For the acoustic characterization of materials, a method is proposed for interpreting experiments with finite-sized transducers and test samples in terms of the idealized situation in which plane waves are transmitted through an infinite plane-parallel layer. The method uses acoustic holography, which experimentally provides complete knowledge of the wave field by recording pressure waveforms at points on a surface intersected by the acoustic beam. The measured hologram makes it possible to calculate the angular spectrum of the beam to decompose the field into a superposition of plane waves propagating in different directions. Because these waves cancel one another outside the beam, the idealized geometry of an infinite layer can be represented by a sample of finite size if its lateral dimensions exceed the width of the acoustic beam. The proposed method relies on holograms that represent the acoustic beam with and without the test sample in the transmission path. The method is described theoretically, and its capabilities are demonstrated experimentally for silicone rubber samples by measuring their frequency-dependent phase velocities and absorption coefficients in the megahertz frequency range.

1.
H. J.
McSkimin
, “
Ultrasonic methods of measuring the mechanical properties of liquids and solids
,”
Physical Acoustics: Principles and Methods
, edited by
W. P.
Mason
(
Academic
,
New York
,
1964
), Vol.
I
, part A, Chap. 10, pp.
271
334
.
2.
J. C.
Bamber
, “
Attenuation and absorption
,”
Physical Principles of Medical Ultrasonics
, 2nd ed. (
Wiley
,
New York
,
2003
), Chap. 4, pp.
93
166
.
3.
J. C.
Bamber
, “
Speed of sound
,” in
Physical Principles of Medical Ultrasonics
, 2nd ed. (
Wiley
,
New York
,
2003
), Chap. 5, pp.
167
190
.
4.
E. L.
Madsen
,
F.
Dong
,
G. R.
Frank
,
B. S.
Garra
,
K. A.
Wear
,
T.
Wilson
,
J. A.
Zagzebski
,
H. L.
Miller
,
K. K.
Shung
,
S. H.
Wang
, and
E. J.
Feleppa
, “
Interlaboratory comparison of ultrasonic backscatter, attenuation, and speed measurements
,”
J. Ultrasound Med.
18
(
9
),
615
631
(
1999
).
5.
F. W.
Kremkau
,
R. W.
Barnes
, and
C. P.
McGraw
, “
Ultrasonic attenuation and propagation speed in normal human brain
,”
J. Acoust. Soc. Am.
70
(
1
),
29
38
(
1981
).
6.
B.
Zeqiri
,
W.
Scholl
, and
S. P.
Robinson
, “
Measurement and testing of the acoustic properties of materials: A review
,”
Metrologia
47
(
2
),
S156
S171
(
2010
).
7.
R.
Bass
, “
Diffraction effects in the ultrasonic field of a piston source
,”
J. Acoust. Soc. Am
30
(
7
),
602
605
(
1958
).
8.
V. A.
Krasil'nikov
and
V. V.
Krylov
,
Introduction to Physical Acoustics
(
Nauka
,
Moscow
,
1984
), in Russian.
9.
J. W.
Goodman
,
Introduction to Fourier Optics
(
McGraw-Hill
,
New York
,
1968
).
10.
L. M.
Brekhovskikh
,
Waves in Layered Media
, 2nd ed. (
Academic
,
New York
,
1980
).
11.
O. A.
Sapozhnikov
, “
High-intensity ultrasonic waves in fluids: Nonlinear propagation and effects
,” in
Power Ultrasonics. Applications of High-Intensity Ultrasound
(
Elsevier
,
Cambridge
,
2015
), Chap. 2, pp.
9
35
.
12.
K. G.
Krishnan
, “
Dispersion of ultrasonic velocity in liquids
,”
Proc. - Indian Acad. Sci., Sect. A
9
(
5
),
382
385
(
1939
).
13.
J. M. M.
Pinkerton
, “
A pulse method for the measurement of ultrasonic absorption in liquids: Results for water
,”
Nature
160
(
4056
),
128
129
(
1947
).
14.
O. A.
Sapozhnikov
and
M. R.
Bailey
, “
Radiation force of an arbitrary acoustic beam on an elastic sphere in a fluid
,”
J. Acoust. Soc. Am.
133
(
2
),
661
676
(
2013
).
15.
O. A.
Sapozhnikov
,
Y. A.
Pishchalnikov
, and
A. V.
Morozov
, “
Reconstruction of the normal velocity distribution on the surface of an ultrasonic transducer from the acoustic pressure measured on a reference surface
,”
Acoust. Phys.
49
(
3
),
354
360
(
2003
).
16.
O. A.
Sapozhnikov
,
S. A.
Tsysar
,
V. A.
Khokhlova
, and
W.
Kreider
, “
Acoustic holography as a metrological tool for characterizing medical ultrasound sources and fields
,”
J. Acoust. Soc. Am.
138
(
3
),
1515
1532
(
2015
).
17.
L. E.
Maggi
,
M. A.
Von Krüger
,
W. C. A.
Pereira
, and
E. E. C.
Monteiro
, “
Development of silicon-based materials for ultrasound biological phantoms
,” in
Proc. 2009 IEEE Int. Ultrason. Symp.
, pp.
1962
1965
(
2009
).
18.
I. S.
Grigoriev
and
E. Z.
Meilikhov
(eds.),
Handbook of Physical Properties
(
CRC Press
,
New York
,
1997
).
19.
O. A.
Sapozhnikov
,
A. E.
Ponomarev
, and
M. A.
Smagin
, “
Transient acoustic holography for reconstructing the particle velocity of the surface of an acoustic transducer
,”
Acoust. Phys.
52
(
3
),
324
330
(
2006
).
20.
D.
Nikolaev
,
S.
Tsysar
,
A.
Krendeleva
,
O.
Sapozhnikov
, and
V.
Khokhlova
, “
Using acoustic holography to characterize absorbing layers
,”
Proc. Mtgs. Acoust.
38
,
045012
(
2019
).
21.
D.
Cathignol
,
O. A.
Sapozhnikov
, and
J.
Zhang
, “
Lamb waves in piezoelectric focused radiator as a reason for discrepancy between O'Neil formula and experiment
,”
J. Acoust. Soc. Am.
101
(
3
),
1286
1297
(
1997
).
22.
O. A.
Sapozhnikov
and
M. A.
Smagin
, “
Finding the dispersion relations for Lamb-type waves in a concave piezoelectric plate by optical visualization of the ultrasound field radiated into a fluid
,”
Acoust. Phys.
61
(
2
),
181
187
(
2015
).
23.
H. T.
O'Neil
, “
Theory of focusing radiators
,”
J. Acoust. Soc. Am.
21
(
5
),
516
526
(
1949
).
24.
V. A.
Del Grosso
and
C. W.
Mader
, “
Speed of sound in pure water
,”
J. Acoust. Soc. Am.
52
(
5B
),
1442
1446
(
1972
).
25.
D. L.
Folds
, “
Speed of sound and transmission loss in silicone rubbers at ultrasonic frequencies
,”
J. Acoust. Soc. Am.
56
(
4
),
1295
1296
(
1974
).
26.
M.
O'Donnell
,
E. T.
Jaynes
, and
J. G.
Miller
, “
General relationships between ultrasonic attenuation and dispersion
,”
J. Acoust. Soc. Am.
63
(
6
),
1935
1937
(
1978
).
27.
K. R.
Waters
,
J.
Mobley
, and
J. G.
Miller
, “
Causality-imposed (Kramers-Kronig) relationships between attenuation and dispersion
,”
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
52
(
5
),
822
823
(
2005
).
28.
A.
Goldstein
,
D. R.
Gandhi
, and
W. D.
O'Brien
, “
Diffraction effects in hydrophone measurements
,”
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
45
(
4
),
972
979
(
1998
).
29.
E. G.
Radulescu
,
P. A.
Lewin
,
A.
Goldstein
, and
A.
Nowicki
, “
Hydrophone spatial averaging corrections from 1 to 40 MHz
,”
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
48
(
6
),
1575
1580
(
2001
).
30.
IEC 62127-3:
Ultrasonics—Hydrophones—Part 3: Properties of Hydrophones for Ultrasonic Fields up to 40 MHz
(
International Electrotechnical Commission
,
Geneva, Switzerland
,
2013
).
31.
K. A.
Wear
, “
Considerations for choosing sensitive element size for needle and fiber-optic hydrophones—Part I: Spatiotemporal transfer function and graphical guide
,”
IEEE Trans. Ultrason., Ferroelectr., Freq. Control
66
(
2
),
318
339
(
2019
).
You do not currently have access to this content.