in a solid. The algorithms are tested with simulated and experimental array data, each containing different noise levels. The performance of the algorithms is evaluated in terms of lateral resolution and sensitivity to noise. It is shown that for the weak noise situation (SNR > 20 dB), time-reversal MUSIC provides significantly enhanced lateral resolution when compared to the total focusing method, breaking the diffraction limit. However, for higher noise levels, the total focusing method is shown to be robust, whilst the performance of time-reversal MUSIC is degraded. The influence of multiple scattering on the imaging algorithms is also investigated and shown to be small.     

Selection Rules for Multiple Quantum NMR Excitation in Solids: Derivation from Time-Reversal Symmetry and Comparison with Simulations and C NMR Experiments

New derivations of selection rules for excitation and detection of multiple quantum coherences in coupled spin-1/2 systems are presented. The selection rules apply to experiments in which the effective coupling Hamiltonian used for multiple quantum excitation is both time-reversal invariant and time-reversible by a phase shift of the radiofrequency pulse sequence that generates the effective couplings. The selection rules are shown to be consequences of time-reversal invariance and time-reversibility and otherwise independent of the specific form of the effective coupling Hamiltonian. Numerical simulations of multiple quantum NMR signal amplitudes and experimental multiple quantum excitation spectra are presented for the case of a multiply ¹³C-labeled helical polypeptide. The simulations and experiments confirm the selection rules and demonstrate their impact on multiple quantum ¹³C NMR spectra in this biochemically relevant case.     

Acoustical imaging through a multiple scattering medium using a time-reversal mirror

Acoustical imaging is based on the ability to focus an acoustic beam inside the zone of interest. This remains an issue through a high-order multiple scattering medium because the electronic delay lines that enable one to focus through a multiple scattering medium are a priori unknown. Using time-reversal principles, we show that images can be obtained through a very disordered medium. Surprisingly, the images are better than those obtained in a homogeneous medium with a classical imaging device.     

Time reversal of speckle noise

Focusing a wave in an unknown inhomogeneous medium is an open problem in wave physics. This work presents an iterative method able to focus in pulse-echo mode in an inhomogeneous medium containing a random distribution of scatterers. By performing a coherent summation of the random echoes backscattered from a set of points surrounding the desired focus, a virtual bright pointlike reflector is generated. A time-reversal method enables an iterative convergence towards the optimal wave field focusing at the location of this virtual scatterer. Thanks to this iterative time-reversal process, it is possible to focus at any arbitrary point in the heterogeneous medium even in the absence of pointlike source. An experimental demonstration is given for the correction of strongly distorted images in the field of medical ultrasound imaging. This concept enables envisioning many other applications in wave physics.