Diffuse field cross-correlations: Scattering theory and electromagnetic experiments.

The passive estimation of impulse responses from ambient noise correlations arouses increasing interest in seismology, acoustics, optics, and electromagnetism. Assuming the equipartition of the noise field, the cross-correlation function measured with noninvasive receiving probes converges towards the difference of the causal and anticausal Green's functions. Here, we consider the case when the receiving field probes are antennas which are well coupled to a complex medium-a scenario of practical relevance in electromagnetism. We propose a general approach based on the scattering matrix formalism to explore the convergence of the cross-correlation function. The analytically derived theoretical results for chaotic systems are confirmed in microwave measurements within a mode-stirred reverberation chamber. This study provides fundamental insight into the Green's function retrieval technique and paves the way for a new technique to characterize electromagnetic antennas.

Open birdcage coil for head imaging at 7T.

PURPOSE: To theoretically describe, design, and test the new geometry of the birdcage coil for 7 Tesla anatomical brain imaging, which includes a large window on top, without deliberately jeopardizing its homogeneity and efficiency. This opencage will not only improve patient comfort but also enable the volunteer to follow functional MRI stimuli. This design could also facilitate the tracking of patient compliance and enable better correction of the movement. METHODS: Via the transfer matrix approach, a birdcage-like coil with a nonperiodic distribution of rungs is constructed with optimized currents in the coil rungs. Subsequently, the coil is adjusted in full-wave simulations. Then, the coil is assembled, fine-tuned, and matched on the bench. Finally, these results are confirmed experimentally on a phantom and in vivo. RESULTS: Indeed, the computed isolation of -14.9 dB between the feeding ports of the coil and the symmetry of the circular polarized mode pattern transmit RF magnetic field ( B1+ ) showed that the coil was properly optimized. An experimental assessment of the developed coil showed competitive transmit efficiency and coverage compared with the conventional birdcage coil of similar size. CONCLUSION: The proposed opencage coil can be designed and work without a dramatic drop of performance in terms of the B1+ field homogeneity, transmit efficiency ( B1+ / Pref ), peak local specific absorption rate ( SAR10g ) and SAR efficiency ( B1+ / SAR10g ).

Localization of unbounded contacts on vibrating elastic plates.

Detection and localization of unbounded contacts in industrial structures are crucial for user safety. However, most structural health monitoring techniques are either invasive, power-consuming, or rely on time-varying baseline comparison. A passive acoustic method is proposed to localize unbounded contacts in plate-like structures, using the acoustic emissions by the contacts when they are excited by ambient noise. The technique consists of computing the correlation matrix of the signals measured by a set of receivers and applying to this matrix a beamforming algorithm accounting for flexural wave dispersion. To validate the technique, an experimental setup is developed in which three idealized unbounded contacts are created on a thin plate excited by a shaker. How the quality of the defect localization depends on the defect type, receiver number, and the characteristics of the noise is investigated. Finally, it is shown that the localization of unbounded contacts is possible using either an acoustic ambient noise source or a more realistic jet engine noise.

Accuracy of Green's function estimation from correlation of diffuse elastic waves on thin plates.

In a reverberant cavity, when a noise field is sufficiently diffuse, the correlation of the signal measured by two sensors provides an estimation of the Green's function (GF) between them. Here, the convergence of this passive estimation in the case of elastic waves on thin plates is studied. A statistical approach is proposed, which relates the similarity between the cross correlation and the GF to the structural properties of the plate and the number of uncorrelated sources. The analysis is sustained by experimental results obtained on an aluminum plate. This study allows us to evaluate the efficiency of passive structural health monitoring of plate-like structures based on noise correlation. Finally, a most interesting finding shows an absolute upper bound of the signal-to-noise ratio for GF quality reconstruction: 4Ns/5, independently of the plate properties.

Selective remote excitation of complex structures using time reversal in audible frequency range.

Generation of elastic waves is a major issue in nondestructive testing. Structural health monitoring of a thin element can be achieved through the analysis of its resonance spectrum. A time reversal mirror (TRM) operating in the audible frequency range (1-10 kHz) is used to remotely excite thin resonant elastic elements. The generation of elastic waves is studied with respect to the geometry of the TRM. It is observed that the quality of focusing only weakly depends on the number of loudspeakers (LS) in the TRM. When the air/plate coupling is at its maximum, the energetic efficiency of the TRM is estimated to be about 0.02%. The TRM is shown to efficiently and selectively excite a small structure embedded in a complex environment such as a hollow cylinder. Finally, the results are discussed in light of the DORT method (French acronym for "decomposition of the time reversal operator"). In particular, the optimal LS placement and emission signals in this configuration to excite individual eigenmodes of a plate is determined.

Enhancing surface coil sensitive volume with hybridized electric dipoles at 17.2 T.

Preclinical MR applications at 17.2 T can require field of views on the order of a few square centimeters. This is a challenging task as the proton Larmor frequency reaches 730 MHz. Most of the protocols at such frequencies are performed with surface transceiver coils for which the sensitive volume and the signal to noise ratio (SNR) is given by their size. Here we propose an approach based on metamaterials in order to enhance the sensitive volume of a commercial surface coil for small animal imaging at 17.2 T. We designed a passive resonator composed of four hybridized electric dipoles placed onto the floor of the MRI bed. Combining numerical and experimental results on a phantom and in vivo, we demonstrate a 20% increase of the sensitive volume in depth and 25% along the rostro-caudal axis while maintaining more than 85% of the local SNR right beneath the surface coil plane. Moreover, our solution gives the ability to double the average SNR in the region between 1.2 and 2 cm away from the loop using a single layer of 1 mm thick metallic wires easy to design and manufacture.

Wireless coils based on resonant and nonresonant coupled-wire structure for small animal multinuclear imaging.

Earlier work on RF metasurfaces for preclinical MRI has targeted applications such as whole-body imaging and dual-frequency coils. In these studies, a nonresonant loop was used to induce currents into a metasurface that was operated as a passive inductively powered resonator. However, as we show in this study, the strategy of using a resonant metasurface reduces the impact of the loop on the global performance of the assembled coil. To mitigate this deficiency, we developed a new approach that relies on the combination of a commercial surface coil and a coupled-wire structure operated away from its resonance. This strategy enables the extension of the sensitive volume of the surface coil while maintaining its local high sensitivity without any hardware modification. A wireless coil based on a two parallel coupled-wire structure was designed and electromagnetic field simulations were carried out with different levels of matching and coupling between both components of the coil. For experimental characterization, a prototype was built and tested at two frequencies, 300 MHz for 1 H and 282.6 MHz for 19 F at 7 T. Phantom and in vivo MRI experiments were conducted in different configurations to study signal and noise figures of the structure. The results showed that the proposed strategy improves the overall sensitive volume while simultaneously maintaining a high signal-to-noise ratio (SNR). Metasurfaces based on coupled wires are therefore shown here as promising and versatile elements in the MRI RF chain, as they allow customized adjustment of the sensitive volume as a function of SNR yield. In addition, they can be easily adapted to different Larmor frequencies without loss of performance.

Modeling of an active terahertz imaging system in brownout conditions.

We present a theoretical evaluation of a subterahertz (subTHz) system to image through a scattering medium composed of scatterers of sizes close to the wavelength. We specifically study the case of sand grain clouds created by helicopter rotor airflow during landing in arid areas. The different powers received by one pixel of a matrix made of subTHz sensors are identified. Photometric and antenna-based sensors are considered. Besides the thermal contribution to the noise, we focus our attention on the radiation backscattered by the brownout. It appears that a configuration where the source and the camera are distant is the most promising configuration and is realistic for embedded systems.

Robust source localization from wavefield separation including prior information.

Strong reverberation is a challenge for narrowband source localization, as most of the existing methods are based on times-of-arrival measurements, that is affected by boundaries. Amongst the methods that explicitly take into account the reverberation, wavefield separation projector processing (WSPP) splits the acoustic wave field into the direct path of the sources and the reverberation. However, WSPP requires a very large number of microphones, making this method impractical. This article studies three ways of alleviating this constraint, extending WSPP by adding different prior information on the wavefield. The first method is based on using the knowledge of the critical distance of the room to decrease the selectivity of the field separation. The second method adds constraints called "virtual measurements" when the room geometry is partially known. Finally, the last method requires a simple calibration step to estimate the Green's functions between each pair of microphones; this also extends the model to weakly inhomogeneous propagation media. It is shown numerically and experimentally that these methods allow a precise source localization, with a reduced number of microphones.

Coda reconstruction from cross-correlation of a diffuse field on thin elastic plates.

This study contributes to the evaluation of the robustness and accuracy of Green's function reconstruction from cross-correlation of strongly dispersed reverberated signals, with disentangling of the respective roles of ballistic and reverberated ("coda") contributions. We conduct a suite of experiments on a highly reverberating thin duralumin plate, where an approximately diffuse flexural wave field is generated by taking advantage of the plate reverberation and wave dispersion. A large number of impulsive sources that cover the whole surface of the plate are used to validate ambient-noise theory through comparison of the causal and anticausal (i.e., positive- and negative-time) terms of the cross-correlation to one another and to the directly measured Green's function. To quantify the contribution of the ballistic and coda signals, the cross-correlation integral is defined over different time windows of variable length, and the accuracy of the reconstructed Green's function is studied as a function of the initial and end times of the integral. We show that even cross-correlations measured over limited time windows converge to a significant part of the Green's function. Convergence is achieved over a wide time window, which includes not only direct flexural-wave arrivals, but also the multiply reverberated coda. We propose a model, based on normal-mode analysis, that relates the similarity between the cross-correlation and the Green's function to the statistical properties of the plate. We also determine quantitatively how incoherent noise degrades the estimation of the Green's function.

Green's Function Retrieval with Absorbing Probes in Reverberating Cavities.

The cross-correlation of a diffuse wave field converges toward the difference between the anticausal and causal Green's functions between two points. This property has paved the way to passive imaging using ambient noise sources. In this Letter, we investigate Green's function retrieval in electromagnetism. Using a model based on the fluctuation dissipation theorem, we demonstrate theoretically that the cross-correlation function strongly depends on the absorption properties of the receivers. This is confirmed in measurements within a reverberation chamber. In contrast to measurements with noninvasive probes, we show that only the anticausal Green's function can be retrieved with a matched antenna. Finally, we interpret this result as an equivalent time-reversal experiment with an electromagnetic sink.

Localization of acoustic sensors from passive Green's function estimation.

A number of methods have recently been developed for passive localization of acoustic sensors, based on the assumption that the acoustic field is diffuse. This article presents the more general case of equipartition fields, which takes into account reflections off boundaries and/or scatterers. After a thorough discussion on the fundamental differences between the diffuse and equipartition models, it is shown that the method is more robust when dealing with wideband noise sources. Finally, experimental results show, for two types of boundary conditions, that this approach is especially relevant when acoustic sensors are close to boundaries.

Experimental study of passive defect localization in plates using ambient noise.

Passive listening methodology has been shown to be a practical and effective method for passive structural health monitoring. In this work, this approach is applied experimentally to monitor the occurrence of defects in thin aluminum plates. A correlation matrix is estimated from noise vibrations recorded on a transducer array. A defect is localized by applying a beamforming algorithm to the difference between the correlation matrices obtained with and without the defect. We successfully detect defects for different kinds of noise sources. Moreover, we show that this technique is robust to detect massive inclusions, holes, and cracks. With a vibrometer, we observe that the fidelity of the estimated transient responses strongly depends on the number of uncorrelated noise sources. Finally, we show that the defect is successfully localized even if the noise source distribution is not uniform, provided that it remains spatially stationary between the states with and without defect. A simple theoretical framework is proposed to interpret these results.

Analysis of the time reversal operator for a scatterer undergoing small displacements.

The method of the time reversal operator decomposition is usually employed to detect and characterize static targets using the invariants of the time reversal operator. This paper presents a theoretical and experimental investigation into the impact of small displacements of the target on these invariants. To find these invariants, the time reversal operator is built from the multistatic response matrix and then diagonalized. Two methods of recording the multistatic response matrix while the target is moving are studied: Acquisition either element by element or column by column. It is demonstrated that the target displacement generates new significant eigenvalues. Using a perturbation theory, the analytical expressions of the eigenvalues of the time-reversal operator for both acquisition methods are derived. We show that the distribution of the new eigenvalues strongly depends on these two methods. It is also found that for the column by column acquisition, the second eigenvector is simply linked to the scatterer displacements. At last, the implications on the Maximum Likelihood and Multiple Signal Classification detection are also discussed. The theoretical results are in good agreement with numerical and 3.4 MHz ultrasonic experiments.

Green's function retrieval and passive imaging from correlations of wideband thermal radiations.

We present an experimental demonstration of electromagnetic Green's function retrieval from thermal radiations in anechoic and reverberant cavities. The Green's function between two antennas is estimated by cross correlating milliseconds of decimeter noise. We show that the temperature dependence of the cross-correlation amplitude is well predicted by the blackbody theory in the Rayleigh-Jeans limit. The effect of a nonuniform temperature distribution on the cross-correlation time symmetry is also explored. Finally, we open a new way to image scatterers using ambient thermal radiations.

Planar metamaterial based on hybridization for directive emission.

We present the first experimental demonstration of a high-directivity using a mu and epsilon near zero (MENZ) metamaterial. We use the hybridization principles to design a planar MENZ structure based on the fishnet unit cell. Resonant mode engineering achieves an effective permittivity and permeability that approaches zeros around 10.5 GHz simultaneously. We use this metamaterial as a superstrate of a microstrip patch antenna. We show that the directivity of the antenna is effectively enhanced compared to that of the patch antenna alone at the desired frequency.

Double-T metamaterial for parallel and normal transverse electric incident waves.

Electric and magnetic hybridized plasmonic modes are obtained by stacking two T-shaped resonators. We show that head-to-toe configuration leads to inverse the hybridization. The frequency shift between the resonances is finely controlled by adjusting the gap between the two resonators. A negative refractive index close to -1 is numerically and experimentally demonstrated at 4.3 GHz for TE waves. This left-handed behavior is similar for parallel and normal TE incident wave vectors. The proposed double-T unit cell is well adapted for developing terahertz and IR metamaterials.

Resonant metalenses for breaking the diffraction barrier.

We introduce the resonant metalens, a cluster of coupled subwavelength resonators. Dispersion allows the conversion of subwavelength wave fields into temporal signatures while the Purcell effect permits an efficient radiation of this information in the far field. The study of an array of resonant wires using microwaves provides a physical understanding of the underlying mechanism. We experimentally demonstrate imaging and focusing from the far field with resolutions far below the diffraction limit. This concept is realizable at any frequency where subwavelength resonators can be designed.

Manipulating spatiotemporal degrees of freedom of waves in random media.

We show that all the spatiotemporal degrees of freedom available in a complex medium can be harnessed and converted into spatial ones. This is demonstrated experimentally through an instantaneous spatial inversion, using broadband ultrasonic waves in a multiple scattering sample. We show theoretically that the inversion convergence is governed by the total number of degrees of freedom available in the medium for a fixed bandwidth and demonstrate experimentally its use for complex media investigation. We believe our approach has potential in sensing, imagery, focusing, and telecommunication.

Characterization of an elastic target in a shallow water waveguide by decomposition of the time-reversal operator.

This paper reports the results of an investigation into extracting of the backscattered frequency signature of a target in a waveguide. Retrieving the target signature is difficult because it is blurred by waveguide reflections and modal interference. It is shown that the decomposition of the time-reversal operator method provides a solution to this problem. Using a modal theory, this paper shows that the first singular value associated with a target is proportional to the backscattering form function. It is linked to the waveguide geometry through a factor that weakly depends on frequency as long as the target is far from the boundaries. Using the same approach, the second singular value is shown to be proportional to the second derivative of the angular form function which is a relevant parameter for target identification. Within this framework the coupling between two targets is considered. Small scale experimental studies are performed in the 3.5 MHz frequency range for 3 mm spheres in a 28 mm deep and 570 mm long waveguide and confirm the theoretical results.