Commentary
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."
5
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.
6
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