TABLE OF CONTENTS

Abstract Introduction Theory of method Experimental system Result and conclusion Acknowledgements References

Abstract

The Synthetic Aperture Focusing Technique (SAFT) has been used for ultrasonic imaging in non-destructive testing (NDT) of materials as well as in the radar field [1]. For the cases where frequency of test is very low (below 100KHz) normally the transducers do not have a broadband frequency response; this causes the wide ringing in time domain. Inspecting high attenuation material such as concrete and wood need very low frequency ultrasonic wave. This work concerns a correlation method for calculating image of flaw. In addition, a simplified method is proposed to reduce the calculations. Using a water tank containing a reflector as flaw tests this method. It is concluded that this method successfully recognises the flaw.

Introduction

SAFT is a digital signal processing (DSP) method for ultrasonic testing. It provides an accurate measurement of the spatial location and extent of flaw contained in objects. There is two systems in SAFT based on number of transducers were used for transmitting and receiving. In conventional SAFT pulse echo system is used, which is defined as the use of a single transducers for both source and receiver scanning [2]. Multi-SAFT is a system in which separate transducer for transmitting and receiving is used [3]. Fig 1 shows the diagram, which is, used for Multi-SAFT the other name for this scheme is pitch catch method. In other aspect SAFT can be in time domain or transform domain, such as frequency domain. The basic SAFT formula for this entire category is as follow:

(1)

Where I[x,y,z] is the pressure of sound which reflected or scattered by point (x,y,z), N is the number of transducers, r_i is the distance from transmitter to point (x,y,z) and from this point to ith receiver and c is the velocity of ultrasound in media.

Fig 1: Pitch catch method

In any method conventional or multi SAFT the measured signal by different receiver must be shifted and added to each other. The result is good if the source produce a sharp wave, which is broadband in frequency domain and as a result is very narrow in time domain. It is an ideal situation and cannot be achieved in real world. For example ringing time for very high frequency ultrasonic transducer, about 80 MHz with 160 MHz bandwidth is, at least, 300ns. Where as for very low frequency probes, about 100KHz, the best transducer which is built has, at least, 100 µs ringing time.
In this paper, a correlation method of the SAFT algorithm is introduced. In addition an innovation calculating method is discussed which reduce the calculation to less than 0.73% of using the introduced method directly. In this method we introduce a correlation matrix which has three dimension, i.e. x n x d, where is the maximum delay time, n is the number of receiving places in each scanning line and d is equal to the number of scanning line. This matrix is calculated before starting to construct image by using SAFT. This is the key, which make the calculation reduce. This method can be used for any testing system, which used SAFT algorithm for constructing the image in 2 or 3 dimensions.

Theory of Method

In study of signals and systems cross-correlation function between two signals, x(n) and y(n) is defined as follow:

(2)

And auto-correlation function is:

(3)

The signal x (t) is maximally correlated (i.e. similar) with itself when x(n+t)=x(n) [4]. By comparing equation 2 and 3 we can say, the signal y(t) is maximally correlated (i.e. similar) with x (n+t) when y(n)=x(n+t).

Because of transducer ringing, the equation one must be write as follow:

(4)

Where I_x,y,z(n) is the time series which reflected and scattered by point (x,y,z), N is the number of receiver, _i is equal r_i/c and X_i(n+_i) is received signal by ith transducer from point (x,y,z).

(Hint: For more convenience we show I_x,y,z(n) by I(n)).

Assume the time series which shows the ringing of ultrasonic transmitter is y(n), then cross-correlation between y(n) and I(n) at time t=0 can show a measurable amount of reflected and scattered ultrasonic wave by point (x,y,z). The t=0 is considered because the flaw may be in any places. The formula can be written as follow:

(5)

By considering equation 4 it can be as follow:

(6 - a)

Or

(6 - b)

By comparing right hand side 6-b with 2 the following equation is the result:

(7)

This is the main equation, which is used in this work.

Correlation Matrix: Equation 7 shows for measuring ultrasonic reflected and scattered pressure in any point (x,y,z) the cross correlation between the transmitted signal and received signal at any receiving point at _i must be calculated and then summing all of them.
The furthest place between transmitter point (x,y,z) and from this point to the receiving point can be find. It is obvious it can not be more than the length of time series X_i(n) when the length convert to number of sampled data.
A three dimensional matrix in which any i,j,k element shows the cross-correlation between y(n) and the received signal by jth receiver in kth scan line at time equal i is calculated. For showing the strength of this method in reducing the calculation, let consider an example. For calculating a 200x150 images when the time series of measured data has length of 650 sample there is 650x200x150x6x9=1.053x10⁹ add operation. The numbers in this formula are, the length of time series, x, y dimension of image, number of scan line and number of receiving point in any line, respectively.
If the correlation matrix is calculated in advance 650x650x6x9=22815000 add operations is needed and after that only 200x150=90000 add operation is necessary for calculating a 2D image. Consequently all necessary add operations are 22905000. By comparing this two number we can see the last operation is less than 2.2% of previous one.

Experimental System

To examine the correlation method in the previous section an experimental system as shown in figure one is stabilised.

Fig 1: Experimental system

In this system following devices are used:

1-	A pulser
2-	A pre amplifier
3-	An analyser
4-	Two transducers
5-	A computer
6-	A scanner
7-	A thank of water

The data is collected from one surface. Choosing sampling frequency and number of sampling are important factors in collecting data in proper manner. Shannon's law states the lower band of sampling frequency. In this experiment because the nominal frequency of probes are 95 kHz, the sampling frequency must be more than 190KHz. Sampling frequency influences the lateral and depth resolution. If f_s be sampling frequency and c be the ultrasound wave velocity then l=c/f_s shows the distance that ultrasound travels between to adjacent point. In this experiment it is 2MHz. Number of samples depending on the system which is under test. For avoiding the effect of back wall echo the time duration, in which sampling is in process must be less than the time, which is necessary for travelling through the media, and reflected from back wall. This time is 360µs in here. When f_s=2MHz is chosen the sampling period is 0.5µs which means 720 samples can be collected before back wall echo become appear. For using correlation method an exact pattern of transducer ringing is needed. Fig 2 shows such pattern for the system, which is used in this experiment.

Fig 2: Transducer's ringing pattern

In fig. 3 one recorded data is shown. There are two areas in data. Area one shows the area in which reflection can be exist from any difference in impedance in media. The starting point of area two shows the starting point of signal, which is reflected, from back wall. The data in area two can not be used for reconstructing image because they are redundancy data or they are from back wall.

Fig 3: Recorded data in one point

Result and conclusion

Fig 4: Reconstructing flaw by.

Fig 5: Reconstructing two flaws.

In this paper a theoretical description of a new time domain SAFT method and a method for reducing calculation has been presented. The method, which is based on the correlation of time series analysis, allows data collection over 2-D aperture to be found into a 3-D representation of ultrasonic reflecting and scattering.
Experimental results have been present for the case of Multi-SAFT in which separate transmitter and receiver are used. If the ringing time of transducer is low not only this algorithm works but also the algorithm can be faster, because only limited number of any time series can be considered for calculating cross-correlation.
It is obvious if ringing time of transducer be more than reflecting time from flaw pulse echo mode can not be used. Otherwise in conventional SAFT which used pulse echo this new method can be used as well. For showing the strength of this algorithm one collection of data which is used in other work [5] are used in here for reconstructing two different flaws, Which are a rectangle 20x23x3 mm and a disk with 13mm diameter and 3mm thickness they are in 4 cm distance from each other. Fig 5 shows the result of reconstructing these two flaws.
During collecting data it was found that the delay time is minimum when receiver transducer passing over the flaw in each scanning line. This can be used for estimating the place of flaw. The result of experiment for same rectangle, when pitch catch method for collecting data is used is shown in Fig.4.
Theoretically this algorithm can be used for reconstructing 3D images.

Acknowledgements

I would like to express my thanks to my supervisor, Dr.P.A.Gaydecki for his advice and encouragement throughout my research.
I would like also to express my thanks to my sponsor, Ministry of Culture and Higher Education in Islamic Republic of IRAN for their financial support and for giving me the chance to pursue my studies in the United Kingdom.

References

1. L. J Busee, Three Dimensional Imaging Using Frequency Domain Synthetic Aperture Focusing Technique, IEEE Trans. on UFFC Vol.30, No. 2, March 1992
2. S.R.Doctor, SAFT the Evolution of a Signal Processing Technique for ultrasonic testing, NDT International Vol. 19 No. 3 June 1986
3. Machteld de Kroon, Peter-Paul van't Veen, Hugo Vos, Multi SAFT: A Flexible Method for Defect Characterisation, NDTnet 1. Jan 1997
4. Fred J.Talor Principles of signal and systems, McGRAW-Hill, 1994
5. H.T.Shandiz and Dr. P.A.Gaydescki, A New SAFT Method in Ultrasonic Imaging at Very Low Frequency by Using Pulse Echo Method

© NDT.net - info@ndt.net

| Top |