Focusing waves with a spatial extent smaller than a half wavelength (i.e., super resolution or sub diffraction limit) is possible using resonators placed in the near field of time reversal (TR) focusing. While a two-dimensional (2D) Helmholtz resonator array in a three-dimensional reverberant environment has limited ability to produce a high-resolution spatial focus in the TR focusing of audible sound, it is shown that acoustic waves propagating out-of-plane with the resonator array are not as strongly affected by the smaller effective wavelength induced by the resonator array, partially negating the effect of the resonators. A physical 2D waveguide is shown to limit the out-of-plane propagation, leading to improved resolution. It is also shown that post processing using an orthogonal particle velocity decomposition of a spatial scan of the focusing can filter out-of-plane particle motion in the near field of the array, which bypasses the effect of the unwanted third spatial dimension of propagation. The spatial resolution in a reverberant environment is shown to improve in the presence of a 2D Helmholtz resonator array and then further improve by adding a 2D waveguide. The resolution among the resonator array is better still without using a waveguide and instead using the partial-pressure reconstruction.
REFERENCES
1.
P. N.
Keating
,
T.
Sawatari
, and
G.
Zilinskas
, “
Signal processing in acoustic imaging
,” Proc. IEEE
67
(4
), 496
–510
(1979
).2.
M.
Kompis
,
H.
Pasterkamp
, and
G. R.
Wodicka
, “
Acoustic imaging of the human chest
,” Chest
120
(4
), 1309
–1321
(2001
).3.
M.
Born
,
E.
Wolf
,
A. B.
Bhatia
,
P. C.
Clemmow
,
D.
Gabor
,
A. R.
Stokes
,
P. A.
Wayman
,
W. L.
Wilcock
, and
P. L.
Knight
, Principles of Optics
(
Cambridge University Press
,
Cambridge, UK
, 2020
).4.
M.
Fink
, “
Time reversed acoustics
,” Phys. Today
50
(3
), 34
–40
(1997
).5.
B. E.
Anderson
,
M.
Griffa
,
C.
Larmat
,
T. J.
Ulrich
, and
P. A.
Johnson
, “
Time reversal
,” Acoust. Today
4
(1
), 5
–16
(2008
).6.
B. E.
Anderson
,
M. C.
Remillieux
,
P.-Y.
Le Bas
, and
T. J.
Ulrich
, “
Time reversal techniques
,” in Nonlinear Acoustic Techniques for Nondestructive Evaluation
, 1st ed., edited by
T.
Kundu
(
Springer and Acoustical Society of America
,
New York
, 2018
), pp. 547
–581
.7.
B.
Van Damme
,
K.
Van Den Abeele
,
Y.
Li
, and
O.
Bou Matar
, “
Time reversed acoustics techniques for elastic imaging in reverberant and nonreverberant media: An experimental study of the chaotic cavity transducer concept
,” J. Appl. Phys.
109
(10
), 104910
(2011
).8.
B. E.
Anderson
,
M.
Clemens
, and
M. L.
Willardson
, “
The effect of transducer directivity on time reversal focusing
,” J. Acoust. Soc. Am.
142
(1
), EL95
–EL101
(2017
).9.
A.
Parvulescu
and
C. S.
Clay
, “
Reproducibility of signal transmissions in the ocean
,” Radio Electron. Eng. UK
29
(4
), 223
–228
(1965
).10.
D. R.
Jackson
and
D. R.
Dowling
, “
Phase conjugation in underwater acoustics
,” J. Acoust. Soc. Am.
89
, 171
–181
(1991
).11.
G. F.
Edelmann
,
H. C.
Song
,
S.
Kim
,
W. S.
Hodgkiss
,
W. A.
Kuperman
, and
T.
Akal
, “
Underwater acoustic communications using time reversal
,” IEEE J. Oceanic Eng.
30
(4
), 852
–864
(2005
).12.
H. C.
Song
, “
An overview of underwater time-reversal communication
,” IEEE J. Oceanic Eng.
41
, 644
–655
(2016
).13.
H. C.
Song
and
W. A.
Kuperman
, “
Time machine in ocean acoustics
,” J. Acoust. Soc. Am.
153
(1
), R1
–R2
(2023
).14.
J. V.
Candy
,
A. W.
Meyer
,
A. J.
Poggio
, and
B. L.
Guidry
, “
Time-reversal processing for an acoustic communications experiment in a highly reverberant environment
,” J. Acoust. Soc. Am.
115
(4
), 1621
–1631
(2004
).15.
S.
Yon
,
M.
Tanter
, and
M.
Fink
, “
Sound focusing in rooms: The time-reversal approach
,” J. Acoust. Soc. Am.
113
(3
), 1533
–1543
(2003
).16.
G.
Ribay
,
J.
de Rosny
, and
M.
Fink
, “
Time reversal of noise sources in a reverberation room
,” J. Acoust. Soc. Am.
117
(5
), 2866
–2872
(2005
).17.
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
).18.
B. E.
Anderson
, “
High amplitude time reversal focusing of sound and vibration
,” Proc. Mtgs. Acoust.
51
, 032001
(2023
).19.
J.-L.
Thomas
,
F.
Wu
, and
M.
Fink
, “
Time reversal focusing applied to lithotripsy
,” Ultrason. Imag.
18
(2
), 106
–121
(1996
).20.
M.
Tanter
,
J.-L.
Thomas
, and
M.
Fink
, “
Focusing and steering through absorbing and aberrating layers: Application to ultrasonic propagation through the skull
,” J. Acoust. Soc. Am.
103
(5
), 2403
–2410
(1998
).21.
G.
Montaldo
,
P.
Roux
,
A.
Derode
,
C.
Negreira
, and
M.
Fink
, “
Ultrasound shock wave generator with one-bit time reversal in a dispersive medium, application to lithotripsy
,” Appl. Phys. Lett.
80
, 897
–899
(2002
).22.
B. E.
Anderson
,
M.
Griffa
,
T. J.
Ulrich
,
P.-Y. L.
Bas
,
R. A.
Guyer
, and
P. A.
Johnson
, “
Crack localization and characterization in solid media using time reversal techniques
,” in Proceedings of the 44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium
, Salt Lake City, Utah
(June 27–30
, 2010
), Paper No. 10–154.23.
M. L.
Willardson
,
B. E.
Anderson
,
S. M.
Young
,
M. H.
Denison
, and
B. D.
Patchett
, “
Time reversal focusing of high amplitude sound in a reverberation chamber
,” J. Acoust. Soc. Am.
143
(2
), 696
–705
(2018
).24.
C. B.
Wallace
and
B. E.
Anderson
, “
High-amplitude time reversal focusing of airborne ultrasound to generate a focused nonlinear difference frequency
,” J. Acoust. Soc. Am.
150
(2
), 1411
–1423
(2021
).25.
B. D.
Patchett
and
B. E.
Anderson
, “
Nonlinear characteristics of high amplitude focusing using time reversal in a reverberation chamber
,” J. Acoust. Soc. Am.
151
(6
), 3603
–3614
(2022
).26.
B. D.
Patchett
,
B. E.
Anderson
, and
A. D.
Kingsley
, “
Numerical modeling of Mach-stem formation in high-amplitude time-reversal focusing
,” J. Acoust. Soc. Am.
153
(5
), 2724
–2732
(2023
).27.
C.
Larmat
,
J.-P.
Montagner
,
M.
Fink
,
Y.
Capdeville
,
A.
Tourin
, and
E.
Clevede
, “
Time-reversal imaging of seismic sources and applications to the great Sumatra earthquake
,” Geophys. Res. Lett.
33
(19
), L19312
, https://doi.org/10.1029/2006GL026336 (2006
).28.
C.
Larmat
,
J.
Tromp
,
Q.
Liu
, and
J.-P.
Montagner
, “
Time-reversal location of glacial earthquakes
,” J. Geophys. Res.
113
(B9
), B09314
, https://doi.org/10.1029/2008JB005607 (2008
).29.
C.
Larmat
,
R. A.
Guyer
, and
P. A.
Johnson
, “
Tremor source location using time-reversal: Selecting the appropriate imaging field
,” Geophys. Res. Lett.
36
(22
), L22304
, https://doi.org/10.1029/2009GL040099 (2009
).30.
C. S.
Larmat
,
R. A.
Guyer
, and
P. A.
Johnson
, “
Time-reversal methods in geophysics
,” Phys. Today
63
(8
), 31
–35
(2010
).31.
R. K.
Ing
and
N.
Quieffin
, “
In solid localization of finger impacts using acoustic time-reversal process
,” Appl. Phys. Lett
87
(20
), 204104
(2005
).32.
D.
Vigoureux
and
J.-L.
Guyader
, “
A simplified time reversal method used to localize vibrations sources in a complex structure
,” Appl. Acoust.
73
(5
), 491
–496
(2012
).33.
D. G.
Albert
,
L.
Liu
, and
M. L.
Moran
, “
Time reversal processing for source location in an urban environment (L)
,” J. Acoust. Soc. Am.
118
(2
), 616
–619
(2005
).34.
S.
Cheinet
,
L.
Ehrhardt
, and
T.
Broglin
, “
Impulse source localization in an urban environment: Time reversal versus time matching
,” J. Acoust. Soc. Am.
139
(1
), 128
–140
(2016
).35.
C.
Heaton
,
B. E.
Anderson
, and
S. M.
Young
, “
Time reversal focusing of elastic waves in plates for educational demonstration purposes
,” J. Acoust. Soc. Am.
141
(2
), 1084
–1092
(2017
).36.
L. A.
Barnes
,
B. E.
Anderson
,
P.-Y.
Le Bas
,
A. D.
Kingsley
,
A. C.
Brown
, and
H. R.
Thomsen
, “
The physics of knocking over LEGO minifigures with time reversal focused vibrations
,” J. Acoust. Soc. Am.
151
(2
), 738
–751
(2022
).37.
A. A.
Maznev
and
O. B.
Wright
, “
Upholding the diffraction limit in the focusing of light and sound
,” Wave Motion
68
, 182
–189
(2017
).38.
E. D.
Golightly
,
B. E.
Anderson
,
A. D.
Kingsley
,
R.
Russell
, and
R.
Higgins
, “
Super resolution, time reversal focusing using path diverting properties of scatterers
,” Appl. Acoust.
206
, 109308
(2023
).39.
A. D.
Kingsley
,
B. E.
Anderson
, and
T. J.
Ulrich
, “
Super-resolution within a one-dimensional phononic crystal of resonators using time reversal in an equivalent circuit model
,” J. Acoust. Soc. Am.
152
(3
), 1263
–1271
(2022
).40.
G.
Lerosey
,
J.
de Rosny
,
A.
Tourin
, and
M.
Fink
, “
Focusing beyond the diffraction limit with far-field time reversal
,” Science
315
(5815
), 1120
–1122
(2007
).41.
F.
Lemoult
,
M.
Fink
, and
G.
Lerosey
, “
Acoustic resonators for far-field control of sound on a subwavelength scale
,” Phys. Rev. Lett.
107
(6
), 064301
(2011
).42.
F.
Lemoult
,
N.
Kaina
,
M.
Fink
, and
G.
Lerosey
, “
Soda cans metamaterial: A subwavelength-scaled phononic crystal
,” Crystals
6
(7
), 82
(2016
).43.
A. A.
Maznev
,
G.
Gu
,
S. Y.
Sun
,
J.
Xu
,
Y.
Shen
,
N.
Fang
, and
S. Y.
Zhang
, “
Extraordinary focusing of sound above a soda can array without time reversal
,” New J. Phys.
17
(4
), 042001
(2015
).44.
A. D.
Kingsley
and
B. E.
Anderson
, “
Time reversal in a phononic crystal using finite-element modeling and an equivalent circuit model
,” JASA Express Lett.
2
(12
), 124002
(2022
).45.
A. D.
Kingsley
,
A.
Basham
, and
B. E.
Anderson
, “
Time reversal imaging of complex sources in a three-dimensional environment using a spatial inverse filter
,” J. Acoust. Soc. Am.
154
(2
), 1018
–1027
(2023
).46.
F.
Lemoult
,
N.
Kaina
,
M.
Fink
, and
G.
Lerosey
, “
Wave propagation control at the depp subwavelength scale in metamaterials
,” Nat. Phys.
9
, 55
–60
(2013
).47.
A. S.
Gliozzi
,
M.
Miniaci
,
F.
Bosia
,
N. M.
Pugno
, and
M.
Scalerandi
, “
Metamaterials-based sensor to detect and locate nonlinear elastic sources
,” Appl. Phys. Lett.
107
, 161902
(2015
).48.
M.
Miniaci
,
A. S.
Gliozzi
,
B.
Morvan
,
A.
Krushynska
,
F.
Bosia
,
M.
Scalerandi
, and
N. M.
Pugno
, “
Proof of concept for an ultrasensitive technique to detect and localize sources of elastic nonlinearity using phononic crystals
,” Phys. Rev. Lett.
118
, 214301
(2017
).49.
A. D.
Kingsley
,
J. M.
Clift
,
B. E.
Anderson
,
J. E.
Ellsworth
,
T. J.
Ulrich
, and
P.-Y. L.
Bas
, “
Development of software for performing acoustic time reversal with multiple inputs and outputs
,” Proc. Mtgs. Acoust.
46
, 055003
(2022
).50.
B. D.
Patchett
,
B. E.
Anderson
, and
A. D.
Kingsley
, “
The impact of room location on time reversal focusing amplitudes
,” J. Acoust. Soc. Am.
150
(2
), 1424
–1433
(2021
).51.
ISO 3741:2010
, “Sound power and energy in reverberant environments” (
International Organization for Standardization
,
Geneva, Switzerland
, 2010
).52.
S. M.
Young
,
B. E.
Anderson
,
R. C.
Davis
,
R. R.
Vanfleet
, and
N. B.
Morrill
, “
Sound transmission measurements through porous screen
,” Proc. Mtgs. Acoust.
26
, 045003
(2017
).53.
F. J.
Fahy
, Sound Intensity
, 2nd ed. (
Routledge and CRC Press
,
London
, UK, 2017
), p. 95
.54.
J. S.
Lawrence
,
K. L.
Gee
,
T. B.
Neilsen
, and
S. D.
Sommerfeldt
, “
Highly directional pressure sensing using the phase gradient
,” J. Acoust. Soc. Am.
144
(4
), EL346
–EL352
(2018
).© 2024 Acoustical Society of America.
2024
Acoustical Society of America
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