Page 12 - Winter 2008

investigated in many applications20-26 and have been addition-
ally refined since they were originally presented, including
application to multiple and anisotropic scattering between/by
27
the targets.
A different theoretical approach has been devel-
oped for the problem of localization and characterization of
several extended scatterers in the presence of multiple scat-
tering. This approach is based upon a different mathematical
technique, called MUltiple SIgnal Classification scheme
(MUSIC), for the SVD analysis of the array response
28,29
Super resolution
One major thrust in TR research is to investigate and develop methods to improve resolution of a TR focus by exceeding the diffraction limit. A point source emits a wave field that is composed of two components: a farfield compo- nent and an evanescent component, which is only present in the extreme nearfield of a given source. The evanescent waves may have higher spatial frequency content and thus higher spatial resolution information; however, evanescent waves decay exponentially away from the source. Thus a TRM in the farfield cannot directly detect evanescent waves from the source. This means that some information is lost in the forward propagation, resulting in imperfect reconstruc- tion of the source. To have perfect reconstruction, as well as to beat the diffraction limit, one must recreate the evanescent wave field of the source.
As was discussed earlier in the example of a time reversed
movie of the pebble in the pond, the pebble ascends from the
water precisely at the focal time. In this manner the outward
propagating ripples are not generated. Now we take the concept
of the pebble movie one step further to aid in understanding
how super resolution may be achieved. The ascending pebble
contains farfield and evanescent components. The incoming,
focused-wave, containing only farfield components, is exactly
out of phase with the ascending pebble. The net effect is to can-
cel the farfield component, leaving only the evanescent compo-
nent. Since the evanescent waves contain higher spatial resolu-
tion information than the farfield waves, the diffraction limit
may be surpassed, leading to super resolution. The pebble
ascending from the water is analogous to producing an acoustic
matrix.
energy sink, described and first demonstrated by Cassereau and 8 30
Fink and de Rosney and Fink. Additional examples of achiev- ing super resolution by using TR include an electromagnetic application developed by Lerosey, de Rosney, Tourin, and Fink,31 and amplification of the nearfield information in
32
In this section we will review a number of applications in development. As there are so many, the following list is not meant to be exhaustive. Application areas discussed here include underwater acoustics, biomedical ultrasound imag- ing and therapy, nondestructive evaluation, and seismology. We will also highlight some of the TR work going on at Los Alamos in collaboration with others.
Propagation of acoustic waves in the ocean is complex, due to multiple reflections at the rough bottom surface and at
acoustics by Conti, Roux, and Kuperman.
Applications
the water–air interface, as well as significant heterogeneity that creates strong scattering. Acoustic wave propagation in shallow water as well as off-shore is usually modeled as prop- agation in a randomly layered waveguide. Multiple scattering at the boundaries and in the bulk of the waveguide can sig- nificantly degrade underwater communications and imaging techniques. With TR, scattering is exploited to improve focusing on specific targets. In fact, Derode, Roux and Fink12 demonstrated that a random, multiple-scattering material placed between the source and a TRM can increase the effec- tive aperture of the mirror itself, thus improving its spatial focusing. The multiple-scattering material functions as a kind of lens during the back propagation. The same results have been obtained in the case of ultrasonic propagation in a
33
37,38 39-42 target detection and underwater communication.
TR focusing techniques are in development for biomed- ical applications as well, for imaging and therapeutic purpos- es. Inhomogeneity inside the medium greatly affects focusing performance in time and space in standard acoustic imaging methods. For instance, spatial heterogeneity in density and velocity leads to beam spreading, and the presence of inter- faces between different materials leads to refraction and scat- tering of the waves. As already demonstrated, TR naturally compensates for these limits, because the information about the medium is encoded in the forward propagation signals recorded at a TRM. Again, the scattering enhances focusing, acting as a lens during the back propagation. Examples of biomedical applications in development include applying TRM’s to localizing kidney stones and focusing high ampli- tudes on them to destroy the stones (lithotripsy therapy), by
43,44
Researchers from the Scripps Institution of Oceanography/University of San Diego, and from the University of Washington (Seattle), have shown not only the feasibility of a TRM for underwater sound and ultra- sound focusing34 but also its robustness35,36 and potential for
waveguide filled with water.
the group at LOA in Paris.
Other applications in develop-
ment include TR for focusing through the skull for brain
tumor hyperthermia therapy, using special corrective tech-
niques to compensate for the high level of attenuation within
ing TR methods for applications in NonDestructive Evaluation (NDE). To our knowledge, the first work in this
49
45-47 48 as well as for brain surgery.
the skull,
There has been considerable effort devoted to develop-
In their work, they developed a TRM for focusing on small defects in tita- nium and duraluminum samples submerged in water tanks. In the presence of multiple defects inside the specimen, the
field was demonstrated by Chakroun et al.
50 An enhancement of these techniques was described by
ITRM is used to focus only on the most reflective scatterer. Kerbrat et al. using the DORT method for selective focusing
on each of a set of scatterers.
51
DORT was used to improve the selective localization of small defects very close to each other, giving rise to multiple scattering among the defects, and for distinguishing them from the multiple scattering due to the
52 has been also applied to the detection of flaws and delamina-
local heterogeneity of the specimen under investigation.
TR
53-54
plate changes the quality of the TR reconstruction of the
tions in thin solid plates.
The presence of defects inside the
10 Acoustics Today, January 2008