wavelet deconvolution before scanning in ultrasonic

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.

0

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

1

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

3

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)

4

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

5

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

6

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

7

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

8

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

9

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.

11

REFERENCES

1. Kuttruff H. Ultrasonics fundamentals and applications. London: Elsevier applied

science, 1991.

2. Silk MG. Ultrasonic transducers for nondestructive testing. Bristol: Adam Hilger

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

ultrasonic testing. Ultrasonics 1995;33(3):187-194.

4. Chang YF, Chern CC. Frequency-wavenumber migration of ultrasonic data. J. of

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.

7. Herment A, Demoment G, Vaysse M. Algorithm for on line deconvolution of

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

generation using the double-pulse excitation. IEEE Instrumentation and Measurement

Technology Conference 1996:394-398.

15. Salazar J, Turo A, Chavez A, Ortega JA, Garcia MJ. Deconvolution problem to

produce ultrasonic short pulses. IEE Proc. Sci. Meas. Technol. 1998;145(6):317-320.

16. Oppenheim V, Schafer RW, Buck JR. Discrete-time signal processing. Second

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.





14

Input System Output i(t) s(t) o(t)

(a)

Input(?) System Desired output

i′(t) s(t) d(t)

(b)

15

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

16

-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)

17

Duralumin

Duralumin

��

30

30

unit: mm

�� Receiver-transducerSource-transducer

Water (thickness=0, 0.2, 0.4, 0.6, 0.8, 1)

18

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

0.8 mm

0.6 mm

0.4 mm

0.2 mm

0. mm

Thickness (water)

(a) (b)

19

Duralumin

��

30

unit: mm

��

30

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)

21

(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

-30

Dep

th (m

m)

(a)0 5 10 15 20

Distance (mm)

-40

-35

-30D

epth

(mm

)

(b)

23

wavelet deconvolution before scanning in ultrasonic

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