Imaging Hilbert Transformed Ultrasonic Data

16 Pages·2003·0.14 MB·English

Imaging Hilbert Transformed Ultrasonic Data
Young-Fo Chang and Shih-Chang Chen

Institute of Applied Geophysics, Institute of seismology, National Chung Cheng
University, Min-hsiung, Chia-yi 621, Taiwan, R.O.C.

Corresponding author: Young-Fo Chang
Tel: [phone] Ext. 6398
Fax: [phone]
E-mail: [email protected]

Research in Nondestructive Evaluation, V13, N2, 97-104, 2001.
1
Imaging Hilbert Transformed Ultrasonic Data
Young-Fo Chang and Shih-Chang Chen
Institute of Applied Geophysics, Institute of seismology, National Chung Cheng
University, Min-hsiung, Chia-yi 621, Taiwan, R.O.C.

Abstract
Automatic or semi-automatic ultrasonic nondestructive evaluation systems
usually scan objects for defects by B-scan or C-scan method. B-scan or C-scan images
are used to evaluate the quality of the object. Complex ultrasonic images can be
quickly and easily produced using Hilbert transform method. Simultaneous real time
displays of the complex and C-scan images is also possible. Some characteristics of
the echoes reflected from the defects do not show up clearly in C-scan image but can
be easily observed in the complex ultrasonic images.
Two specimens, one with a blind hole and the other with 16 blind holes were
scanned. The C-scan image and complex images were displayed simultaneously in
order to compare the resolution of the images. The experimental results showed that
the attributes of instantaneous amplitude can enhance the weak events but the
resolution of the image has apparently not been improved. The advantage of the
instantaneous phase and instantaneous frequency attributes are that they are very
2
sensitive to the boundaries of the holes. Though the images may look noisy they
really offer an opportunity to show the holes that C-scan image can not.

Introduction
Because of its flexibility, accuracy and ability to detect small defects, the
ultrasonic nondestructive evaluation method (NDE) is one of the most popular
nondestructive testing methods [1]. The ultrasonic images can be constructed by using
B-scan or C-scan techniques. B-scan is the very commonly used method, in which the
amplitudes of time history are converted to color or gray scales and they are displayed
side by side along the scanning direction. The conventional C-scan image depends on
amplitude of the signal in a gate window exceeding a particular threshold. The images
are usually processed and displayed in time domain. The location and size of the
defect may be shown in image and the image resolution depends on the hardware and
software used in the scanning. However, some low amplitude signal reflected from
the defects may be missing.
The image resolution can be improved by using small, narrow beam, high
frequency transducers. It also can be achieved by using the digital signal processing
methods that reduce the noise and enhance the useful signals. The most commonly
used digital signal processing methods are the blocking filter, which extracts the used
signals from the frequency domain [2], migration method, which moves the crack
image from its apparent position to true position and improves the image resolution
[3], and deconvolution method, which minimizes the effects of beam spreading [4-6].
Hilbert transform is widely used in digital signal processing [7]. It is especially
useful in designing the blocking filter [8]. The complex traces of the seismic waves
3
are used in stratigraphic interpretation and in structural mapping of the low-amplitude
events [9, 10]. The ultrasonic velocity of the graphite, which has heterogeneous
structure and high attenuation of the ultrasonic waves, can be measured by Hilbert
transform method [11]. The accuracy of the velocity measurement for the examined
object can be improved using Hilbert transform method for processing of laser
Doppler vibrometer signals [12]. The arbitrarily shaped objects in the optical image
can be enhanced two-dimensionally with the radial Hilbert transform technique [13].
In this study, C-scans were made on the specimens with blind holes in them.
Hilbert transform was used to obtain complex ultrasonic echoes and to display the
images with different instantaneous attributes. The resolutions of the images are
compared with C-scan image.

Theory
The ultrasonic echoes we detected are the real part of the complex signals. The
imaginary part of the complex signals can be obtained using Hilbert transform method
on the real part. Some of the echoes’ characteristics may be seen in the complex
domain more easily and clearly than in the real part domain.
The echo scanning on a specimen is a real time series x (n) and the imaginary
r
part x (n) is the quadrature, which is a 90-degree phase-shifted version of the real
i
part and can be obtained by Hilbert transform [14].
x (n) = H(x (n)) (1)
i r
Where H is Hilbert transform and the operator of Hilbert transform in frequency
4
domain is,
−i, f > 0
{
H(f) = (2)
i, f < 0
The x (n) and x (n) form a Hilbert transform pair, thus the complex echo
r i
x(n) is written as,
x(n) = x (n)+ix (n) (3)
r i
The instantaneous amplitude A(n) , instantaneous phase θ(n) and
instantaneous frequency w(n) are:
A(n) = (x2(n)+ x2(n))1/2 (4)
r i
θ(n) = tan−1(x (n) x (n)) (5)
i r
dθ(n)
w(n) = (6)
dn
The image of the instantaneous amplitude can also be constructed as C-scan
image does and the maximum attributes exceeding a particular threshold in the instant
time gate window are found. The instantaneous phase and frequency may have a high
degree of variation. Therefore, the instantaneous phase and frequency are smoothed in
time and the images are displayed at a given instant time.

Apparatus
A single probe pulse echo technique was adapted. The apparatus is commonly
used in nondestructive evaluation. A Panametrics of 20 MHz contact longitudinal
5
wave transducer (V116) with diameter 0.125 inch was employed in the experiments.
The pulser/receiver (Panametrics 5058PR) operating in the pulse-echo mode was used
to transmit and receive the electrical signal. A digital oscilloscope (Tektronix 11402A)
converts the analog signals to digital signals. A personal computer reads the digital
signals from the oscilloscope and processes the signals. The scans were implemented
on the top surface of the specimens using honey as couplant. Since no automatic tools
were used in this research, the measurements were carried out manually. The spacial
sampling rate was 1 mm. The configuration of the apparatus used is shown in Fig. 1.

Experimental Results
1. Specimen with one blind hole
A 3cm × 5cm × 5cm Duralumin block with one 3 mm diameter cylindrical blind
hole was scanned. The configuration of the specimen is shown in Fig. 2. The extent of
the scan is 15 mm. The C-scan image is shown in Fig. 3a and the images of the
instantaneous amplitude, phase and frequency shown in Figs. 3b, c and d, respectively.
All the images were displayed by a gray scale. In the instantaneous amplitude and
frequency images, the black and white express respectively the maximum and
minimum value of the attributes and the change from black to white is linear. In the
instantaneous phase image, the maximum and minimum phases are expressed in white
6
and the middle of the phase, between the maximum and minimum phases, is
expressed in black.
The flaw in C-scan image (Fig. 3a) is blurred as the frequency content of
reflected echoes is not broad enough, the beam-width is not very narrow, the flaw and
transducer are of the same size, and also the experiment has some errors. Since the
instantaneous amplitude measures the reflectivity strength, the weak signals in the
instantaneous amplitude image (Fig. 3b) can be enhanced. Therefore, the hole in
instantaneous amplitude image is larger than that in C-scan image, but the resolution
of the instantaneous amplitude image is apparently not improved. The instantaneous
phase image (Fig. 3c) shows a very clear boundary of the hole because it is a
measurement of the continuity of events on a C-scan image. Consequently, the
discontinuity boundary in the C-scan image is enhanced. The hole in the
instantaneous frequency image (Fig. 3d) looks like a cross 3 mm in height and 3 mm
in width. The step size of the scan is 1mm. So the area of the cross is where the center
of the transducer can be located above the hole. The instantaneous frequency is the
estimation of the temporal rate change of the instantaneous phase. Therefore, the
boundary of the hole can be seen more realistically.
2. Specimen with 16 blind holes
The configuration of the specimen with 16 blind holes is shown in Fig. 4. The
7
extent of scan is 35 mm. The C-scan image, the instantaneous amplitude, phase and
frequency images are shown in Figs. 5a, b, c and d, respectively. The crosses in the
figures are the positions of the centers of the hole.
Since the image is blurred (Fig. 5a), it is not easy to discriminate all the holes in
the figure, especially when the distances between the holes are small. Although the
weak events have been enhanced in the instantaneous amplitude image (Fig. 5b), the
resolution of the image has apparently not been approved. The instantaneous phase is
very sensitive to the discontinuity boundary of the flaws. Therefore, the boundary of
the holes in the instantaneous phase image (Fig. 5c) can be observed as black or white
area. The instantaneous frequency image (Fig. 5d) also shows holes as black or white
area except for the hole located at the left-bottom of the specimen. The variations of
the instantaneous phase and instantaneous frequency are very high. Thus, the images
may look noisy but they provide an opportunity to show the flaws that C-scan image
can not.

Discussion and conclusions
The calculation of the complex ultrasonic images can be easily and quickly
implemented by a personal computer using the Fast Fourier Transform algorithm. The
complex ultrasonic images may be shown at real time as C-scan image of the
8
automatic ultrasonic NDT scan system.
Not all the defects in the object can be seen in the complex images but some of
the defects which are not easily discriminated in the C-scan image can be observed
clearly in the complex images. Thus, C-scan image and the complex images are
complementary. If the ultrasonic NDT apparatus is equipped with a complex image
mode, then the defects in the object may be evaluated more correctly.
9
Reference
1. J. Blitz, and G. Simpson. Ultrasonic methods of nondestructive testing, p. 264.
Chapman & Hall, London (1996)
2. J. Zhao, P.A. Gaydecki, and F.M. Burdekin. Ultrasonics 33:187 (1995)
3. Y.F. Chang, and C.C. Chern. J. of Nondestructive Evaluation 19:1 (2000)
4. W. Vollmann. IEEE Trans. Sonics Ultras. SU29 2:78 (1982)
5. S.W. Cheng, and M.K. Chao. NDT & E International 29:293 (1996)
6. R. Kazys, and L. Svilainis. Ultrasonics 35:367 (1997)
7. S.L. Hahn, Hilbert transforms in signal processing, p. 442. Artech House, Boston
(1996)
8. A.V. Oppenheim, and R.W. Schafer. Discrete-time signal processing 2nd ed., p.
870. Prentice-Hall, New Jersey (1998)
9. M.T. Taner, F. Koehler, and R.E. Sheriff. Geophysics 44:1041 (1979)
10. O. Yilmaz. Seismic Data Processing, p. 526. Society of Exploration
Geophysicists, Tulsa (1987)
11. R.E. Guerjouma, A. Mouchtachi, Y. Jayet, and J.C. Baboux. Proceedings of the
IEEE Ultrasonics Symposium 829 (1992)
12. V.A. Grechikhin, and B.S. Rinkevichius. Optics and Lasers in Engineering
30:151 (1998)
13. J.A. Davis, D.E. McNamara, and D.M. Cottrell. Optics Letters 25:99 (2000)
14. R.N. Bracewell. The Fourier transform and its applications 2nd ed., p.474.
McGraw-Hill, New York (1986)
10