# Time reversal signal processing

Last updated

Time reversal signal processing [1] is a signal processing technique that has three main uses: creating an optimal carrier signal for communication, [2] reconstructing a source event, [3] [4] [5] [6] and focusing high-energy waves to a point in space. A Time Reversal Mirror (TRM) is a device that can focus waves using the time reversal method. TRMs are also known as time reversal mirror arrays since they are usually arrays of transducers. TRM are well-known and have been used for decades in the optical domain. They are also used in the ultrasonic domain.

## Overview

If the source is passive, i.e. some type of isolated reflector, an iterative technique can be used to focus energy on it. The TRM transmits a plane wave which travels toward the target and is reflected off it. The reflected wave returns to the TRM, where it looks as if the target has emitted a (weak) signal. The TRM reverses and retransmits the signal as usual, and a more focused wave travels toward the target. As the process is repeated, the waves become more and more focused on the target.

Yet another variation is to use a single transducer and an ergodic cavity. Intuitively, an ergodic cavity is one that will allow a wave originating at any point to reach any other point. An example of an ergodic cavity is an irregularly shaped swimming pool: if someone dives in, eventually the entire surface will be rippling with no clear pattern. If the propagation medium is lossless and the boundaries are perfect reflectors, a wave starting at any point will reach all other points an infinite number of times. This property can be exploited by using a single transducer and recording for a long time to get as many reflections as possible.

## Theory

The time reversal technique is based upon a feature of the wave equation known as reciprocity: given a solution to the wave equation, then the time reversal (using a negative time) of that solution is also a solution. This occurs because the standard wave equation only contains even order derivatives. Some media are not reciprocal (e.g. very lossy or noisy media), but many very useful ones are approximately so, including sound waves in water or air, ultrasonic waves in human bodies, and electromagnetic waves in free space. The medium must also be approximately linear.

Time reversal techniques can be modeled as a matched filter. If a delta function is the original signal, then the received signal at the TRM is the impulse response of the channel. The TRM sends the reversed version of the impulse response back through the same channel, effectively autocorrelating it. This autocorrelation function has a peak at the origin, where the original source was. It is important to realize that the signal is concentrated in both space and time (in many applications, autocorrelation functions are functions of time only).

Another way to think of a time reversal experiment is that the TRM is a "channel sampler". The TRM measures the channel during the recording phase, and uses that information in the transmission phase to optimally focus the wave back to the source.

## Experiments

A notable researcher is Mathias Fink of École Supérieure de Physique et de Chimie Industrielles de la Ville de Paris. His team has done numerous experiments with ultrasonic TRMs. An interesting experiment [7] involved a single source transducer, a 96-element TRM, and 2000 thin steel rods located between the source and the array. The source sent a 1 μs pulse both with and without the steel scatterers. The source point was measured for both time width and spatial width in the retransmission step. The spatial width was about 6 times narrower with the scatterers than without. Moreover, the spatial width was less than the diffraction limit as determined by the size of the TRM with the scatterers. This is possible because the scatterers increased the effective aperture of the array. Even when the scatterers were moved slightly (on the order of a wavelength) in between the receive and transmit steps, the focusing was still quite good, showing that time reversal techniques can be robust in the face of a changing medium.

In addition, José M. F. Moura of Carnegie Mellon University has led a research team working to extend the principles of Time Reversal to electromagnetic waves, [8] and they have achieved resolution in excess of the Rayleigh resolution limit, proving the efficacy of Time Reversal techniques. Their efforts are focused on radar systems, and trying to improve detection and imaging schemes in highly cluttered environments, where Time Reversal techniques seem to provide the greatest benefit.

## Applications

The beauty of time reversal signal processing is that one need not know any details of the channel. The step of sending a wave through the channel effectively measures it, and the retransmission step uses this data to focus the wave. Thus one doesn't have to solve the wave equation to optimize the system, [9] one only needs to know that the medium is reciprocal. Time reversal is therefore suited to applications with inhomogeneous media.

An attractive aspect of time reversal signal processing is the fact that it makes use of multipath propagation. Many wireless communication systems must compensate and correct for multipath effects. Time reversal techniques use multipath to their advantage by using the energy from all paths.

Fink imagines a cryptographic application based on the ergodic cavity configuration. The key would be composed of the locations of two transducers. One plays the message, the other records waves after they have bounced throughout the cavity; this recording will look like noise. When the recorded message is time reversed and played back, there is only one location to launch the waves from in order for them to focus. Given that the playback location is correct, only one other location will exhibit the focused message wave; all other locations should look noisy.

## Related Research Articles

Elastography is any of a class of medical imaging modalities that map the elastic properties and stiffness of soft tissue. The main idea is that whether the tissue is hard or soft will give diagnostic information about the presence or status of disease. For example, cancerous tumours will often be harder than the surrounding tissue, and diseased livers are stiffer than healthy ones.

Time of flight (ToF) is the measurement of the time taken by an object, particle or wave to travel a distance through a medium. This information can then be used to measure velocity or path length, or as a way to learn about the particle or medium's properties. The traveling object may be detected directly or indirectly. Time of flight technology has found valuable applications in the monitoring and characterization of material and biomaterials, hydrogels included.

A mathematical or physical process is time-reversible if the dynamics of the process remain well-defined when the sequence of time-states is reversed.

Ultrasonic testing (UT) is a family of non-destructive testing techniques based on the propagation of ultrasonic waves in the object or material tested. In most common UT applications, very short ultrasonic pulse waves with centre frequencies ranging from 0.1-15 MHz and occasionally up to 50 MHz, are transmitted into materials to detect internal flaws or to characterize materials. A common example is ultrasonic thickness measurement, which tests the thickness of the test object, for example, to monitor pipework corrosion and erosion. Ultrasonic testing is extensively used to detect flaws in welds.

Sound from ultrasound is the name given here to the generation of audible sound from modulated ultrasound without using an active receiver. This happens when the modulated ultrasound passes through a nonlinear medium which acts, intentionally or unintentionally, as a demodulator.

A scanning acoustic microscope (SAM) is a device which uses focused sound to investigate, measure, or image an object. It is commonly used in failure analysis and non-destructive evaluation. It also has applications in biological and medical research. The semiconductor industry has found the SAM useful in detecting voids, cracks, and delaminations within microelectronic packages.

A parametric array, in the field of acoustics, is a nonlinear transduction mechanism that generates narrow, nearly side lobe-free beams of low frequency sound, through the mixing and interaction of high frequency sound waves, effectively overcoming the diffraction limit associated with linear acoustics. The main side lobe-free beam of low frequency sound is created as a result of nonlinear mixing of two high frequency sound beams at their difference frequency. Parametric arrays can be formed in water, air, and earth materials/rock.

Underwater acoustics is the study of the propagation of sound in water and the interaction of the mechanical waves that constitute sound with the water, its contents and its boundaries. The water may be in the ocean, a lake, a river or a tank. Typical frequencies associated with underwater acoustics are between 10 Hz and 1 MHz. The propagation of sound in the ocean at frequencies lower than 10 Hz is usually not possible without penetrating deep into the seabed, whereas frequencies above 1 MHz are rarely used because they are absorbed very quickly.

Ultrasonic transducers and ultrasonic sensors are devices that generate or sense ultrasound energy. They can be divided into three broad categories: transmitters, receivers and transceivers. Transmitters convert electrical signals into ultrasound, receivers convert ultrasound into electrical signals, and transceivers can both transmit and receive ultrasound.

Electromagnetic acoustic transducer (EMAT) is a transducer for non-contact acoustic wave generation and reception in conducting materials. Its effect is based on electromagnetic mechanisms, which do not need direct coupling with the surface of the material. Due to this couplant-free feature, EMATs are particularly useful in harsh, i.e., hot, cold, clean, or dry environments. EMATs are suitable to generate all kinds of waves in metallic and/or magnetostrictive materials. Depending on the design and orientation of coils and magnets, shear horizontal (SH) bulk wave mode, surface wave, plate waves such as SH and Lamb waves, and all sorts of other bulk and guided-wave modes can be excited. After decades of research and development, EMAT has found its applications in many industries such as primary metal manufacturing and processing, automotive, railroad, pipeline, boiler and pressure vessel industries, in which they are typically used for nondestructive testing (NDT) of metallic structures.

The photoacoustic Doppler effect is a type of Doppler effect that occurs when an intensity modulated light wave induces a photoacoustic wave on moving particles with a specific frequency. The observed frequency shift is a good indicator of the velocity of the illuminated moving particles. A potential biomedical application is measuring blood flow.

Mathias Fink, born in 1945 in Grenoble, is a French physicist, professor at ESPCI Paris and member of the French Academy of Sciences.

In the field of industrial ultrasonic testing, ultrasonic thickness measurement (UTM) is a method of performing non-destructive measurement (gauging) of the local thickness of a solid element based on the time taken by the ultrasound wave to return to the surface. This type of measurement is typically performed with an ultrasonic thickness gauge.

Ultrasound-modulated optical tomography (UOT), also known as Acousto-Optic Tomography (AOT), is a hybrid imaging modality that combines light and sound; it is a form of tomography involving ultrasound. It is used in imaging of biological soft tissues and has potential applications for early cancer detection. As a hybrid modality which uses both light and sound, UOT provides some of the best features of both: the use of light provides strong contrast and sensitivity ; these two features are derived from the optical component of UOT. The use of ultrasound allows for high resolution, as well as a high imaging depth. However, the difficulty of tackling the two fundamental problems with UOT have caused UOT to evolve relatively slowly; most work in the field is limited to theoretical simulations or phantom / sample studies.

A capacitive micromachined ultrasonic transducer (CMUT) is a relatively new concept in the field of ultrasonic transducers. Most of the commercial ultrasonic transducers today are based on piezoelectricity. CMUTs are the transducers where the energy transduction is due to change in capacitance. CMUTs are constructed on silicon using micromachining techniques. A cavity is formed in a silicon substrate, and a thin layer suspended on the top of the cavity serves as a membrane on which a metallized layer acts an electrode, together with the silicon substrate which serves as a bottom electrode.

Phase conjugation is a physical transformation of a wave field where the resulting field has a reversed propagation direction but keeps its amplitudes and phases.

Super-resolution photoacoustic imaging is a set of techniques used to enhance spatial resolution in photoacoustic imaging. Specifically, these techniques primarily break the optical diffraction limit of the photoacoustic imaging system. It can be achieved in a variety of mechanisms, such as blind structured illumination, multi-speckle illumination, or photo-imprint photoacoustic microscopy in Figure 1.

Photoacoustic microscopy is an imaging method based on the photoacoustic effect and is a subset of photoacoustic tomography. Photoacoustic microscopy takes advantage of the local temperature rise that occurs as a result of light absorption in tissue. Using a nanosecond pulsed laser beam, tissues undergo thermoelastic expansion, resulting in the release of a wide-band acoustic wave that can be detected using a high-frequency ultrasound transducer. Since ultrasonic scattering in tissue is weaker than optical scattering, photoacoustic microscopy is capable of achieving high-resolution images at greater depths than conventional microscopy methods. Furthermore, photoacoustic microscopy is especially useful in the field of biomedical imaging due to its scalability. By adjusting the optical and acoustic foci, lateral resolution may be optimized for the desired imaging depth.

Deep learning in photoacoustic imaging combines the hybrid imaging modality of photoacoustic imaging (PA) with the rapidly evolving field of deep learning. Photoacoustic imaging is based on the photoacoustic effect, in which optical absorption causes a rise in temperature, which causes a subsequent rise in pressure via thermo-elastic expansion. This pressure rise propagates through the tissue and is sensed via ultrasonic transducers. Due to the proportionality between the optical absorption, the rise in temperature, and the rise in pressure, the ultrasound pressure wave signal can be used to quantify the original optical energy deposition within the tissue.

Laszlo Adler is an American physicist and a Taine McDougal Professor Emeritus in the Department of Integrated Systems Engineering at the Ohio State University. He is known for his work in Ultrasonics, Acousto-optics, and Nondestructive Evaluation of Materials. He is a holocaust survivor and has been active in scientific research for over 60 years.

## References

1. Anderson, B. E., M. Griffa, C. Larmat, T.J. Ulrich, and P.A. Johnson, “Time reversal,” Acoust. Today, 4 (1), 5-16 (2008). https://acousticstoday.org/time-reversal-brian-e-anderson/
2. B. E. Anderson, T. J. Ulrich, P.-Y. Le Bas, and J. A. Ten Cate, “Three dimensional time reversal communications in elastic media,” J. Acoust. Soc. Am. 139(2), EL25-EL30 (2016).
3. Scalerandi, M., A.S. Gliozzi, B.E. Anderson, M. Griffa, P.A. Johnson, and T.J. Ulrich, “Selective source reduction to identify masked sources using time reversal acoustics,” J. Phys. D Appl. Phys. 41, 155504 (2008).
4. Anderson, B.E., T.J. Ulrich, M. Griffa, P.-Y. Le Bas, M. Scalerandi, A.S. Gliozzi and P.A. Johnson, “Experimentally identifying masked sources applying time reversal with the selective source reduction method,” J. Appl. Phys. 105(8), 083506 (2009).
5. Larmat, C.S., R.A. Guyer, and P.A. Johnson, “Time-reversal methods in geophysics,” Physics Today 63(8), 31-35 (2010).
6. Anderson, B.E., M. Griffa, T.J. Ulrich, and P.A. Johnson, “Time reversal reconstruction of finite sized sources in elastic media,” J. Acoust. Soc. Am. 130(4), EL219-EL225 (2011).
7. Parvasi, Seyed Mohammad; Ho, Siu Chun Michael; Kong, Qingzhao; Mousavi, Reza; Song, Gangbing (1 January 2016). "Real time bolt preload monitoring using piezoceramic transducers and time reversal technique—a numerical study with experimental verification". Smart Materials and Structures. 25 (8): 085015. Bibcode:2016SMaS...25h5015P. doi:10.1088/0964-1726/25/8/085015. ISSN   0964-1726. S2CID   113510522.