Wavelet Deconvolution before Scanning in Ultrasonic ...
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Wavelet Deconvolution before Scanning in Ultrasonic
Nondestructive Testing
Young-Fo Chang
Institute of Applied Geophysics, National Chung Cheng University, Min-hsiung,
Chia-yi 621, Taiwan, R.O.C.
INSIGHT - Non-Destructive Testing & Condition Monitoring, 2002, V44,
N11, 694-699.
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Wavelet Deconvolution before Scanning in Ultrasonic
Nondestructive Testing
Young-Fo Chang
Institute of Applied Geophysics, National Chung Cheng University, Min-hsiung,
Chia-yi 621, Taiwan, R.O.C.
Abstract
Image resolution in the ultrasonic nondestructive testing (NDT) can be
improved using both hardware techniques and digital signal processing methods. The
hardware techniques must be implemented before scanning, whereas the digital signal
processing methods can be performed before or after scanning. The prefiltering and
postfiltering deconvolution methods are the most commonly used digital signal
processing methods for compressing the wavelet and improving the image resolution.
In this study, a programmable and flexible prefiltering technique is proposed to
enhance the image resolution for the ultrasonic NDT. The responses in the system are
treated as a black box, including not only the transducer but also all apparatus,
couplant, coupling effects, and specimen, for the prefiltering deconvolution. The
special designed input can be calculated and input into the system for
precompensating the system response to obtain a desired output with a compressed
wavelet before scanning. Using this method in ultrasonic NDT experiments, the
vertical resolution of the image can be substantially enhanced and in addition the
horizontal resolution of the image could be improved slightly.
Keywords: deconvolution; digital signal processing; ultrasonic NDT
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I. INTRODUCTION
Image resolution of the ultrasonic nondestructive testing (NDT) can be
improved using various hardware and software techniques [1,2]. The hardware
techniques include using high power and low noise apparatus; as well as broadband,
well damped, narrow beam and focused transducers [2] that can effectively enhance
the image resolution. The software technique considers here is a digital signal
processing method, which can increase the signal to noise ratio (SNR) and compress
the wavelet, thus improving the image resolution.
Some most commonly used digital signal processing methods for improving the
image resolution of ultrasonic NDT are block filtering, migration, and deconvolution.
Block filtering extracts useful signals from the frequency domain [3]. The migration
method can transform the flaw image from its apparent position to the true position
and the resolution of the image can be greatly improved [4,5]. The deconvolution
method can compress the wavelet and improve the flaw sizing accuracy. This method
can be subdivided into the postfiltering technique which generates an estimate of the
target system impulse response, and the prefiltering technique which calculates the
required driving function to generate a desired output [6].
In the postfiltering technique, recorded signals are convolved with a
deconvolution filter. The fast iterative deconvolution method for echographic signals
was proposed for quasi-real time deconvolution [7]. Vollmann had used the Wiener
deconvolution filter to better the B-scan image [8], and the C-scan image can be also
processed with two-dimensional Wiener filter [3]. The signal of interest is
deconvolved with an inverse reference-signal for improving the range resolution [6,
9], and it can also be deconvolved with a simulated transducer response [6]. The
deconvolution method can reduce the transducer blurring effect and improve the
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resolution of the ultrasonic C-scan image [10]. The echoes reflected from the
delaminations in thin composite plates could be enhanced with the aid of the L1 norm
deconvolution [11]. The comparison of deconvolution methods in ultrasonic NDT
was presented in [12, 13].
In the prefiltering technique, the system is convolved with an inverse system
response before scanning. Silk outlined the theory of prefiltering technique by
modifying the driving pulse shape [2]. The spectral division technique is performed
for calculating the driving function to generate a desired output [6]. The axial
resolution of a medical image can be improved by precompensating the electrical
excitation applied to the transducer [14,15]. The traditional prefiltering technique
considers that the dominant factor of the system response is the transducer. Therefore
an inverse transducer response is calculated and used as the driving function to
generate a desired output. But the frequency content of a signal from an impulsive
source is not subject to control and it is influenced by the transducer, the degree of
coupling and the attenuation of material. In many cases, the best SNR is observed
over a limited range of frequencies.
In this study, we consider that not only the transducer response but also all
apparatus, couplant, coupling effects, and specimen can affect the recorded signal.
Thus the system can be regarded as a black box, and no detailed knowledge of the
ultrasonic system is necessary. If the system is linear for the ultrasonic echo used in
the study, the echo recorded by the system can be considered as the result of
convolution the input with the system. According to the convolutional model, the
desired output of the echo with compressed wavelet recorded by the system can be
obtained by inputting a special designed input for precompensating the system
response. When the special designed input is entered into the system and is processed
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with the system, the special designed input can be treated as the deconvolutional filter
and it is convolved with the system, thus the output of the system will be similar to
the desired output. Therefore a better result than the traditional prefiltering technique
can be expected. This technique is performed only once before scanning and the
resolution of the ultrasonic image can be largely improved. Below there is a
description of the deconvolution procedure, and the feasibility of this method is tested
by physical experiments.
II. THEORY
In a noise free environment and a linear system, the system response can be
expressed using the convolutional model (Fig. 1a). In the time domain, the system
response can be expressed as
o(t)=i(t)∗s(t) (1)
where t is time; i(t), s(t) and o(t) are the input, system and output, respectively. The
symbol * is the convolution operator. s(t) is composed of the responses of the system
and can be expressed as
s(t)=w1(t)*w2(t)*‧‧‧* w8(t) (2)
where w1(t), w2(t), w3(t), w4(t), w5(t), w6(t), w7(t) and w8(t) are the responses of
the function generator, source-transducer, the coupling effect between the
source-transducer and specimen, couplant, specimen, the coupling effect between the
receiver-transducer and specimen, receiver-transducer and the digital oscilloscope,
respectively. We do not know every response in w1(t)-w8(t) but assume the combined
response s(t) as a black box. In the frequency domain, according to the convolution
theory [16], they can be expressed as
S(f)=O(f)/I(f) (3)
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where f is frequency; S(f), O(f) and I(f) are the Fourier transforms of the s(t), o(t) and
i(t), respectively. What is the specially designed input, i′(t), that must be delivered to
the system when we hope to obtain a desired output d(t) (Fig. 1b)? In the time domain,
this process can be expressed as
i′(t)*s(t)=d(t) (4 )
In the frequency domain, it is
I′(f)=D(f)/S(f)=D(f)•I(f)/O(f) (5)
where I′(f) and D(f) are the Fourier transforms of the i′(t) and d(t) , respectively. The
special designed input i′(t) in the time domain can be obtained by
i′(t)=IFT(D(f)•I(f)/O(f)) (6)
where IFT indicates the inverse Fourier transform. When i(t)=d(t), equation (6) can be
rewritten as
i′(t)=IFT(I(f)2/O(f)) (7)
The solution becomes unstable as the magnitude of O(f) approaches zero. This may
be circumvented by redefining O(f) as a small, positive threshold when it has a
magnitude less than some preset threshold [6]. We input the i(t) into the system and
measure output o(t) from the system. If the desired output is assumed as i(t), then the
special designed input i′(t) can be calculated via Eq. (7).
III. EXPERIMENTS
1. THEORY TEST
Firstly, we try to verify the feasibility of this theory by a physical experiment
using the double-probe reflection technique. The testing apparatus and the
arrangement of the measurement are shown in Fig. 2. A pair of 2.25 MHz contacted
longitudinal wave transducers (Panametrics V133S) with a diameter of 0.25 inch were
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mounted onto a duralumin specimen of 3 cm thickness using honey as couplant. The
longitudinal wave velocity of the duralumin is 6400 m/s. An arbitrary function
generator (HP 33120A) is used to store the input i(t) and the special designed input
i′(t). The stored signal in the arbitrary function generator is periodically sent out to
excite the source-transducer; meanwhile, the arbitrary function generator send out a
synchronous signal (SYN) to trigger the digital oscilloscope (Tektronix TDS420).
The digital oscilloscope, which surveys and records the signals, and the arbitrary
function generator are controlled by the personal computer using the general purpose
interface bus (GPIB).
A one cycle 2.25 MHz sine wave (Fig. 3a), whose dominant frequency is the
same as the frequency of the transducer, is produced by the arbitrary function
generator to excite the source-transducer. The echo reflected from the bottom of the
specimen and detected by the system is shown in Fig. 3b. When the desired output is
the 2.25 MHz sine wave, the special designed input can be calculated using Eq. (7)
and the result is shown in Fig. 3c. The special designed input is transmitted from
personal computer to the arbitrary function generator to replace the 2.25 MHz sine
wave, and then the reflected echo detected by the system is shown in Fig. 3d. The
observed desired output is quite similar to the 2.25 MHz sine wave although slight
discrepancy does exist between the two signals. As shown in Fig. 3d, the low level
ringing in the signal was induced during calculation of the special designed input
since the limited length signals are used for calculation the special designed input;
thus it is an artifact of the processing.
The experimental results show that this is a practical method when the system is
linear and the system response is a black box. The wavelet can be compressed before
scanning using this deconvolution method. Adopting the compressed wavelet to scan
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the specimen, the resolution of the image will be enhanced.
2. SCANNING TEST
Resolution is defined as the minimum distance between two objects so that one
can recognize that there are two objects. It can be subdivided into vertical and
horizontal resolution [17]. Vertical resolution is the minimum thickness of a thin
crack that the thickness of the flaw can be detected. Horizontal resolution is the
minimum horizontal distance between two cracks so that the two cracks can be
detected.
2.1. THIN CRACK DETECTION
A thin water layer specimen is designed to test the vertical resolution. The
configuration of the specimen and the arrangement of the measurement are shown in
Fig. 4. Two duralumin blocks with a thickness of 3 cm are separated by a thin water
layer and the thickness of the thin water layer changes from 0 to 1 mm with a linear
increment during the experiments. The double-probe reflection technique is used to
detect the thickness of the thin water layer and the longitudinal wave velocity of water
is 1500 m/s. Figs. 5a and b are the A-scan images measured on the specimen using
one cycle 2.25 MHz sine wave and the special designed input to excite the
source-transducer, respectively. The dashed lines in the figure are the theoretical
arrival times of the echoes reflected from the bottom of the thin water layer.
The echoes reflected from the top of the thin water layer can be clearly seen in
Figs. 5a and b, and its arrival time is 9.4 µs. The echoes reflected from the bottom of
thin water layer are buried in the sidelobe of the wavelet and can not be seen since the
wavelet of the echo is too broad, as shown in Fig. 5a, using the 2.25 MHz sine wave
to excite source-transducer. On the other hand, the bottom reflected echoes can be
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seen in Fig. 5b for the 0.4 to 1 mm-thick thin water layers, using the special designed
input to excite the source-transducer. The minimum thickness of a bed in order to
separate distinctly the top and base of the bed is the resolvable limit and it is about 1/4
wavelength [17]. Thus, it is about 0.2 mm in our case. However, the echo reflected
from the bottom of the 0.2 mm-thick thin water layer can not be seen here since it is
weaker than the echo reflected from the top of the thin water layer. The improvement
of the vertical resolution for detecting the thickness of the thin layer (crack) is
verified when using this technique.
2.2. SLIT CRACK DETECTION
A specimen with vertical silt is designed to test the horizontal resolution. The
configuration of the specimen and arrangement of measurement are shown in Fig. 6.
A long duralumin block bonded to two small duralumin blocks separated by an air
gap is used to simulate the vertical silt. Three kinds of slit widths (2, 4 and 6 mm) are
examined. Figs. 7, 8 and 9 are the B-scan images scanned on the specimen for the slits
with the widths of 2, 4 and 6 mm, respectively. In Figs. 7a, 8a and 9a, a one cycle
2.25 MHz sine wave was used to excite the source-transducer; whereas in Figs. 7b, 8b,
and 9b, we used the special designed input to drive the source-transducer. The lines in
these figures are the positions of the slit locations.
When the width of the slit is small, the slit is similar to a point scatter and only a
diffracted-pattern in the image can be seen. In both Figs. 7a and b, the echoes
reflected from the bonding interfaces of the duralumin blocks are very clear across the
images and a point diffracted pattern is superimposed on them. Although the slit in
the images can not be successfully detected since the width of the slit is 2 mm, some
anomalies can be still recognized. The anomalies in Fig. 7a extend from 6 to 18 mm
for the distance and from 30 to 38 mm for the depth, and in Fig. 7b 8-16 mm for
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distance and 30-33 mm for depth. The wavelet has been compressed before scanning
and so the extent of the depth is only 3 mm in Fig. 7b. However the slit can be still
recognized in the images.
Shown in Fig. 8 are the B-scan images for the 4 mm-wide slit. The echoes
reflected from the bonding interfaces of the two duralumin blocks are little weaker
than that reflected from the slit and two diffracted-patterns diffracted from the two top
corners of the slit are superimposed on them. In both Figs. 8a and b, the slits can be
successfully detected. The slit images in Figs. 8a and b extend horizontally 6-18 mm
and 7-17 mm, respectively. The B-scan images for the 6 mm-wide slit are shown in
Fig. 9. The echoes reflected from the slit are stronger than those reflected from the
bonding interfaces of the duralumin blocks, and two diffracted-patterns are
superposed on them. In both Figs. 9a and b the slit can be successfully detected,
although the one in Fig. 9b is clearer than that in Fig. 9a. The slit images in Figs. 9a
and b extend horizontally 5-18 mm and 7-17 mm, respectively.
This technique can not surmount the limitation of the horizontal resolution (Fig.
7). However when using this technique to scan the slit, the vertical resolution of the
image is enhanced, the widths of the slit images are close to the true widths (Figs.
7-9), and the slit image becomes clear (Fig. 9b).
IV. DISCUSSIONS
The performance of this method depends primarily on whether the system is
linear or nonlinear. Fortunately, the system is usually operating under linear
conditions, i.e. if we reduce the input by half then we can get half of the output.
Although the observed desired output (Fig. 3d) is not exactly the same as the desired
output (Fig. 3a), but they are alike especially the mainlobe, indicating that the system
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is almost linear. Therefore, the wavelet can be compressed before scanning and the
vertical resolution of image is substantially improved (Fig. 5). According to this
theory, the sound beam has not been compressed then the horizontal resolution of the
image can be only slightly improved (Figs. 7-9).
The input signal and the desired output are not necessarily the same. If we wish
the desired output to be a spike in order to obtain a very high image resolution, thus a
strong ringing of the observed desired output will be induced during calculation of the
special designed input using the limited data points [18]. The optimum desired output
is a wavelet with a short duration time and the frequency content is similar to the
system response. It is not useful to exceed the frequency limit of the system since no
ultrasonic waves can be excited and recorded outside the system response. A delay of
desired output can provide a better observed desired output [18], so in this study the
desired output is delayed 16 µs (Fig. 3d). The delay time of the observed desired
output could be easily corrected when measuring on a standard specimen of known
thickness.
This technique is programmable and flexible when changing the transducers and
specimen in an operational environment. Since the attenuation of the duralumin is
slight for the echo used in this study, the echoes reflected from the flaws at different
depth will have the same propagation effect, although the propagation distances are
different. Thus they will also have the similar waveforms. If a strong attenuation
material is tested, the propagation effects will be different for the echoes reflected
from the flaws at different depth. Therefore, the system responses are different for
those flaws. In order to use this technique to detect those flaws in the strong
attenuation materials, the time history of the echoes must be divided into several time
gate windows. Assuming that the propagation effects are the same in each time gate
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window, the special designed input can be calculated in order to detect the flaws in
this time date window.
The noise is very low in this study. Therefore, the spectral division technique
used to calculate the special designed input is stable. If the noise is high, the Eq. (1)
becomes
o ( t ) = i ( t ) ∗ s ( t ) + n ( t )
( 8 )
where n(t) is the random noise and the spectral division technique may become
unstable. In addition, other inverse methods [6,12,13], Wiener filter [3] or iterative
deconvolution methods [15,19] can also be used in a noisy environment to calculate
the deconvolution filter for compensating the system response.
V. CONCLUSION
In this study, we consider that the system response (including all apparatus,
transducers, couplant, coupling effects, and specimen) is linear and is a black box.
The spectral division technique was used to calculate the special designed input to
precompensate the system response. Then the special designed input is sent to the
system, which is like a deconvolutional filter and convolutes with the system, so the
output of the system will be similar to the desired output. The observed desired output
has a compressed wavelet, therefore the resolution of the ultrasonic image can be
improved using the output to scan the object. Based on the experimental results, we
can conclude that using this wavelet deconvolution method for the ultrasonic NDT the
vertical resolution of the image can be substantially enhanced, and the horizontal
resolution of the image is improved slightly.
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REFERENCES
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Ltd, 1984.
3. Zhao J, Gaydecki PA, Burdekin FM. Investigation of block filtering and
deconvolution for the improvement of lateral resolution and flaw sizing accuracy in
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Nondestructive Evaluation 2000;19(1):1-10.
5. Chang YF, Ton RC. Kirchhoff migration of ultrasonic images. Materials evaluation
2001;59(3):413-417.
6. Hayward G, Lewis JE. A theoretical approach for inverse filter design in ultrasonic
applications. IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 1989;36(3):356-364.
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echographic signals. Acoustical imaging 1980;10:325-345.
8. Vollmann W. Resolution enhancement of ultrasonic B-scan images by
deconvolution. IEEE Trans. Sonics Ultrason. 1982;SU29:78-83.
9. Carpenter RN, Stepanishen PR. Am improvement in the range resolution of
ultrasonic pulse echo systems by deconvolution. J. Acoust. Soc. Am.
1984;75(4):1084-1091.
10. Cheng SW, Chao MK. Resolution improvement of ultrasonic C-scan images by
deconvolution using the monostatic point-reflector spreading function (MPSF) of the
transducer. NDT & E International 1996;29(5):293-300.
11. Kazys R, Svilainis L. Ultrasonic detection and characterization of delaminations in
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thin composite plates using signal processing techniques. Ultrasonics 1997;35:367-383.
12. Chen H, Hsu WL, Sin SK. A comparison of wavelet deconvolution techniques for
ultrasonic NDT. International Conference on Acoustics, Speech, and Signal Processing
1988;2:867-870.
13. Sin SK, Chen CH. A comparison of deconvolution techniques for ultrasonic
nondestructive evaluation of materials. IEEE Trans. Image Processing 1992;1(1):3-10.
14. Salazar J, Turo A, Espinosa G, Garcia M. A theoretical approach for short pulse
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edition, New Jersey: Prentice Hall, 1999, p60.
17. Sheriff RE. Seismic stratigraphy. Boston: International human resources
development corporation, 1980.
18. Robinson EA, Treitel S. Geophysical signal analysis. Prentice-Hall, 1980.
19. Bennia A, Riad SM. An optimization technique for iterative frequency-domain
deconvolution. IEEE Trans. Instrumentation Measurement 1990;39(2):358-362.
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FIGURE CAPTIONS
Fig. 1 Configuration of calculation the deconvolutional filter before scanning. (a)
Input, i(t), is transmitted to the system, s(t), and the output, o(t), outputted
from the system. (b) What is the special designed input, i′(t), if we hope to
obtain the desired output, d(t),?
Fig. 2 Testing apparatus and the measurement arrangement used in this study.
Fig. 3 Signals used, observed and calculated in the experiments. (a) the input and
desired output signal, one cycle 2.25 MHz sine wave. (b) the observed signal
reflected from the bottom of the specimen. (c) the special designed input (d)
observed desired output reflected from the bottom of the specimen.
Fig. 4 Configuration of a thin water layer specimen. Six kinds of thickness of the
thin water layers (0, 0.2, 0.4, 0.6, 0.8 and 1 mm) are tested.
Fig. 5 A-scan images for the thin water layer specimen, using (a) one cycle 2.25
MHz sine wave, (b) special designed input to excite the source-transducer.
Fig. 6 Configuration of a vertical silt specimen. Three kinds of width of the slits (2, 4
and 6 mm) are tested.
Fig. 7 B-scan images for 2 mm width slit, using (a) one cycle 2.25 MHz sine wave,
(b) special designed input to excite the source-transducer.
Fig. 8 B-scan images for 4 mm width slit, using (a) one cycle 2.25 MHz sine wave,
(b) special designed input to excite the source-transducer.
Fig. 9 B-scan images for 6 mm width slit, using (a) one cycle 2.25 MHz sine wave,
(b) special designed input to excite the source-transducer.
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Input System Output i(t) s(t) o(t)
(a)
Input(?) System Desired output
i′(t) s(t) d(t)
(b)
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B
)
Personal computer (486)
Arbitrary function generator (HP 33120A)
Digital oscilloscope (Tektronix TDS420)
Speci
Source-transducer (Panametrics A133S
Receiver-transducer (Panametrics A133S)
GPI
SYN
Ultrasound
men
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-1 0 1 2Time (micro sec.)
Input signal
Observed signal
0 10 20 30 4Time (micro sec.)
0
Special designed input
22 24 26 28 30Travel time (micro sec.)
Observed desired output
(a) (c)
(d)9 10 11 12 13
Travel time (micro sec.)(b)
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Duralumin
Duralumin
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unit: mm
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Water (thickness=0, 0.2, 0.4, 0.6, 0.8, 1)
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9 10 11 12Travel time (micro sec.)
1 mm
0.8 mm
0.6 mm
0.4 mm
0.2 mm
0. mm
Thickness (water)
9 9.5 10 10.5 11 1Travel time (micro sec.)
1.5
1 mm
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0.6 mm
0.4 mm
0.2 mm
0. mm
Thickness (water)
(a) (b)
19
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unit: mm
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Receiver-transducerSource-transducerScanning
Duralumin DuraluminSlit (width=2,4,6)
20
0 5 10 15 20
Distance (mm)
-40
-35
-30D
epth
(mm
)
(a) (b)0 5 10 15 20
Distance (mm)
-40
-35
-30
Dep
th (m
m)
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(a)0 5 10 15 20
Distance (mm)
-40
-35
-30D
epth
(mm
)
(b)0 5 10 15 20
Distance (mm)
-40
-35
-30
Dep
th (m
m)
22
0 5 10 15 20
Distance (mm)
-40
-35
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Dep
th (m
m)
(a)0 5 10 15 20
Distance (mm)
-40
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epth
(mm
)
(b)
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