Time Reversal Focusing Research Articles

Time reversal of surface plasmons

<p style='text-indent:20px;'>We study in this work the so-called "instantaneous time mirrors" in the context of surface plasmons. The latter are associated with high frequency waves at the surface of a conducting sheet. Instantaneous time mirrors were introduced in [<xref ref-type="bibr" rid="b3">3</xref>], with the idea that singular perturbations in the time variable in a wave-type equation create a time-reversed focusing wave. We consider the time-dependent three-dimensional Maxwell's equations, coupled to Drude's model for the description of the surface current. The time mirror is modeled by a sudden, strong, change in the Drude weight of the electrons on the sheet. Our goal is to characterize the time-reversed wave, in particular to quantify the quality of refocusing. We establish that the latter depends on the distance of the source to the sheet, and on some physical parameters such as the relaxation time of the electrons. We also show that, in addition to the plasmonic wave, the time mirror generates a free propagating wave that offers, contrary to the surface wave, some resolution in the direction orthogonal to the sheet. Blurring effects due to non-instantaneous mirrors are finally investigated.</p>

Low-frequency sound source localization in enclosed space based on time reversal method

This study investigates sound source localization (SSL) in enclosed space at low frequencies. Reverberation and noise are important factors that affect localization result. Time reversal technology has the characteristics of compensating the multipath effect and adaptive focus, therefore, it can realize (SSL) in enclosed space. In order to improve the spatial resolution of localization, the recovery of the second transmitting signal received after time reversal is completed by the compressive sensing algorithm. We propose time reversal sparse Bayesian learning (TR-SBL) method to solve the problem of SSL. Firstly, time reversal focusing model of sound source propagation in the enclosed space is established. Then compressive sensing algorithm is performed on the second received signal, a sparse Bayesian framework is used to solve the localization problem. The time reversal method can overcome the reverberation interference in the enclosed space, and the compressive sensing algorithm can improve the spatial resolution. A series of simulations, which can be compared with the time reversal method and L1 norm method, are carried out to verify the localization performance of the proposed method, including simulations of sound sources with different frequencies, signal-to-noise ratios (SNRs), absorption coefficients, and positions. The algorithm is also evaluated in a reverberation chamber using sound sources with different frequencies. The numerical simulations and experimental results show that the proposed method achieves good localization performance in a low-SNR and reverberation environment, the spatial resolution is up to 0.1 m for a sound source with a frequency of 125 Hz.

Correcting for Target Motion in Time-Reversal Spectral Focusing

It is well-known that an iterative time-reversal (TR) process, applied via a distributed sensing system, can be used to produce a space-time waveform that maximizes the energy scattered from a stationary target back to the sensors. The TR process accomplishes this by automatically focusing energy, both spatially and spectrally, on the stationary target. When scatterers are moving, however, the TR focusing can break down. This article shows how to modify the TR process so that it automatically focuses energy on a moving target. This new TR process automatically generates a distributed beam that: 1) follows the target as it moves and 2) enhances the target resonances by concentrating the energy spectrally. This focusing occurs without a priori knowledge of the target’s location or spectral response. The new TR algorithm is derived through a careful analysis of the idealized case of a single isotropic moving point scatterer. This article includes simulations that compare the TR focus both with and without the new modification. Although the simulations are carried out for the electromagnetic case, the theory applies equally well to the acoustic case when the target speed is significantly less than the ambient sound speed. Appendices are included with details of the calculations and with analysis of the range of relative velocities for which the modified TR process should be used.

Super-resolution within a one-dimensional phononic crystal of resonators using time reversal in an equivalent circuit model.

An equivalent circuit model has been developed to model a one-dimensional waveguide with many side-branch Helmholtz resonators. This waveguide constitutes a phononic crystal that has been shown to have decreased phase speed below the resonance frequency of an individual resonator. This decreased phase speed can be exploited to achieve super-resolution using broadband time reversal focusing techniques. It is shown that the equivalent circuit model is capable of quantifying this change in phase speed of the crystal and also the small-scale wave-resonator interactions within the crystal. The equivalent circuit model enables the parameterization of the physical variables and the optimization of the focusing bandwidth by balancing the combination of increasing resolution and decreasing amplitude near the resonance frequency. It is shown that the quality factor-in this case, the quality factor determined by the geometric shape of each resonator-controls the range of frequencies that are strongly affected by the Helmholtz resonators.

IEEE President K. J. Ray Liu, “Follow Multiple Paths,” Changing the World With Microwave Time Reversal Focusing

This is the sixth in our Microwave Pioneer series in which we are privileged to provide our readers with a very special subject: current IEEE President K. J. Ray Liu. Professor Liu's inclusion in this series is not due to his position as leader of the IEEE, but rather to his influence and leadership in the field of indoor surveillance and tracking using microwaves. His discovery, demonstration, and application, of microwave multi-path time reversal focusing for use in positioning and tracking, when coupled with recent advances in wireless communications, are primed to have worldwide impact. The imminent roll-out of commercial systems through Professor Liu's company, Origin Wireless AI, could change the very nature of our society through its many potential applications in indoor monitoring, tracking, and motion sensing using existing Wi-Fi infrastructure. The implications for both improved security and health care in the home and office – as well as the accompanying controversies over issues of privacy, are profound. It is appropriate that an individual who has already had a considerable role in shaping our local signal processing and microwave fields, as well as the broader IEEE community, should extend his influence to our society at large. With 12 books, 18 book chapters, 6 special issue journal releases, more than 800 refereed journal and conference publications, over 70 patents and dozens of editorials and magazine pieces, you will certainly appreciate Professor Liu's multi-path impact as you read about his multi-path career!

Super-resolution, time-reversal focusing using path-diverting scatterers

This presentation will discuss the possibility of using path-diverting scatterers in time reversal focusing to achieve super resolution. In particular, use of a one-dimensional pipe system with varying lengths of diverting pipes is shown to decrease the effective wave speed. This provides insight, albeit in an extreme case, of how scatterers can force sound to travel a longer path as the waves converge to the focal location. As the effective wave speed decreases, the spatial extent of the focusing decreases, creating an apparent super resolution when compared to the speed of sound in an unaltered pipe system. Previous work achieved super resolution with what they described as scatterers, but it is likely that their scatterers are better classified as resonators, and consequently, it has yet to be shown that scatterers can be used to obtain super resolution.

COMSOL modeling of time reversal focusing in a periodic network of Helmholtz resonators

This presentation will outline the physical and practical considerations for conducting a COMSOL simulation of time reversal focusing in air. Attempts to obtain sub-diffraction-limited time reversal focusing, along with physical and practical consideration, will be presented. Physical considerations include end-corrections, resonator shape and placement, computational domain and anechoic terminations. Practical considerations include mesh size and temporal length. While conducting a time domain study in COMSOL, mesh size is related to the highest frequency and the simulation length is related to the lowest frequency. To maximize computational resources, the simulation uses a restricted bandwidth. Extending the bandwidth is accomplished by combining multiple simulations. Comparison to previous super resolution studies as well as the authors’ equivalent circuit model will also be discussed.

Multitype Damage Imaging in Concrete Modeling Based on Time Reversal Technique

It is necessary to develop effective methods for visually detecting concrete damage because minor damage can affect the performance of concrete materials. However, the non-homogeneous nature of concrete materials limits the application of imaging algorithms that have been widely used in aerospace and mechanical fields; thus, obtaining high-resolution imaging maps is difficult. In this study, feasibility research on concrete damage detection was conducted using the time reversal focusing imaging algorithm. A new method for characterizing various concrete damage conditions with focusing curves was proposed. ABAQUS software was utilized to establish five types of concrete damage, and the imaging quality of the proposed method was evaluated in Python. The effect of the relative position of the damage and the sensors was analyzed. The focusing curve was extracted from the imaging area to further explain the image information. The numerical simulation results show that time reversal focusing had better damage localization than the forward algorithm; time focusing also improved the spatial focusing quality. In addition, focusing curves were used to extract information from the main lobe and to determine the size and location of the damage.

Exploring conditions required for the subwavelength focusing of sound in the near field of an array of resonators using time reversal

This presentation will discuss the time reversal focusing of audible sound over an array of Helmholtz resonators. The presence of the resonators modifies the phase speed of waves, thereby lowering the effective wavelength, in the near field of the focus. It is shown experimentally what conditions are necessary to obtain super resolution. Frequencies above the resonators’ resonance frequency do not result in super resolution. In order to achieve super resolution in the plane of the resonators, the focused waves must be confined to propagate only in the plane of the resonators. When waves converged in three dimensions, super-resolution was not observed but when a 2-D waveguide was used, and super-resolution was observed.

Nonlinear acoustic phenomena in high amplitude time reversal focusing of airborne sound in a 1-D system

Time reversal (TR) is a process that can be used to generate high amplitude focusing of sound. It has been previously shown that using TR in reverberant environments to cause high amplitude foci will in fact have multiple nonlinear properties including waveform steepening and a nonlinear increase in peak pressure compressions. This study investigates the removal of one possible cause for these phenomena: free-space Mach stems. By isolating the focus into a 1-D system, the potential formation of Mach stems is eliminated so that remaining effects can be qualitatively observed. To achieve this, a system of pipes is used to restrict the focused waves to be planar in a 1-D reverberant environment. Preliminary results have shown that waveform steepening effects remain as expected but that the nonlinear increase in compression amplitudes disappears, which is consistent with the idea that free-space Mach stems cannot be formed in a 1-D system.

Development of software for performing acoustic time reversal with multiple inputs and outputs

At Brigham Young University, acoustic time reversal experiments are conducted in solids and fluid media. The experimental setup involves synchronized generation and acquisition hardware. The synchronized hardware allows for multi-channel generation, and in some cases, multi-channel acquisition of time reversal focusing. A LabVIEW application has been compiled to increase ease of use and repeatability for the students conducting experiments. Forward and backward steps of time reversal are conducted through this simple user interface. The software is also able to control a 2D positioning system that allows for the measurement of the spatial extent of a time reversal focus. Modifications to traditional time reversal processing, such as inverse filtering and one-bit processing, may be easily implemented in the software. This presentation describes the hardware and software that help to facilitate time reversal research. Ideas from this presentation may help others develop time reversal data acquisition systems.

Time-reversal focusing of ultrashort pulses through thin scattering media.

When ultrashort pulses propagate through a disordered medium, scattering occurs and the intensity of the ballistic component decreases drastically. This limits the applicability of time-resolved nonlinear optical spectroscopy and microscopy. The wavefront shaping technique makes it possible to focus light through the scattering medium; however, complete time-reversal of the ultrashort pulses (as short as 10 fs) is still a very challenging problem. This is due to the in-depth characterization and precise control needed for such pulses in the time domain in order to compress down the Fourier-transform limit. In this work, we develop new spatiotemporal wavefront shaping techniques to focus ultrashort pulses at the target position through a thin scattering medium. Compared to other studies, one significant advantage of this method is that most of the characterization of the spectrally-resolved transmission matrix and temporal profile of the ultrashort pulses can be done using single-beam geometry. An interferometer with external reference is necessary to measure the difference of the phase profile between the focused and reference pulses. Furthermore, the number of controllable phase components in the spectral domain is not limited by the spectral correlations of the speckle patterns because we used a pulse shaper in the time domain to optimize the temporal properties of the ultrashort focused pulse. Our new method provides increased flexibility and precise control for manipulating extremely ultrashort pulses through thin scattering media in order to achieve time-reversal focusing at the target position.

FEM-based time-reversal enhanced ultrasonic cleaning

Pipe fouling is a challenging problem in many industrial applications. Current cleaning techniques require halting the production during the cleaning phase and the existing methods are unable to do targeted cleaning, even though fouling is often localized to certain areas inside the pipeline. To address this issue, we use FEM-simulated, time-reversed signals to focus ultrasound power onto a pre-determined location: a fouled pipe residing inside a Plexiglas container. Ultrasound cleaning with similar acoustic power was compared to the time-reversal enhanced method in terms of cleaning efficiency. The cleaning efficiency was determined by measuring how much fouling, by mass, both protocols removed from the surface of a Plexiglas pipe, using similar input electric power and equal cleaning time. Our results indicate that the proposed time-reversal-based technique removes three times more fouling than the standard ultrasound cleaning without focusing. The study extends our previous paper on FEM-based time-reversal focusing [1].

Generation of a focused nonlinear difference frequency using high-amplitude time reversal focusing of airborne ultrasound

Time reversal (TR) focusing of high-amplitude airborne ultrasound can be used to create a difference frequency. Methods are employed to increase the amplitude of the focus. These methods include creating a miniature reverberation chamber, using multiple sources, and using the clipping processing method. The use of a beam blocker to make the sources more omnidirectional is also examined, and it is found that for most source/microphone orientations, the use of a beam blocker increases the amplitude of the focus. A high-amplitude focus of 134 dB peak re 20 μPa sound pressure level with a center frequency of about 38 kHz is generated using eight sources. Then, using four sources centered at 36.1 kHz and another four sources centered a 39.6 kHz, nonlinear difference frequency content centered at 3.5kHz is observed in the focus signal. The difference frequency amplitude grows quadratically with increasing primary frequency amplitude. When using beam blockers, the difference frequency content propagates away from the focal location with higher amplitude than when beam blockers are not used. This is likely due to the differences in the directionality of the converging waves during TR focusing.

Equivalent circuit model to study super resolution in time reversal focusing in a periodic network of Helmholtz resonators

This presentation will introduce equivalent circuit modeling techniques that have been used to simulate the focusing of acoustic signals in a 1-D waveguide. The presence of resonators in the near field of the focus location decreases the effective wavelength of the focus and leads to super resolution. A circuit is created that represents the complete waveguide with the sources. Circuit elements are used to represent both resonators and the propagation of the wave. The spatial extent is simulated at individual frequencies using additional circuit junctions. The wideband response is determined by the superposition of the individual frequency results. Important parameters such as resonator density and the quality factor of the resonators are examined and their influence on the focus will be presented. Methods for solving the circuit models and improving computational efficiency will also be discussed.

Extraction of seabed properties in mid-frequency range using waveguide invariant applied to broadband signals

One of the fundamental problems in shallow water environments is to assess the seabed properties. The waveguide invariant can be used in both passive and active sonar processing, source ranging, time reversal focusing, and in geoacoustic inversion processes. In Pekeris waveguide, the waveguide invariant value is approximately 1 and the slope of the interfering acoustic intensity fringes relates to the bottom sound speed. Using the slope of the striations as a variable, the spacing of the interference in range (or frequency) can be related to the penetration of energy into the bottom. The depth given by spacing of real arrivals has an effective depth of penetration which depends on the geoacoustic properties of the bottom sediments. Here, we study the frequency dependence of the waveguide invariant due to sediment layer structure and physical properties and provide a detailed data/model comparison for a shallow water range independent waveguide and extract the seabed properties for the frequency band 1.5 to 4.0 kHz using recent data obtained in shallow water environments. [Work supported by ONR 321OA.]

Quantifying nonlinear characteristics in time reversal focusing of airborne sound

Time reversal can be used to focus sound to a chosen location within a reverberant environment. Virtual sources in the reverberant environment increase the amplitude of the focusing. Recent investigations into the focusing of high-amplitude sound waves, up to peak levels of 200 dB, has led to the observation of nonlinear characteristics in the focus event. This study investigates these nonlinear characteristics, including distortion of the focus wave, shift in harmonic content, and nonlinear increase in the peak pressure compressions. This study also attempts to quantify a threshold where the focus events begin to transition from a linear to the nonlinear regime. Additionally, a comparison of the microphones and transducers used to record these focus events is made in order to both verify the levels of pressure attained, and to ensure that microphone distortion is not the cause of the nonlinear features in the focusing.

Knocking over LEGO minifigures with time reversal focused vibrations: Understanding the physics and developing a museum demonstration

Time reversal (TR) of impulse responses can be used to focus wave energy, even in a reverberant environment. A demonstration of TR focusing was developed to knock over a targeted LEGO minifigure, standing among other minifigures (who remain standing), by focusing plate vibrations under the target minifigure\rquote s feet. In order to achieve a high degree of repeatability, the physics of the demonstration needed to be understood. A laser Doppler vibrometer was used to compare the motion of the minifigure and the plate directly beneath it. Speaker shakers are used to generate motion of the plate. If their induced vibration was too large the minifigure loses contact with the plate prematurely, causing it to be in the air when the main focused vibrations arrive. If the minifigure is in contact with the plate when the focused vibrations arrive then the minifigure is launched into the air before toppling on its side. This demonstration was optimized to be a two-player-game museum exhibit in a wave propagation museum hosted by ETH Zurich in Switzerland. This demonstration illustrates the power of focused vibrations.

High-amplitude time reversal focusing of airborne ultrasound to generate a focused nonlinear difference frequency.

Time reversal (TR) focusing of airborne ultrasound in a room is demonstrated. Various methods are employed to increase the amplitude of the focus. These methods include creating a small wooden box (or chamber) to act as a miniature reverberation chamber, using multiple sources, and using the clipping processing method. The use of a beam blocker to make the sources more omnidirectional is also examined, and it is found that for most source/microphone orientations, the use of a beam blocker increases the amplitude of the focus. A high-amplitude focus of 134 dB peak re 20 μPa sound pressure level with a center frequency of about 38 kHz is generated using TR. Using four sources centered at 36.1 kHz and another four sources centered at 39.6 kHz, nonlinear difference frequency content centered at 3.5 kHz is observed in the focus signal. The difference frequency amplitude grows quadratically with increasing primary frequency amplitude. When using beam blockers, the difference frequency content propagates away from the focal location with higher amplitude than when beam blockers are not used. This is likely due to the differences in the directionality of the converging waves during TR focusing.

The impact of room location on time reversal focusing amplitudes

Time reversal (TR) is a signal processing technique often used to generate focusing at selected positions within reverberant environments. This study investigates the effect of the location of the focusing, with respect to the room wall boundaries, on the amplitude of the focusing and the uniformity of this amplitude when focusing at various room locations. This is done experimentally with eight sources and two reverberation chambers. The chambers are of differing dimensions and were chosen to verify the findings in different volume environments. Multiple spatial positions for the TR focusing are explored within the rooms' diffuse field, against a single wall, along a two-wall edge, and in the corners (three walls). Measurements of TR focusing at various locations within the room show that for each region of study, the peak amplitude of the focusing is quite uniform, and there is a notable and consistent increase in amplitude for each additional wall that is adjacent to the focal location. A numerical model was created to simulate the TR process in the larger reverberation chamber. This model returned results similar to those of the experiments, with spatial uniformity of focusing within the room and increases when the focusing is near adjacent walls.