- International Symposium on NDT Contribution to the Infrastructure Safety Systems, 1999 NOV 22-26 Torres, published by UFSM, Santa Maria, RS, Brazil

TABLE OF CONTENTS

Abstract Introduction Distortion Model Algorithm Results Conclusion Acknowledgements References

Abstract

The Synthetic Aperture Focusing Technique (SAFT) has been used to restore ultrasonic images obtained either from B or C scans with focusing distortion. With the use of this technique an improvement of the image resolution can be obtained, without the use of the traditional ultrasonic lenses. This work shows the pratical implementation of SAFT for scan B, by presenting an algorithm and the resulting image. For SAFT to work properly, it is necessary to know accurately the path traveled by the ultrasound from the transducer to target and back again. Therefore a geometrical model of ultrasonic signal and its correlation to adjacent scan A lines are used to restore the image. In order to minimize the execution time of this algorithm, the correlation is calculated only between few lines adjacent to the analyzed line, in a correlation window. The results obtained with our algorithm implemented in C language, is quick and efficient in improving the lateral resolution to the images submitted to it.

Introduction

The advances in modern computer hardware and software applications are making a substantial impact on the analysis and display of NDT data. In this paper, the application of the Synthetic Aperture Focusing Technique (SAFT) has been used to restore ultrasonic images obtained either from B or C scans with focusing distortion. With the use of this technique an improvement of the image resolution can be obtained, without the use of the traditional ultrasonic lenses. The images of both the B or the C scan has a lateral resolution limited by the focus of the ultrasonic transducer. The techniques traditionally used to improve the lateral resolution are using additional lens or using the synthetic focus. The use of lens make the beam more collimated, but introduces a considerable loss in the transmitted signal. The use of the synthetic focus is efficient and does not introduce additional losses, but can only be employed in a digital signal acquisition system.

The synthetic focus is based on the geometrical reflection or ray acoustic model [1-3]. In this model the focus of the ultrasonic transducer is assumed to be a point of constant phase which all the sound rays pass through before diverging in a cone whose angle is determined by the diameter of the transducer and the focal length. If a reflecting target is located beneath the focal point and within the cone, it is a simple matter to calculate the path length and the transit time for a signal traveling along the ray. The width of the cone at a given range corresponds to the aperture width that can be synthesized, and the path length that the signal must travel corresponds to the phase shift seen in the signal for that transducer position. With this information one can construct a corrected data set that incorporates the advantages of the larger transducer aperture.

Fig 1: Transducer beam width on the test block, showing the inspection position x1 and the defect position at x2

Fig 2: Distorted image resulting due to the beam width during a B-scan. The defect is at position (x2,d2).

In Fig. 1 we schematically see the transducer at the point x1 and a wave front just passing the defect zone at the position x2 at distance d2 from the boarder respectively. This transducer characteristics results in an image as shown in Fig. 2 from a single round hole in an iron block of width d.

The resulting broad image from the scanning is due the transducer aperture width, as shown in Fig. 3. Schematically the A-scan signals with the time shift required to focus on a point directly below the transducer at the center-scan position, corresponding to the B-scan of Fig. 2. The wave amplitude normally falls off away from the center but that is not shown in this figure.

The implemented algorithm uses the geometric model to recalculate points from lines in A-scan and thereafter correlate this signals to improve the obtained image. The sections that follows describe the basis and computational procedures and compare the experimental results.

Fig 3: Schematics of A-scan signals which compose the B-scan image of Fig. 2.

Distortion Model

The distortion model due to the transducer aperture cone is based on a geometrical reflection model discussed in [3]. The algorithm works in three dimensions, but only two dimensions are used in this paper. Considering the Fig. 1, the distance d₂ is where an echo from the defect at x₂ appears at x₁. The true distance d₂ can be calculate from the relation:


d3 = [ d22 + (x1 - x2 )2 ]1/2 or in a more generic form,
dn = [ dA2 + (xA - xn )2 ]1/2	(1)

where x_A is the x position of the A-scan line which is being analyzed;

xn is the position of a A-scan line near to the xA line;

dn is the distance between the front block surface and the reflection of the ultrasonic pulse from the position xn ;

dA is the distance from the front block surface and the pulse due to the reflection of the ultrasonic signal obtained at position xA.

The technique known as SAFT use this equation to eliminate or at least minimize the effects of the transducer aperture beam width over an B-scan or C-scan image. To use this technique we need to calculate, for each image line the position where the signal should be inside an adjacent line and thereafter a correlation has to be made. In practice we use a window with a certain number of lines, which fits in the transducer's beam aperture. The figures 4a, 4b and 4c show the corrections as implemented in this work, by using a four line window.

Fig. 4a shows a sequence of A-scans lines or time records of the reflected signals received by the transducer as it moves across the block, and the dotted line shows the effect of the beam width, which is the time shift required to focus on a point directly below the transducer at the center-scan position. Fig. 4b shows the SAFT process for the line at x₁,

a	b	c
Fig 4: Correction process by time shifting of the A-scan lines Fig. 4a shows the A-scan sequence lines with the dotted line showing the curvature due the beam aperture. Fig. 4b shows the SAFT process for line at x1, which presents the echo signal due to the defect at x2. Fig. 4c illustrates the SAFT process for the line at x2 (at the true position) corrected

Which presents the echo signal due to the defect at x₂, together with the position of the two adjacent lines (four line window), corrected in such a manner as if it appears that the defect were originated at x₁. After this correction the correlation between these five lines is made which results in zero. The Fig. 4c illustrate the SAFT for the line at x₂, which presents the corrected signal positions for x₂, and because the defect is as assumed in x₂, the correlation between the five lines is now maximum.

As we have seen, signals from the adjacent positions (consisting of the aperture) are shifted by the appropriate phase and added to the first signal. If the assumption was correct, the summation results in an enhanced response; if wrong, there is a poor correlation or zero.

The correlation process between the lines in the window region adjacent to the line to be corrected is made only after the correction procedure has taken place. This correlation is obtained by the summation over the adjacent lines as follow [4]:

(2)

If m is the total number of adjacent lines (the correlation window width.), to the line A, and k are the different distances from the test piece surface, the corrected resulting line x_r (k) is then calculated according to the equation (2).

Algorithm

The algorithm consists of two parts: first the distortion correction of the points along the A-scan lines is calculated and second the correlation between the analyzed line and the adjacent lines belonging to the correlation window is obtained. Differently from correlation normally used in image processing, this correlation is made in one direction due to the nature of the distortion.

For the description of this algorithm, the following considerations in C language is made: Variables: wid and hig are the width height of the image, imag is the vector where the pixel values corresponding to the B-scan are stored, win stores the window width used in the correlation, sum_prod is the vector where the resulting sums and products from the correlation process are stored, distx is the horizontal distance in pixels between the actual line in the widow and the image line, dif is the difference between the defect point and its false reflection, as calculated by equation (1), A is the traveled distance of the ultrasonic wave in the test block, and B is the distance between two A-scan lines, both in mm.

The summary of the C - like Algorithm is as follows:

// sum_prod vector initialization:

....

for( i=0; i < h ; i++ )

sum_prod[ i ] = 0;

k = (int ) win /2 ;

for ( j = k ; j < wid - k ; j++ )

{

// scanning the adjacent lines of the line which is under process, to this line the index j is
// attributed, and for the adjacent lines the index j1

for ( j1 = j - k ; j1 < j + k ; j1++ )

{

distx = abs ( j - j1 );

for ( i1 = 0 ; i1 < hig ; i1++ )

{

// correction calculation, according to equation (1) for each point in the window

dif_f = sqrt ( pow ( i1 * A, 2 )+ pow( dist * B, 2) ) - (float )( i1 * A );

dif_i = (int ) (dif_f / A );

sum_prod[ i1 ] = ( char ) ( imag [ j1 * wid + i1 - dif_i -

128 * ( char ) (imag [ j * wid + i1 ] - 128 ) + (char) sum_prod[ i1 ];

}

for ( ix =0 ; ix < hig ; ix ++ )

{

sum_prod[ ix ] = (char ) (sum_prod [ ix ] / win) ;

imag [ j * wid + ix ] = ( u_char ) sum_prod [ ix ] +128 ) ;

}

}

} // end of SAFT algorithm.

Results

The implemented algorithm has been applied to B-scans obtained with a sampling frequency of 100 MHz, which gives for an iron test block a sound propagation speed of 5900 m/s. The A value of the algorithm is the sound speed divided by the frequency or 0.059 mm, which gives about 17 samples per mm. The B value considered for this results 0,35 mm which corresponds the resolution of our transducer x-y scanning driving system.

Fig 5: View of the steel test block, with 12 drilled holes - dimensions in mm (not shown in scale)

An example of the A-scan signals obtained from line 380 through line 465 by scanning our the test block from Fig. 5 is shown in Fig. 6. The denser part at the left of this figure corresponds to the first surface and the denser part at right corresponds to the bottom of the block. The central region at Fig. 6 shows the defects due to the 4mm holes, and because the missing focus both holes appears as one denser region, without any definition.

Fig 6: Sequence of A-scans obtained from a region (arround the 4mm holes ) of the test block, from Fig. 5

Fig 7: Image generated by the SAFT algorithm, where the two 4mm holes can now be seen with more detail.

Applying the described algorithm to the scans of Fig. 6 we obtained Fig. 7, where the separation between the two 4 mm holes now can be seen with much more definition. The Fig. 8 shows details of B-scan on the block of Fig.5 before and after the SAFT process. The bottom part of Fig. 8 is the resulting image, in where the drilled holes are better separated then shown in the top image.

Fig 8: Details of the original B-scan image (top ) and after processed with SAFT algorithm (bottom). The scale on the bottom image corresponds to 10 mm.

Conclusion

The surface mapping SAFT program as implemented in this work shows an efficient and quick process, giving a more accurate image of the holes then could be obtained from the raw data. The basic SAFT algorithm is successful in producing correlated A-scans which, given the correct surface coordinates, results in improved resolution, and decreased position errors, for both transversal and longitudinal data. The major difficulty encountered in this work is related to obtain a constant speed A-scan and the correct corresponding surface coordinates. In our case the x, y coordinates were obtained from an adapted "computer mouse" to our coordinate frame, build over a water tank in which the test block were scanned. Nevertheless this work shows that the image enhancement available with SAFT allows to use the flat transducer geometry which is more practical to use, since it can be applied to data in the course of a normal ultrasonic inspection.

Acknowledgment

The experimental work of this paper has been done at the "Program de Pós Graduação em Engenharia de Minas, Metalurgia e de Materiais - PPGEM " under the coordination of professor Dr. Telmo Strohaecher.

References

1. Frederick, J.R. "Ultrasonic Engineering" - John Willey & Sons, Inc. 1965
2. Kino, G.S. "Acoustic Waves: Devices, Imaging, and Analog Signal Processing" - Prentice-Hall, Inc. 1987
3. Johnson, A.J. and Barina, B.A. "The effects of Surface Mapping Corrections with Synthetic-Aperture Focusing Techniques on Ultrasonic Imaging" IEEE Trans Vol. SU- 30 No.5 - 1983
4. Doctor,S.R. Hall,T.E., Reid,L.D. "SAFT - The Evolution of Signal Processing for Ultrasonic Testing" - NDT International, Vol.19 No. 3 - 1986
5. Krautkrämer J. and Krautkrämer H. "Ultrasonic Testing of Materials" - Springer Verlag 1983
6. Gonzalez, R.C. and Woods, R.E. "Digital Image Processing" - Addison Wesley Pub. - 1992.

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