Time Reversal



            Before the following excerpts, let me comment on the possibilities.


            It has been shown in experiments that time reversal of acoustics “re-creates the source” of the original sound.  In other words, the time reversed sound un-coalesces to the same point of the original sound.  We see a similar effect with light via holograms.  We record the interference pattern of light from an object, then re-create the photonic representation of that object in 3D space.  Sound is interference patterns of waves, sight is interference patterns of waves. 
The next step would be to say that any interference pattern of waves, of a certain phenomena, could be recorded and time reversed to re-produce that original phenomena. A sci-fi story waiting to happen :)


Of course, it would all depend on the resolution and dynamic range of your transducers, and the speed of your hardware/operating system.  (Hopefully not Windows)


(re Star Trek: a precursor to transporter technology and holodecks?????)






Excerpts from various articles on Time Reversal. 
Mathias Fink seems to be the founder of such research.






"No one has ever seen a block of matter explode and the fragments spontaneously gather to form the original block, or see a drop of ink re-form after dilution in a glass of water," says Mathias Fink. Many physicists have been obsessed with reversing time, i.e., challenging the irreversibility of macroscopic physical phenomena. Although the equations of standard mechanics and quantum mechanics can be reversed on a microscopic scale, macroscopic phenomena have always proved to be irreversible because of the huge amount of particles involved.

However, since relatively little data is required for the full description of a wave field in wave physics, it becomes feasible to conduct time-reversing experiments with sound waves. The equations describing wave propagation are "invariant by reversing the direction of time." In other words this means that the answers to the equations are always the same whether time is moving from the past to the future or vice versa. The only prerequisite is to disregard the dissipation of energy into heat; this is usually the case with sonic or ultrasonic frequencies, i.e., ranging from a few hertz to some dozen megahertz.




A system of piezoelectric transducers


Mathias Fink, who began to address the subject in 1987, came up with the idea of "reversing in time" the ultrasounds emitted by an object. He recorded the emitted wave and analyzed it to produce a reversed wave which in turn propagated backwards and re-focused on the initial emitter. He used reversed "acoustic retinas", so to speak, to do this. The "retinas" are in fact a network of piezoelectric transducers that can act either as a microphone or as a loud-speaker. In other words, the transducers can act as sensors by generating an electric current when they pick up a sound wave but they can also act as emitters by generating a sound wave when they are charged with electric current.

That is how the first time-reversing mirror was engineered. It is a device consisting of a system of piezoelectric transducers. Each transducer is connected to an electronic chain including an amplifier and an analog-to-digital converter. The sound signals picked up by the transducer travel through the chain and are stored in the memories. The signals are then reversed by reading the memories backwards and a "time-reversed" wave is reconstituted.

Unlike optical mirrors where imaginary projections of reflected light rays converge on the vanishing point, the beams do converge on a point in time-reversing mirrors




From non-destructive testing to the destruction of kidney stones


The time-reversing mirror is an amazing device that has opened the door to vast prospects, including applications already in the works. "The most advanced application to date is the non-destructive testing of materials," adds Mathias Fink, and indeed, a time-reversing mirror has been tested as part of a major joint effort with Snecma. The goal of the testing was to detect defects in titanium alloys. The alloys have an extremely heterogeneous microstructure that generates a loud background echo making it impossible to see defects with a weak contrast. However, these tiny defects can cause jet engines to explode, explaining why the French company was so keen on assessing the detection capabilities of a time-reversing mirror that could pinpoint defects half the size of those detected by a General Electric engineered technology. Indeed the American company's technique was considered as the most efficient until now.

The most promising applications are undoubtedly in the medical field. Actually, the first time-reversing mirrors designed by Mathias Fink's team were for a new type of lithotriptor, a device using ultra-sound to destroy kidney stones. Ultrasounds or X-rays are commonly used to pinpoint kidney stones. 70% of the several thousand ulstrasounds emitted to destroy a kidney stone miss the target because when the body moves, so does the stone. However the time-reversing mirror has solved this problem by using a group of the mirror's components to light the designated area. The kidney stone then reflects the signals and the mirror picks up, automatically amplifies and sends the signals back to the source, i.e., the stone.

A 64 track time-reversing mirror has already been engineered with support from ANVAR. The mirror works in real-time, uses a network of transducers with a 20 cm. diameter, and sends back 1,000 signals per second, resulting in promising clinical results. "The machine we have designed has worked remarkably well in hospital and showed that the ultrasonic beam keeps tracking the moving stone," explains Mathias Fink.




A wealth of applications based on a simple idea


Other applications, now being researched at the "Wave and Acoustics" Laboratory, will eventually be engineered. For instance, focusing ultrasound waves through the skull for surgical purposes is being researched with the neurosurgery ward at the Val de Grâce Hospital in Paris. Project goal is to use ultrasound hyperthermia to home in on and destroy a small tumor pinpointed by MRI (Magnetic Resonance Imaging).

The technique is being considered for mine-detection and more generally for underwater acoustics. Other fields for exploration are underwater telecommunications where the time-reversing technique that can compensate for any defects in the propagation channel might play a major role in the future. In the long run, time-reversal could be used to project stereophonic sound or create a sound traveling to just one person. Last, the technique is used in hydrodynamics for the accurate measuring of turbulent flows, and is expected to help us to acquire a better understanding of how turbulence forms.

Indeed, as Mathias Fink says, "Time-reversal has a wealth of applications." A modest man, he quickly adds, "It's the simplest idea on earth: reverse time and send it back."






In classical mechanics, a time-reversal experiment with a large number of particles is impossible. Because of the high sensitivity to initial conditions, one would need to resolve the positions and velocities of each particle with infinite accuracy. Thus, it would require an infinite amount of information, which is of course out of reach. In wave physics however, the amount of information required to describe a wave field is limited and depends on the shortest wavelength of the field. Thus we can propose an acoustic equivalent of the experiment we mentioned above. We start with a coherent transient pulse, let it propagate through a disordered highly scattering medium, then record the scattered field and time-reverse it: surprisingly, it travels back to its initial source, which is not predictable by usual theories for random media. Indeed, to study waves propagation in disordered media theoreticians, who find it difficult to deal with one realization of disorder, use concepts defined as an average over the realizations, which naturally leads to the diffusion approximation. But the corresponding equation is not time-reversal invariant and thus fails in describing our experiment. Then, to understand our experimental results and try to predict new ones, we have developed a finite elements simulation based on the real microscopic time-invariant equation of propagation. The experimental and numerical results are found to be in very good agreement.






Acoustic time-reversal mirrors (TRMs) can characterize rough surfaces. In one TRM technique, an echo is detected by an array of transducers, whereupon each signal at each transducer is reversed in time and rebroadcast (last in, first out) back along the incoming path. The resulting cacophony of signals amazingly converges into a single pulse of sound located at the source of the echo. (See the article "Time Reversed Acoustics" in Physics Today, March 1997, page 34.) Now, in exploring the robustness and limits of the technique, Mathias Fink (University of Paris VII) and his colleagues have found that, by moving the TRM before the signals are retransmitted, they could determine both the root-mean-square height and the surface-height autocorrelation function of rough surfaces. The second of these statistical measures has been particularly difficult to determine, requiring either point-by-point mapping of the surface, which is slow, or a less accurate double-echo technique without the strong correlations introduced by time reversal. Among the applications for this technique are measuring arterial walls in vivo, exploring the sea floor, and determining the interfacial roughness between two solids. (J. H. Rose et al., J. Acoust. Soc. Am. 106, 716, 1999; P. Roux et al., J. Acoust. Soc. Am. 106, 724, 1999.) -sgb