Ultrasonic non-destructive testing (UNDT) plays an important role in ensuring the quality of cylindrical components of equipment such as pipes and axles. As the acoustic beam width widens along propagation depths, the diffraction of acoustic wave becomes serious and the images of defects will be interfered with. To precisely evaluate the dimensions of defects and flaws concealed in components, the synthetic aperture focusing technique (SAFT) is introduced to enhance the image resolutions. Conventional SAFTs have been successfully implemented for the ultrasonic imaging of normal cylinders, while solutions for complex ones, such as variable-diameter cylinders, are still lacking. To overcome this problem, a frequency-domain SAFT for variable-diameter cylindrical components is proposed. This algorithm is mainly based on acoustic field extrapolation, which is modified from cylindrical phase shift migration with the aid of split-step Fourier. After a series of extrapolations, a high-resolution ultrasound image can be reconstructed using a particular imaging condition. According to the experimental results, the proposed method yields low side lobes and high resolutions for flat transducers. Its attainable angular resolution relies on the transducer diameter D and scanning radius R and approximates D/(2R).

1.
B.
Rajani
and
K.
Yehuda
, “
Non-destructive inspection techniques to determine structural distress indicators in water mains
,” in
Evaluation Control of Water Loss in Urban Water Networks
,
Valencia, Spain
(
June 21–25, 2004
).
2.
K.
Makino
,
J.
Yohso
,
H.
Sakamoto
, and
H.
Ishiduka
, “
Hollow axle ultrasonic crack detection for conventional railway vehicles
,”
Q. Report RTRI
46
(
2
),
78
84
(
2005
).
3.
G. Y.
Zhao
and
C.
Lu
, “
Time domain/frequency domain SAFT imaging in thin-diameter rod
,”
Appl. Mech. Mater.
380
,
3648
3652
(
2013
).
4.
G. C.
Eastland
,
T. M.
Marston
, and
P. L.
Marston
, “
Reversible bistatic and monostatic synthetic aperture sonar filtering
,”
J. Acoust. Soc. Am.
129
(
4
),
2686
(
2011
).
5.
T. M.
Marston
,
J. L.
Kennedy
, and
P. L.
Marston
, “
Coherent and semi-coherent processing of limited-aperture circular synthetic aperture (CSAS) data
,” in
Oceans IEEE
,
Waikoloa, HI
(
September 19–22, 2011
), pp.
1
6
.
6.
S. R.
Doctor
,
T. E.
Hall
, and
L. D.
Reid
, “
SAFT—The evolution of a signal processing technology for ultrasonic testing
,”
NDT Int.
19
(
3
),
163
167
(
1986
).
7.
K.
Nagai
, “
Fourier domain reconstruction of synthetic focus acoustic imaging system
,”
Proc. IEEE
72
(
6
),
748
749
(
1984
).
8.
K. J.
Langenberg
,
M.
Berger
,
T.
Kreutter
,
K.
Mayer
, and
V.
Schmitz
, “
Synthetic aperture focusing technique signal processing
,”
NDT Int.
19
(
3
),
177
189
(
1986
).
9.
K.
Mayer
,
R.
Marklein
,
K. J.
Langenberg
, and
T.
Kreutter
, “
Three-dimensional imaging system based on Fourier transform synthetic aperture focusing technique
,”
Ultrasonics
28
(
4
),
241
255
(
1990
).
10.
L. J.
Busse
, “
Three-dimensional imaging using a frequency-domain synthetic aperture focusing technique
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
39
(
2
),
174
179
(
1992
).
11.
R. H.
Stolt
, “
Migration by Fourier transform
,”
Geophysics
43
(
1
),
23
48
(
1978
).
12.
T.
Stepinski
, “
An implementation of synthetic aperture focusing technique in frequency domain
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
54
(
7
),
1399
1408
(
2007
).
13.
T.
Olofsson
, “
Phase shift migration for imaging layered objects and objects immersed in water
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
57
(
11
),
2522
2530
(
2010
).
14.
T.
Olofsson
,
M. H.
Skjelvareid
, and
A.
Barkefors
, “
Ultrasonic imaging of immersed objects using migration techniques
,” in
Proceedings of the 2010 8th European Conference on Synthetic Aperture Radar (EUSAR)
,
Aachen, Germany
(
June 7–10, 2010
), pp.
1
4
.
15.
M. H.
Skjelvareid
,
T.
Olofsson
,
Y.
Birkelund
, and
Y.
Larsen
, “
Synthetic aperture focusing of ultrasonic data from multilayered media using an omega-k algorithm
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
58
(
5
),
1037
1048
(
2011
).
16.
T.
Lukomski
,
T.
Stepinski
, and
J.
Kowal
, “
Synthetic aperture focusing technique with virtual transducer for immersion inspection of solid objects
,”
Insight-Non-Destruct. Test. Cond. Monitor.
54
(
11
),
623
627
(
2012
).
17.
H.
Wu
,
J.
Chen
,
K.
Yang
, and
X.
Hu
, “
Ultrasonic array imaging of multilayer structures using full matrix capture and extended phase shift migration
,”
Meas. Sci. Technol.
27
(
4
),
045401
(
2016
).
18.
T.
Lukomski
, “
Full-matrix capture with phased shift migration for flaw detection in layered objects with complex geometry
,”
Ultrasonics
70
,
241
247
(
2016
).
19.
C.
Yang
,
K.
Qin
, and
Y.
Li
, “
Real-time ultrasonic imaging for multi-layered objects with synthetic aperture focusing technique
,” in
Proceedings of the 2014 IEEE International Instrumentation and Measurement Technology Conference (I2MTC)
,
Montevideo, Uruguay
(
May 12–15, 2014
), pp.
561
566
.
20.
K.
Qin
,
C.
Yang
, and
F.
Sun
, “
Generalized frequency-domain synthetic aperture focusing technique for ultrasonic imaging of irregularly layered objects
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
61
(
1
),
133
146
(
2014
).
21.
M. H.
Skjelvareid
,
Y.
Birkelund
, and
Y.
Larsen
, “
Synthetic aperture focusing of outwardly directed cylindrical ultrasound scans
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
59
(
11
),
2460
2469
(
2012
).
22.
M. H.
Skjelvareid
,
Y.
Birkelund
, and
Y.
Larsen
, “
Internal pipeline inspection using virtual source synthetic aperture ultrasound imaging
,”
NDT & E Int.
54
,
151
158
(
2013
).
23.
S.
Wu
,
M. H.
Skjelvareid
,
K.
Yang
, and
J.
Chen
, “
Synthetic aperture imaging for multilayer cylindrical object using an exterior rotating transducer
,”
Rev. Sci. Inst.
86
(
8
),
083703
(
2015
).
24.
H.
Jin
,
J.
Chen
,
E.
Wu
, and
K.
Yang
, “
Frequency-domain synthetic aperture focusing for helical ultrasonic imaging
,”
J. Appl. Phys.
121
(
13
),
134901
(
2017
).
25.
P. L.
Stoffa
,
J. T.
Fokkema
,
R. M.
de Luna Freire
, and
W. P.
Kessinger
, “
Split-step Fourier migration
,”
Geophysics
55
(
4
),
410
421
(
1990
).
26.
E. G.
Williams
,
Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography
(
Academic Press
,
New York
,
1999
), pp.
115
182
.
27.
J. F.
Claerbout
,
Imaging the Earth's Interior
(
Blackwell Scientific
,
New York
,
1985
),
p. 398
.
28.
K.
Baik
,
C.
Dudley
, and
P. L.
Marston
, “
Acoustic quasi-holographic images of scattering by vertical cylinders from one-dimensional bistatic scans
,”
J. Acoust. Soc. Am.
130
(
6
),
3838
3851
(
2011
).
29.
D.
Garcia
,
L. L.
Tarnec
,
S.
Muth
,
E.
Montagnon
,
J.
Porée
, and
G.
Cloutier
, “
Stolt's fk migration for plane wave ultrasound imaging
,”
IEEE Trans. Ultrason. Ferroelectr. Freq. Control
60
(
9
),
1853
1867
(
2013
).
30.
F.
Simonetti
,
L.
Huang
, and
N.
Duric
, “
On the spatial sampling of wave fields with circular ring apertures
,”
J. Appl. Phys.
101
(
8
),
083103
(
2007
).
31.
D. S.
Plotnick
,
P. L.
Marston
, and
T. M.
Marston
, “
Fast nearfield to farfield conversion algorithm for circular synthetic aperture sonar
,”
J. Acoust. Soc. Am.
134
(
5
),
4078
(
2013
).
32.
H.
Jin
,
S.
Wu
, and
K.
Yang
, “
A frequency synthetic aperture focusing technique for eccentric circular scanning
,” in
Proceedings of the 2016 IEEE International Ultrasonics Symposium (IUS)
,
Tours, France
(
September 18–21, 2016
), pp.
1
4
.
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