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Improved ultrasonic image generation through tomographic image fusion
Ultrasonics 37 (1999) 433–443 www.elsevier.nl/locate/ultras
Improved ultrasonic image generation through tomographic image fusion I.D. Hall *, A. McNab, G. Hayward Ultrasonic Research Group, Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1WX, UK Received 1 February 1998
Abstract Techniques for the generation of quantitative ultrasonic images in non-destructive testing have generally involved a substantial cost in terms of data storage and computational time, and thus have found limited application. Preference has therefore been given to the more straightforward imaging methods, such as main beam projection, that detect the presence of defects and provide a limited flaw sizing capability. The relatively small number of flaws requiring detailed examination, coupled with substantial increases in available data storage and computational power, has made it possible to use a number of straightforward tomographic reconstruction methods to produce images of flaws contained within the material under examination. These can then be fused together into a single image from which more accurate measurements of flaw size, shape and orientation can be made. The three tomographic methods that have been implemented in this work are reflection tomography, time-of-flight diffraction tomography and transmission tomography. Selection of images used in the fusion process depends on the nature of the flaw, as each of these methods identifies different characteristics of the flaw shape. The reconstruction methods have been used to generate images from a variety of flaws contained within aluminum cylinders, some or all of the images being fused to produce the final flaw image. Time domain measurements used in the reconstruction were then applied to simulate the application of multi-element arrays for data acquisition and the subsequent tomographic images evaluated. © 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Fuzzy logic; Image fusion; NDT; Tomography
1. Introduction Tomographic techniques have been used widely in biomedical [11] and seismic [8] applications, but until relatively recently, these techniques have been too expensive, in terms of computational power and data storage, for widespread application to non-destructive testing (NDT ). Two of the most widely used defect imaging methods in ultrasonic NDT are main beam projection and SAFT (synthetic aperture focusing technique). Main beam projection is one of the most basic imaging methods currently in use. Signals from each A-scan are simply projected onto a 2-D plane along a line starting from the transmitter position and following the central probe axis. Since the beam is not perfectly focused, but has a finite beam spread, targets in the far field become distorted. Another drawback is that a target detected by the edge of the spreading beam will be incorrectly * Corresponding author. Fax: +44-141-552-2487. E-mail address: [email protected] (I.D. Hall )
positioned along the central beam at that position, for example a point reflector will become an arc, and specular reflectors appear oversized. SAFT is a technique that uses A-scan data to reconstruct defect images. For each transmitter location, every pixel in the image is provisionally considered a possible reflector position. All echoes with transit times corresponding to the distance from any particular transmitter position to each separate pixel are added up, having equal phase only if they are genuine echoes from a reflector in this pixel [4]. The drawbacks of using this imaging method are that the reconstruction time is often long, especially when the method is extended to any data acquisition set-up more complex than pulse echo. Available computing resources have increased significantly in recent years and have therefore ceased to have the same influence on the choice of NDT technique employed for defect characterization. The generation of tomographic images for NDT applications is fundamentally different from that for medical and seismic applications; this is mainly due to the nature of the objects
0041-624X/99/$ – see front matter © 1999 Published by Elsevier Science B.V. All rights reserved. PII: S0 0 4 1 -6 2 4 X ( 9 9 ) 0 0 01 5 - 3
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under examination. Engineering components can generally be considered isotropic and homogeneous, which cannot be assumed for either medical or seismic applications. In addition, there is often a large acoustic mismatch between the specimen under test and the defect, and thus little or no ultrasound can be transmitted through the defect, the amount of sound transmitted depending on the defect type and orientation. These factors contribute to the selection of alternative imaging methods for NDT applications. In this work, a number of elementary tomographic methods have been chosen, and a selection of the reconstructed images fused together to obtain a more representative image of the defect under examination. The tomographic methods selected to permit a number of transmit and receive probe combinations are reflection tomography, time-of-flight diffraction tomography and transmission tomography. These methods differ in their computational complexity and the quality of the images that have been reconstructed. The pulse echo reflection and the transmission reconstruction algorithms are not very computationally intensive as they involve backprojection of ultrasonic data along arcs and sections of the image, respectively, which is not computationally intensive to implement. The time-of-flight diffraction and pitch catch reflection reconstruction methods require the backprojection of the data over elliptical paths and are therefore more computationally intensive. In addition, the time-of-flight diffraction reconstruction algorithm utilizes a more complex system of transmit and receive locations when compared to the other reconstruction algorithms, thus adding to the computational complexity. For this reason, the time-of-flight diffraction method is restricted to only a small number of transmitter locations in order to obtain an acceptable balance between image quality and reconstruction time. For the other methods, the reconstruction time and image quality are deemed acceptable for the amount of data used. The methodology of reconstructing a number of simple tomographic images was chosen over the development of a single more complex reconstruction algorithm, using all of the acquired data to maintain theoretical simplicity, leading to lower computational requirements and greater flexibility for the user. The fusion process is governed primarily by the nature of the defect under examination. For example, if the flaw is planar (e.g., a crack), then the reflection and time-of-flight diffraction reconstruction methods will give the position of the defect end-points; with the addition of the transmission image, it becomes possible to resolve any ambiguity about the defect type, i.e., it can be determined whether the defect is a single planar defect or two point reflectors. If the nature of the defect is unknown, then the individual tomographic images reconstructed can be utilized to obtain sufficient infor-
mation on the defect nature for the fusion process to be completed satisfactorily. In this paper, the tomographic methods used for image reconstruction are explained briefly. The reflection and time-of-flight diffraction methods utilize the timeof-flight of the ultrasonic pulses reflected or diffracted from the defect to reconstruct images of the crosssectional reflectivity function, whereas the transmission tomography method uses the shadow cast by the flaw to generate defect images. An outline of the fuzzy logic method used for fusion of the reconstructed images is also presented. In order to validate the chosen imaging approach, experimental time domain data are obtained from aluminum cylinders containing simulated defects. The defect images reconstructed from these data and the fused images are used to demonstrate the performance of the tomographic image fusion approach to defect imaging.
2. Tomographic reconstruction 2.1. Reflection This is the most common and widely used method of generating tomographic images in NDT [12] and is suitable for obtaining images from a wide variety of defect types. Reflection tomography employs ultrasonic pulses to excite echoes from the boundaries of flaws contained in the cross-section of the object field, illuminated in sequence by a number of ultrasonic beams. The beams may come from a variety of sources, a single transducer, or a pair of transducers, depending on the user requirements. A-scan data are then collected and used to reconstruct a pseudo-image of the cross-sectional reflectivity function. In the present case, two methods for data collection have been considered, pulse-echo (a single transducer for transmit and receive) and pitchcatch (two transducers; one for transmission and the other for reception). Both of these methods are applicable to data acquisition using multi-element arrays. The pulse echo [1] case is illustrated in Fig. 1, whereby an ultrasonic transducer placed in contact with the object under test at position w and transmits a wavefront c that diverges in the object with an angle, a, illuminating the test specimen as shown in the figure. The output from the transducer is an A-scan (detected voltage as a function of time). The measured delay time, corresponding to the time taken for the ultrasonic pulse to travel from the transmitter to the defect and back to the receiver, can be used to obtain spatial distance information according to q=tc/2, where q is the distance between the reflector and the transmitter, t is the elapsed time, and c is the sound velocity in the material. One projection value is the composite sum of all contributions from reflecting objects situated on an arc,
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locations are utilized, then a similar approach to image reconstruction can be employed, with the circular arcs being replaced by ellipsoids. 2.2. Time-of-flight diffraction tomography
Fig. 1. Data collection model for pulse echo reflection tomography. A single transducer at a number of positions, w , transmits a beam of c ultrasound into the test specimen that diverges at an angle, a. Any defects contained within the test specimen reflect energy back to the transducer; these reflection data are then backprojected along circular paths to reconstruct a defect image.
whose radius corresponds to the echo delay time, and whose center is located at the transducer position. The measured projections are then backprojected over the ray paths with projection values measured from a different number of transducer positions being summed such that the arc intersections define the reconstructed object. The pitch catch method [2] uses a pair of scanned transducers, with a fixed separation, held in contact with the object, one for transmission and the other for reception. Thus, the time of flight obtained from the A-scan represents the time of flight from the source to the receiver, via a reflector (the defect). The time of flight defines an ellipse as opposed to an arc in the pulse echo configuration; the foci of the ellipses are situated at the source and receiver locations, as shown in Fig. 2. As described previously, if multiple source and receive
Fig. 2. Data collection model for pitch-catch reflection tomography. A pair of transducers separated by a constant angle, 2b, are used in place of the single transducer in the pulse echo method. The transmitter, Tx0, transmits a beam of ultrasound into the material that is reflected to the receiver, Rx0, via any defects present. This process is repeated for a chosen number of transmitter ( Tx1, Tx2, …) locations with the reflection data being backprojected along elliptical paths to reconstruct a defect image.
Time-of-flight diffraction [3] techniques provide information on the position, shape and size of defects by the interpretation of ultrasonic signals received with either a single or twin probe system. This reconstruction method is more specialized than the simpler reflection tomography methods and may therefore provide additional information about the defect structure. Diffraction tomography uses the diffracted signals from defect boundaries to reconstruct flaw images. The data are collected using transducers that are sufficiently small as to approximate point sources. This assumption will be justified in Section 4. The objective is to transmit ultrasound into the specimen from a single transmit location and to receive the signals diffracted from the defect at a number of points along the receiver aperture. The image is reconstructed in the spatial domain by a coherent summation of elliptic functions whose parameters depend on the transmitter and receiver locations and the time of flight of the diffracted signals. Fig. 3(a) shows a typical data acquisition model for a linear aperture. This algorithm is easily adaptable to any sampling geometry; the data acquisition system used on a cylindrical object for a single transducer position is shown in Fig. 3(b). For each transmitter position on the aperture D, the scattered signals are detected with the receiver scanning the aperture. For example, let (x , 0) and (x , 0) be the positions of the transmitter t r and receiver, respectively. The source and receiver are assumed to approximate point sources. Since the system is based on time-of-flight diffraction, the broadband signal transmitted by an elementary source of width dx is in the form Re[s(t) ejvt], where s(t) is the pulse t envelope, and v is the angular frequency. The signal, du, scattered from an isotropic point reflector placed at (x, y) and received by an elementary receiver width, dx , is [3]: r du(t, x , x )=Re{s[t−d(x , x , x, y)/c] t r r t ×ejv(t−d(xr, xt, x, y)/c)}dx dx , r t where d(x , x , x, y) is the path length from transmitter r t to receiver via the scatterer and is given by: d(x , x , x, y)=[(x −x)2+y2]1/2+[(x −x)2+y2]1/2 r t r t and c is the ultrasonic propagation velocity. Note that the time factor d(x , x , x, y)/c defines a r t time-dependent function, that in the space domain is an ellipse with foci at (x , 0) and (x , 0), passing through r t the point reflector (x, y). The assumptions are that the material is non-attenuating and that all scatterers are in
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Fig. 3. (a) Data collection model for time-of-flight diffraction tomography for linear apertures. The transmitter, Tx, is scanned along the aperture, D. For each transmitter position, the receiver, Rx, is scanned along the entire aperature, D, acquiring diffraction information about the defect at (x, y). These data are then backprojected to reconstruct an image of the defect. (b) This method can be easily adapted to other scanning geometries; the experimental data acquisition set-up utilized for the cylindrical test specimens considered here is shown in Fig. 6.
the far field, so the amplitude decreases as 1/(R R ), 1 2 where R and R are as shown in Fig. 3 and correspond 1 2 to the separation between the defect and the transmitter and receiver respectively. Image formation consists of processing all received signals for all chosen transmitter positions in the aperture D. 2.3. Transmission tomography Transmission tomography methods for non-destructive testing applications are fundamentally different from the methods used in medical applications, mainly due to the physical properties of the materials under test. In medical applications, the human body contains regions of differing acoustic velocity, so a velocity profile of the body can be reconstructed from time-of-flight measurements. This is not the case for the majority of engineering components, as they are by nature made of a single material, and therefore, the velocity changes across the object cross-section are negligible. Moreover, there is usually a large acoustic mismatch between the defect and surrounding media, so the majority of ultrasound is either reflected or diffracted by the defect. For NDT applications, other methods have to be considered. These are usually based on the shadow projected by the flaw [4]. Transmission tomography has been used in the present work to improve images reconstructed using other tomographic methods. An obscuration method [5] has been implemented, based on the principle that the defect will totally reflect an incident ultrasonic beam, which does not propagate to the receiver position. Therefore, a flaw will cast a shadow that depends on its size and position with respect to the transmitter, as illustrated in Fig. 4. A binary system is used typically, so that if a signal is received, a value of 1 is assigned to the receiver. If no
signal is detected, then a zero is assigned to the receiver. Any regions of zeros can then be backprojected, and an image of the flaw reconstructed. The backprojection involves using segments, as shown in Fig. 4(a), with the receiver permitted to be at any location around the specimen under test. If a number of transmitter positions are used, then the backprojected sectors will overlap in the region of the flaw and superimpose to give a darker region, which will correspond to the flaw. A straightforward example is shown in Fig. 4(b). The smallest flaw that can be detected depends largely on the beam width of the transducer used; it is not possible to detect small defects when utilizing transducers with a relatively wide beamwidth. However, it is possible to detect larger defects using transducers with a small beamwidth.
3. Image fusion A composite image can be generated from the set of reconstructed flaw images. This has been achieved using a fuzzy logic pixel fusion technique [6,9]. Fuzzy logic represents a powerful framework for data processing, as it allows processing commands to be expressed as a set of rules that bear a resemblance to the human decision-making process [10]. Fuzzy sets are generally defined by characteristic membership functions. These functions give the level of membership of a particular object to the fuzzy set. The set is used to determine the level of membership of the pixel to the final flaw image. If the pixel is definitely a member of the flaw image, then the weighting associated with the pixel will be 1. If the pixel is definitely not contained in the flaw image then the weighting will be 0, and for all other pixels, which could be contained in the final image, a weighting of between 0 and 1 is applied, depending on the member-
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Fig. 4. Transmission tomography for NDT applications is based on the assumption that any defect within the test specimen will totally reflect any incident ultrasonic beam; thus, the defect will cast a shadow as far as the receiver is concerned: (a) the shadow cast by the flaw from a single transmitter location; (b) backprojection of the shadow regions obtained from a number of different transmitter locations to reconstruct an image of the defect.
ship function. If the pixel amplitude is greater or less than the chosen threshold, then it may or may not be part of the final image. If the pixel amplitude is close to the threshold, then the probability of the pixel being contained in the flaw image is higher than if the amplitude is small when compared to the threshold. This is reflected in the pixel weighting, as seen in the membership function. A number of membership functions were evaluated, with the final choice shown in Fig. 5. All functions examined took a similar form to that shown in Fig. 5, but with the number of pixels receiving a pixel weighting of 1 being increased (i.e. a number of pixel amplitudes have a weighting of 1 rather than a single
pixel amplitude as shown in the figure). This has the effect of increasing the number of pixels that are definitely contained within the final defect image, which in turn can lead to an undesirable increase in the thickness of the defect boundaries. This method of image fusion has the advantages that it is quick and simple to implement. The threshold value, T , for determining which pixels c represent the defect and those that do not was determined using the Ostu thresholding method [7], which is based on discriminant analysis, as defined in Appendix A. A fuzzy logic function is determined for each image, and then the weighted pixel amplitudes are summed to give a composite image of the flaw. Another factor that has a large influence on the final flaw image is the pixel amplitude at which the pixel weighting is zero. For the reflection and diffraction images reconstructed here, the lower cut-off point was chosen between 0.25T and c 0.5T , with the upper cut-off being situated at the maxic mum pixel amplitude for the image. For the transmission image, the lower cut-off was chosen between 0.5T and c 0.75T , but with the upper cut-off being unchanged. The c increase in the cut-off value is necessary to remove the large quantity of information contained within the image that is not related to the flaw under examination.
Fig. 5. Fuzzy logic membership function utilized for image fusion, where T indicates the fusion threshold for the tomographic images c determined using the Ostu thresholding method described. The other figure of merit of the fusion function is the user-defined zero weighting cut-off.
4. Experimental configuration An imaging system was constructed to acquire tomographic data from cylindrical objects up to a diameter
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Fig. 6. Scanning system used to obtain A-scan data for image reconstruction. The cylindrical test specimen can clearly be seen in the center of the scanning system. The two 5 MHz. Panametrics transducers, driven using a Panametrics 5052PR pulser/receiver, are located in spring-loaded holders to allow them to be held lightly in contact with the object under test.
of 100 mm, as shown in Fig. 6. The pair of transducers used to obtain the tomographic data are mounted on two rings of 160 mm surrounding the object. This allows the transducers to be placed anywhere on the circumference of the object under test. The transducers are held in spring-loaded holders to keep them lightly in contact with the object. Good coupling between the transducers and the object was obtained using a thin layer of coupling gel. All of the specimens investigated were made of aluminum and contained a number of represen-
tative flaw types. Three defect types were considered, the first being a simulated inclusion (7 mm side-drilled hole), the second a smaller, simulated inclusion (1.2 mm side-drilled hole), as shown in Fig. 7(a), and the final defect was a simulated planar flaw (25×2 mm slot), as shown in Fig. 7(b). The cylindrical geometry has been chosen to allow access to the flaw from all angles. The transducers used for data acquisition were a pair of Panametrics broadband videoscan transducers, with a center frequency of 5 MHz. These were driven using a Panametrics 5052PR pulser/receiver. The received signals were digitized using a HP 54502A 400 MHz digitizing oscilloscope, which was controlled, and waveform data obtained using a GPIB interface linked to a personal computer. The transducers were positioned manually in the desired location around the object, with the resulting data being stored before being used to determine the time of flight between the source, the defect and the receiver. These time measurements were made using a first-arrival estimator algorithm [8], which involves setting up two adjacent windows in time and moving them along the A-scan. At each point on the trace, a sum of the absolute amplitudes for both the leading and following window were calculated. The ratio of these sums defines a characteristic amplitude function whose maximum value gives the time of flight of the ultrasonic pulse. One of the main considerations for image generation for NDT applications is the time taken to reconstruct the image. The reconstruction and fusion algorithms were implemented on a Sun Ultra Sparc workstation, enabling typical reconstruction times of less than a minute for each image, with the image fusion process being almost instantaneous. The transducers employed were cylindrical in shape but are considered to be point sources due to the transducer/object contact conditions and the nature of
Fig. 7. Specimens used to evaluate the performance of the image reconstruction and fuzzy logic fusion tools presented here were all cylindrical aluminum objects of 75 mm diameter and contained a number of representative defects. The defects considered here with their positions and dimensions displayed are: (a) 1.2 mm and 7 mm inclusion; (b) simulated 25×2 mm planar defect.
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the image reconstruction. That is, as the object is cylindrical and the transducer face flat, then the region of contact between the two can be considered to be a line. In addition, the frequency of the ultrasound used was 5 MHz, which had a wavelength of 1.2 mm in aluminum. This is small when compared to the object size of 75 mm. In addition, the reconstructed image is a 2-D slice of the object cross-section, so the line approximates to a point source in the reconstruction plane. The divergence within the object was measured to be ±35° for an aluminum cylinder of 75 mm diameter, providing good coverage of the aluminum samples.
5. Experimental results In order to validate the improvement in image quality obtained through fusing alternative images of a defect, data taken from the simulated flaws were reconstructed. All of the flaws were situated at a radius of 17.5 mm within aluminum cylinders of 75 mm diameter.
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For the specimen containing the 7 mm circular inclusion the first image reconstructed was the pulse echo reflection image, shown in Fig. 8(a). A-scans were captured at 72 equally spaced positions around the circumference of the cylindrical sample, giving a 5° angular separation between transmitter locations. The reconstructed image of the defect is nearly circular in shape, and has a diameter of approximately 7 mm; the actual defect boundary has been placed on the image for reference. The next image shown in Fig. 8(b) was generated using the pitch catch reflection algorithm. To obtain this, a pair of transducers set an angular distance of 65° apart were used, and the time of flight of the reflected pulses was determined for a transmitter separation of 5°. The boundary of the defect is shown in white and it can be seen that the boundary has not been reconstructed in its entirety. This is due to the lower amplitude signals, reflected from this part of the boundary caused by beam spreading in the far field, being swamped by the stronger reflections from the other side of the boundary where the incident ultrasonic energy is
Fig. 8. Reconstructed images of a 7 mm circular inclusion in an aluminum cylinder with actual flaw boundary marked: (a) pulse echo reflection tomography image reconstructed with a 5° angular transmitter separation; (b) pitch catch reflection tomography image reconstructed with a 5° angular transmitter separation and a 65° transmitter to receiver separation; (c) time-of-flight diffraction tomography image reconstructed with a 90° transmitter separation and a 10° receiver separation; and (d ) transmission tomography image reconstructed with a 20° transmitter separation and a 10° receiver separation.
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Fig. 9. Fused image of the 7 mm circular inclusion with flaw boundary included. The images fused were the pulse echo reflection tomography image, pitch catch reflection tomography image, time-of-flight diffraction tomography image and transmission tomography image.
stronger. The third image shown in Fig. 8(c) was reconstructed using the time-of-flight diffraction tomography algorithm. For this image, four transmit locations equally spaced around the object circumference were chosen. The ultrasonic energy scattered by the defect was then collected, over the circumference of the sample, at 10° intervals. The reconstructed image does not give a good indication of the flaw shape or orientation, the actual defect boundary being shown in white on the image. This can be explained by the fact that a strongly diffracted signal can only be obtained from the defect when the angle of incidence to the defect is favorable. In this case, a number of the diffracted pulses received were not of sufficient quality for the time-of-flight determination method to give an accurate time value, resulting in a deterioration of the image. The final image reconstructed is the transmission image, and is shown in Fig. 8(d ). A-scan data were taken with a transmitter separation of 20° and a 10° angular separation between the receiver locations. In this case, the resulting image gives a reasonably good indication of the defect size, shape and position. When the individual images had been reconstructed, they were fused together, as shown in Fig. 9. The resulting fused images demonstrate an improved indication of flaw size and shape, especially in the region where little information could be obtained from the two reflection images. In addition, there is a ‘hot’ spot on
the left-hand side of the defect boundary, originally from the pitch-catch reflection image, which corresponds to the region of the defect boundary illuminated by the most transmitter locations. It should be possible to reduce, if not remove, this artifact by normalization of the images prior to fusion. For the sample containing the simulated smaller inclusion, the same data acquisition system was used, except that no recognizable transmission image was obtainable due to the small defect size when compared to the transmitter beam width. The pulse-echo and pitch-catch reflection images are shown in Fig. 10(a) and (b), respectively, and the diffraction image is shown in Fig. 10(c). All three images clearly show a small defect, but there is a considerable amount of noise present in the images. It is also apparent that as well as coinciding at the reflector’s position, the arcs crowd together at neighbouring positions, thus introducing unwanted blurring [13]. The fusion of the three images is shown in Fig. 11, and it is apparent that there is improved characterization of the defect. It can be seen in the fused image that the majority of noise that was in the individual images has been removed, thus giving an improved indication of flaw size, orientation and position. Considering that the wavelength of the ultrasound compared to the flaw size of 1.2 mm is 1.28 mm in aluminum, at 5 MHz, then the image resolution obtained is good. The final defect to be evaluated was a simulated planar defect, a 2 mm wide, 25 mm long slot in the specimen shown in Fig. 7(b). The data acquisition system was the same as before, and the pulse-echo reflection image is shown in Fig. 12(a). This image clearly shows one end of the slot, but gives a poor image of the other, in terms of both the position and the representation of the end of the slot as a single point. This can be explained in terms of the data acquisition arrangement relative to the flaw orientation within the object. For a number of transmitter locations, the end point of the defect is effectively hidden from the transmitter by the body of the slot, and therefore, little information about that end point is obtainable. The pitch-catch reflection and diffraction images shown in Fig. 12(b) and (c), respectively, give improved images of both the defect end-points and the distance between the two points. If these three images alone are considered, then the specimen would be interpreted as containing two-point reflector type defects. The transmission image shown in Fig. 12(d ) clearly shows that the defect is planar in nature. The image gives a good indication of the defect orientation. However, it does not give a satisfactory indication of the defect length or width due to diffraction effects around the ends of the slot. This image could be improved by increasing the number of transmit and receive locations used to obtain data for the image reconstruction.
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Fig. 10. Reconstructed images of a 1.2 mm inclusion in an aluminum cylinder with the defect boundary shown: (a) pulse echo reflection tomography image reconstructed with a 5° angular transmitter separation; (b) pitch catch reflection tomography image reconstructed with a 5° angular transmitter separation and a 65° transmitter to receiver separation; (c) time-of-flight diffraction tomography image reconstructed with a 90° transmitter separation and a 10° receiver separation.
The fused image generated from the four images described above is given in Fig. 13. It clearly shows the end points of the slot, the distance between them being 25 mm. The body of the slot is poorly represented, as it does not extend to the end points as required for correct characterization of the defect, but it does give a good indication of the slot orientation, and improvement of the transmission image reconstruction would lead to improved imaging of the flaw body. Very little informa-
Fig. 11. Fused image of the 1.2 mm inclusion with the defect boundary included for clarity. The images fused were the pulse echo reflection tomography image, pitch catch reflection tomography image and timeof-flight diffraction tomography image. The image represents an area of 45 mm×45 mm.
tion about the width of the defect can be obtained from the fused image, but it does show considerable improvement over the transmission tomography image.
6. Conclusions and future work A flexible imaging system, based on the fusion of up to four tomographic images, has been presented. It uses the images reconstructed from time domain information to generate a single defect image. This approach demonstrates the potential for increasing the amount of information obtained about the defect under examination, where A-scan data are acquired using either a single transducer, or a pair of transducers mechanically scanned around the test specimen. In future, multielement arrays could be considered for data acquisition, thus obviating the need for mechanical scanning. Examples of images generated using all imaging methods have been presented for three simple simulated defects contained within aluminum cylinders. Although the samples tested were cylindrical in geometry, the image reconstruction algorithms presented here are independent of object geometry. To this end, it is intended to link the image reconstruction to a CAD model of the component to allow easier visualization of flaws with respect to the object geometry [14]. To increase the reliability of imaging methods, it is desirable to account for a single bounce before and/or after the flaw in the reconstruction algorithms, thus giving more information about the flaw for the same number of A-scans used presently, since indirectly reflected beams can be used to improve the image quality when all parts of the flaw cannot be directly isonified due to access restrictions. This involves using reflections from the backwall of the test specimen to obtain more detail about any defects embedded in the specimen. To
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Fig. 12. Reconstructed images of a 25 mm×2 mm slot in an aluminum cylinder with an actual flaw boundary shown: (a) pulse echo reflection tomography image reconstructed with a 5° angular transmitter separation; (b) pitch catch reflection tomography image reconstructed with a 5° angular transmitter separation and a 65° transmitter to receiver separation; (c) time-of-flight diffraction tomography image reconstructed with a 90° transmitter separation and a 10° receiver separation; and (d ) transmission tomography image reconstructed with a 20° transmitter separation and a 10° receiver separation.
achieve this, the geometry of the backwall must be known; if the backwall is a flat surface, then the backprojection is along circular arcs. However, if the backwall has a more complex geometry (i.e for the cylindrical
test specimens considered here), then the backprojection will be along more complex curves determined by the backwall geometry. The fact that the backwall geometry must be known is a drawback of this image enhancement
Fig. 13. Fused image of the simulated planar defect with the flaw boundary marked The images fused were the pulse echo reflection tomography image, pitch catch reflection tomography image, time-of-flight diffraction tomography image and transmission tomography image.
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method, but if the reconstruction is linked to a CAD model of the component, then this information will be available. Further work is progressing in this area.
Acknowledgements This work has been carried out under a Case studentship with a grant from the Engineering and Physical Sciences Research Council ( UK ) and Rolls-Royce PLC.
Appendix: Ostu thresholding method [7] This global thresholding technique is based on discriminant analysis. The thresholding operation is regarded as the partitioning of the pixels into two classes, C and C , (e.g., object and background ) at 0 1 gray level, t. That is, C ={0, 1,…, t) and C = 0 1 {t+1, t+2,…, l−1} where l is the number of levels in the grayscale image. Let s2 , s2 , and s2 be the withinW B T class, between class and total variance, respectively. An optimal threshold can be determined by minimizing one of the three possible criterion functions with respect to t: s2 s2 s2 l= B , g= B , k= T . s2 s2 s2 W T W Of the above three criterion functions, g is the simplest. Thus, the optimal threshold, T , is: c T =Arg Min g, c tµG where G={0, 1, 2,…, l−1} is a set of positive integers
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representing gray levels, where: l−1 l−1 s2 = ∑ (i−m )2p , m = ∑ ip , T T i T i i=0 i=0 t s2 =v v ( m m )2, v = ∑ p , v =1−v , B 0 1 0 1 0 i 1 0 l=0 m m −m t t , m = t , m =∑ ip . m = T 0 v t i 1 1−v i=0 0 0
References [1] B.S. Hoyle, F. Wiegand, Electronic Lett. 24 (1988) 605–606. [2] D.A. Hutchins, D.K. Mak, J.K. Hu, in: Ultrasonics Int. 87 Conf. Proc. (1987) 860–864. [3] L. Capineri, H.G. Tattersal, J.A.G. Temple, M.G. Silk, Ultrasonics 30 (1992) 275–288. [4] J. Krautkramer, H. Krautkramer, Ultrasonic Testing of Materials, 4th edition, Springer, Berlin, 1990. [5] M.A. Seiraffi, Acoustical Imaging 19 (1992) 933–937. [6 ] F. Russo, G. Ramponi, IEEE Trans. Instrum. Meas. 43 (1994) 288–294. [7] P.K. Sanoo, Comput. Vis. Grap. Image Process. 41 (1988) 233–260. [8] R.P. Bording, A. Gersztenkorn, L.R. Lines, J.A. Scales, S. Treitel, Geophys. J. 90 (1987) 285–303. [9] X.E. Gross, NDT Data Fusion, Arnold, London, 1997. [10] H. Bandemar, S. Gottwald, Fuzzy Sets Fuzzy Logic Fuzzy Methods: With Applications, Wiley, Chichester, UK, 1993. [11] R.K. Mueller, M. Kaveh, G. Wade, Proc. IEEE 67 (1979) 567–587. [12] S.J. Norton, M. Linzer, Ultrasonic Imaging 1 (1979) 154–184. [13] P.D. Hanstead, in: Ultrasonics Int. 87 Conf. Proc. (1987) 12–19.. [14] I.H. Cornwell, Software systems for interpretation of ultrasonic NDT data, Ph.D. thesis, University of Strathclyde, 1997.
Improved ultrasonic image generation through tomographic image fusion I.D. Hall *, A. McNab, G. Hayward Ultrasonic Research Group, Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow G1 1WX, UK Received 1 February 1998
Abstract Techniques for the generation of quantitative ultrasonic images in non-destructive testing have generally involved a substantial cost in terms of data storage and computational time, and thus have found limited application. Preference has therefore been given to the more straightforward imaging methods, such as main beam projection, that detect the presence of defects and provide a limited flaw sizing capability. The relatively small number of flaws requiring detailed examination, coupled with substantial increases in available data storage and computational power, has made it possible to use a number of straightforward tomographic reconstruction methods to produce images of flaws contained within the material under examination. These can then be fused together into a single image from which more accurate measurements of flaw size, shape and orientation can be made. The three tomographic methods that have been implemented in this work are reflection tomography, time-of-flight diffraction tomography and transmission tomography. Selection of images used in the fusion process depends on the nature of the flaw, as each of these methods identifies different characteristics of the flaw shape. The reconstruction methods have been used to generate images from a variety of flaws contained within aluminum cylinders, some or all of the images being fused to produce the final flaw image. Time domain measurements used in the reconstruction were then applied to simulate the application of multi-element arrays for data acquisition and the subsequent tomographic images evaluated. © 1999 Published by Elsevier Science B.V. All rights reserved. Keywords: Fuzzy logic; Image fusion; NDT; Tomography
1. Introduction Tomographic techniques have been used widely in biomedical [11] and seismic [8] applications, but until relatively recently, these techniques have been too expensive, in terms of computational power and data storage, for widespread application to non-destructive testing (NDT ). Two of the most widely used defect imaging methods in ultrasonic NDT are main beam projection and SAFT (synthetic aperture focusing technique). Main beam projection is one of the most basic imaging methods currently in use. Signals from each A-scan are simply projected onto a 2-D plane along a line starting from the transmitter position and following the central probe axis. Since the beam is not perfectly focused, but has a finite beam spread, targets in the far field become distorted. Another drawback is that a target detected by the edge of the spreading beam will be incorrectly * Corresponding author. Fax: +44-141-552-2487. E-mail address: [email protected] (I.D. Hall )
positioned along the central beam at that position, for example a point reflector will become an arc, and specular reflectors appear oversized. SAFT is a technique that uses A-scan data to reconstruct defect images. For each transmitter location, every pixel in the image is provisionally considered a possible reflector position. All echoes with transit times corresponding to the distance from any particular transmitter position to each separate pixel are added up, having equal phase only if they are genuine echoes from a reflector in this pixel [4]. The drawbacks of using this imaging method are that the reconstruction time is often long, especially when the method is extended to any data acquisition set-up more complex than pulse echo. Available computing resources have increased significantly in recent years and have therefore ceased to have the same influence on the choice of NDT technique employed for defect characterization. The generation of tomographic images for NDT applications is fundamentally different from that for medical and seismic applications; this is mainly due to the nature of the objects
0041-624X/99/$ – see front matter © 1999 Published by Elsevier Science B.V. All rights reserved. PII: S0 0 4 1 -6 2 4 X ( 9 9 ) 0 0 01 5 - 3
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under examination. Engineering components can generally be considered isotropic and homogeneous, which cannot be assumed for either medical or seismic applications. In addition, there is often a large acoustic mismatch between the specimen under test and the defect, and thus little or no ultrasound can be transmitted through the defect, the amount of sound transmitted depending on the defect type and orientation. These factors contribute to the selection of alternative imaging methods for NDT applications. In this work, a number of elementary tomographic methods have been chosen, and a selection of the reconstructed images fused together to obtain a more representative image of the defect under examination. The tomographic methods selected to permit a number of transmit and receive probe combinations are reflection tomography, time-of-flight diffraction tomography and transmission tomography. These methods differ in their computational complexity and the quality of the images that have been reconstructed. The pulse echo reflection and the transmission reconstruction algorithms are not very computationally intensive as they involve backprojection of ultrasonic data along arcs and sections of the image, respectively, which is not computationally intensive to implement. The time-of-flight diffraction and pitch catch reflection reconstruction methods require the backprojection of the data over elliptical paths and are therefore more computationally intensive. In addition, the time-of-flight diffraction reconstruction algorithm utilizes a more complex system of transmit and receive locations when compared to the other reconstruction algorithms, thus adding to the computational complexity. For this reason, the time-of-flight diffraction method is restricted to only a small number of transmitter locations in order to obtain an acceptable balance between image quality and reconstruction time. For the other methods, the reconstruction time and image quality are deemed acceptable for the amount of data used. The methodology of reconstructing a number of simple tomographic images was chosen over the development of a single more complex reconstruction algorithm, using all of the acquired data to maintain theoretical simplicity, leading to lower computational requirements and greater flexibility for the user. The fusion process is governed primarily by the nature of the defect under examination. For example, if the flaw is planar (e.g., a crack), then the reflection and time-of-flight diffraction reconstruction methods will give the position of the defect end-points; with the addition of the transmission image, it becomes possible to resolve any ambiguity about the defect type, i.e., it can be determined whether the defect is a single planar defect or two point reflectors. If the nature of the defect is unknown, then the individual tomographic images reconstructed can be utilized to obtain sufficient infor-
mation on the defect nature for the fusion process to be completed satisfactorily. In this paper, the tomographic methods used for image reconstruction are explained briefly. The reflection and time-of-flight diffraction methods utilize the timeof-flight of the ultrasonic pulses reflected or diffracted from the defect to reconstruct images of the crosssectional reflectivity function, whereas the transmission tomography method uses the shadow cast by the flaw to generate defect images. An outline of the fuzzy logic method used for fusion of the reconstructed images is also presented. In order to validate the chosen imaging approach, experimental time domain data are obtained from aluminum cylinders containing simulated defects. The defect images reconstructed from these data and the fused images are used to demonstrate the performance of the tomographic image fusion approach to defect imaging.
2. Tomographic reconstruction 2.1. Reflection This is the most common and widely used method of generating tomographic images in NDT [12] and is suitable for obtaining images from a wide variety of defect types. Reflection tomography employs ultrasonic pulses to excite echoes from the boundaries of flaws contained in the cross-section of the object field, illuminated in sequence by a number of ultrasonic beams. The beams may come from a variety of sources, a single transducer, or a pair of transducers, depending on the user requirements. A-scan data are then collected and used to reconstruct a pseudo-image of the cross-sectional reflectivity function. In the present case, two methods for data collection have been considered, pulse-echo (a single transducer for transmit and receive) and pitchcatch (two transducers; one for transmission and the other for reception). Both of these methods are applicable to data acquisition using multi-element arrays. The pulse echo [1] case is illustrated in Fig. 1, whereby an ultrasonic transducer placed in contact with the object under test at position w and transmits a wavefront c that diverges in the object with an angle, a, illuminating the test specimen as shown in the figure. The output from the transducer is an A-scan (detected voltage as a function of time). The measured delay time, corresponding to the time taken for the ultrasonic pulse to travel from the transmitter to the defect and back to the receiver, can be used to obtain spatial distance information according to q=tc/2, where q is the distance between the reflector and the transmitter, t is the elapsed time, and c is the sound velocity in the material. One projection value is the composite sum of all contributions from reflecting objects situated on an arc,
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locations are utilized, then a similar approach to image reconstruction can be employed, with the circular arcs being replaced by ellipsoids. 2.2. Time-of-flight diffraction tomography
Fig. 1. Data collection model for pulse echo reflection tomography. A single transducer at a number of positions, w , transmits a beam of c ultrasound into the test specimen that diverges at an angle, a. Any defects contained within the test specimen reflect energy back to the transducer; these reflection data are then backprojected along circular paths to reconstruct a defect image.
whose radius corresponds to the echo delay time, and whose center is located at the transducer position. The measured projections are then backprojected over the ray paths with projection values measured from a different number of transducer positions being summed such that the arc intersections define the reconstructed object. The pitch catch method [2] uses a pair of scanned transducers, with a fixed separation, held in contact with the object, one for transmission and the other for reception. Thus, the time of flight obtained from the A-scan represents the time of flight from the source to the receiver, via a reflector (the defect). The time of flight defines an ellipse as opposed to an arc in the pulse echo configuration; the foci of the ellipses are situated at the source and receiver locations, as shown in Fig. 2. As described previously, if multiple source and receive
Fig. 2. Data collection model for pitch-catch reflection tomography. A pair of transducers separated by a constant angle, 2b, are used in place of the single transducer in the pulse echo method. The transmitter, Tx0, transmits a beam of ultrasound into the material that is reflected to the receiver, Rx0, via any defects present. This process is repeated for a chosen number of transmitter ( Tx1, Tx2, …) locations with the reflection data being backprojected along elliptical paths to reconstruct a defect image.
Time-of-flight diffraction [3] techniques provide information on the position, shape and size of defects by the interpretation of ultrasonic signals received with either a single or twin probe system. This reconstruction method is more specialized than the simpler reflection tomography methods and may therefore provide additional information about the defect structure. Diffraction tomography uses the diffracted signals from defect boundaries to reconstruct flaw images. The data are collected using transducers that are sufficiently small as to approximate point sources. This assumption will be justified in Section 4. The objective is to transmit ultrasound into the specimen from a single transmit location and to receive the signals diffracted from the defect at a number of points along the receiver aperture. The image is reconstructed in the spatial domain by a coherent summation of elliptic functions whose parameters depend on the transmitter and receiver locations and the time of flight of the diffracted signals. Fig. 3(a) shows a typical data acquisition model for a linear aperture. This algorithm is easily adaptable to any sampling geometry; the data acquisition system used on a cylindrical object for a single transducer position is shown in Fig. 3(b). For each transmitter position on the aperture D, the scattered signals are detected with the receiver scanning the aperture. For example, let (x , 0) and (x , 0) be the positions of the transmitter t r and receiver, respectively. The source and receiver are assumed to approximate point sources. Since the system is based on time-of-flight diffraction, the broadband signal transmitted by an elementary source of width dx is in the form Re[s(t) ejvt], where s(t) is the pulse t envelope, and v is the angular frequency. The signal, du, scattered from an isotropic point reflector placed at (x, y) and received by an elementary receiver width, dx , is [3]: r du(t, x , x )=Re{s[t−d(x , x , x, y)/c] t r r t ×ejv(t−d(xr, xt, x, y)/c)}dx dx , r t where d(x , x , x, y) is the path length from transmitter r t to receiver via the scatterer and is given by: d(x , x , x, y)=[(x −x)2+y2]1/2+[(x −x)2+y2]1/2 r t r t and c is the ultrasonic propagation velocity. Note that the time factor d(x , x , x, y)/c defines a r t time-dependent function, that in the space domain is an ellipse with foci at (x , 0) and (x , 0), passing through r t the point reflector (x, y). The assumptions are that the material is non-attenuating and that all scatterers are in
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Fig. 3. (a) Data collection model for time-of-flight diffraction tomography for linear apertures. The transmitter, Tx, is scanned along the aperture, D. For each transmitter position, the receiver, Rx, is scanned along the entire aperature, D, acquiring diffraction information about the defect at (x, y). These data are then backprojected to reconstruct an image of the defect. (b) This method can be easily adapted to other scanning geometries; the experimental data acquisition set-up utilized for the cylindrical test specimens considered here is shown in Fig. 6.
the far field, so the amplitude decreases as 1/(R R ), 1 2 where R and R are as shown in Fig. 3 and correspond 1 2 to the separation between the defect and the transmitter and receiver respectively. Image formation consists of processing all received signals for all chosen transmitter positions in the aperture D. 2.3. Transmission tomography Transmission tomography methods for non-destructive testing applications are fundamentally different from the methods used in medical applications, mainly due to the physical properties of the materials under test. In medical applications, the human body contains regions of differing acoustic velocity, so a velocity profile of the body can be reconstructed from time-of-flight measurements. This is not the case for the majority of engineering components, as they are by nature made of a single material, and therefore, the velocity changes across the object cross-section are negligible. Moreover, there is usually a large acoustic mismatch between the defect and surrounding media, so the majority of ultrasound is either reflected or diffracted by the defect. For NDT applications, other methods have to be considered. These are usually based on the shadow projected by the flaw [4]. Transmission tomography has been used in the present work to improve images reconstructed using other tomographic methods. An obscuration method [5] has been implemented, based on the principle that the defect will totally reflect an incident ultrasonic beam, which does not propagate to the receiver position. Therefore, a flaw will cast a shadow that depends on its size and position with respect to the transmitter, as illustrated in Fig. 4. A binary system is used typically, so that if a signal is received, a value of 1 is assigned to the receiver. If no
signal is detected, then a zero is assigned to the receiver. Any regions of zeros can then be backprojected, and an image of the flaw reconstructed. The backprojection involves using segments, as shown in Fig. 4(a), with the receiver permitted to be at any location around the specimen under test. If a number of transmitter positions are used, then the backprojected sectors will overlap in the region of the flaw and superimpose to give a darker region, which will correspond to the flaw. A straightforward example is shown in Fig. 4(b). The smallest flaw that can be detected depends largely on the beam width of the transducer used; it is not possible to detect small defects when utilizing transducers with a relatively wide beamwidth. However, it is possible to detect larger defects using transducers with a small beamwidth.
3. Image fusion A composite image can be generated from the set of reconstructed flaw images. This has been achieved using a fuzzy logic pixel fusion technique [6,9]. Fuzzy logic represents a powerful framework for data processing, as it allows processing commands to be expressed as a set of rules that bear a resemblance to the human decision-making process [10]. Fuzzy sets are generally defined by characteristic membership functions. These functions give the level of membership of a particular object to the fuzzy set. The set is used to determine the level of membership of the pixel to the final flaw image. If the pixel is definitely a member of the flaw image, then the weighting associated with the pixel will be 1. If the pixel is definitely not contained in the flaw image then the weighting will be 0, and for all other pixels, which could be contained in the final image, a weighting of between 0 and 1 is applied, depending on the member-
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Fig. 4. Transmission tomography for NDT applications is based on the assumption that any defect within the test specimen will totally reflect any incident ultrasonic beam; thus, the defect will cast a shadow as far as the receiver is concerned: (a) the shadow cast by the flaw from a single transmitter location; (b) backprojection of the shadow regions obtained from a number of different transmitter locations to reconstruct an image of the defect.
ship function. If the pixel amplitude is greater or less than the chosen threshold, then it may or may not be part of the final image. If the pixel amplitude is close to the threshold, then the probability of the pixel being contained in the flaw image is higher than if the amplitude is small when compared to the threshold. This is reflected in the pixel weighting, as seen in the membership function. A number of membership functions were evaluated, with the final choice shown in Fig. 5. All functions examined took a similar form to that shown in Fig. 5, but with the number of pixels receiving a pixel weighting of 1 being increased (i.e. a number of pixel amplitudes have a weighting of 1 rather than a single
pixel amplitude as shown in the figure). This has the effect of increasing the number of pixels that are definitely contained within the final defect image, which in turn can lead to an undesirable increase in the thickness of the defect boundaries. This method of image fusion has the advantages that it is quick and simple to implement. The threshold value, T , for determining which pixels c represent the defect and those that do not was determined using the Ostu thresholding method [7], which is based on discriminant analysis, as defined in Appendix A. A fuzzy logic function is determined for each image, and then the weighted pixel amplitudes are summed to give a composite image of the flaw. Another factor that has a large influence on the final flaw image is the pixel amplitude at which the pixel weighting is zero. For the reflection and diffraction images reconstructed here, the lower cut-off point was chosen between 0.25T and c 0.5T , with the upper cut-off being situated at the maxic mum pixel amplitude for the image. For the transmission image, the lower cut-off was chosen between 0.5T and c 0.75T , but with the upper cut-off being unchanged. The c increase in the cut-off value is necessary to remove the large quantity of information contained within the image that is not related to the flaw under examination.
Fig. 5. Fuzzy logic membership function utilized for image fusion, where T indicates the fusion threshold for the tomographic images c determined using the Ostu thresholding method described. The other figure of merit of the fusion function is the user-defined zero weighting cut-off.
4. Experimental configuration An imaging system was constructed to acquire tomographic data from cylindrical objects up to a diameter
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Fig. 6. Scanning system used to obtain A-scan data for image reconstruction. The cylindrical test specimen can clearly be seen in the center of the scanning system. The two 5 MHz. Panametrics transducers, driven using a Panametrics 5052PR pulser/receiver, are located in spring-loaded holders to allow them to be held lightly in contact with the object under test.
of 100 mm, as shown in Fig. 6. The pair of transducers used to obtain the tomographic data are mounted on two rings of 160 mm surrounding the object. This allows the transducers to be placed anywhere on the circumference of the object under test. The transducers are held in spring-loaded holders to keep them lightly in contact with the object. Good coupling between the transducers and the object was obtained using a thin layer of coupling gel. All of the specimens investigated were made of aluminum and contained a number of represen-
tative flaw types. Three defect types were considered, the first being a simulated inclusion (7 mm side-drilled hole), the second a smaller, simulated inclusion (1.2 mm side-drilled hole), as shown in Fig. 7(a), and the final defect was a simulated planar flaw (25×2 mm slot), as shown in Fig. 7(b). The cylindrical geometry has been chosen to allow access to the flaw from all angles. The transducers used for data acquisition were a pair of Panametrics broadband videoscan transducers, with a center frequency of 5 MHz. These were driven using a Panametrics 5052PR pulser/receiver. The received signals were digitized using a HP 54502A 400 MHz digitizing oscilloscope, which was controlled, and waveform data obtained using a GPIB interface linked to a personal computer. The transducers were positioned manually in the desired location around the object, with the resulting data being stored before being used to determine the time of flight between the source, the defect and the receiver. These time measurements were made using a first-arrival estimator algorithm [8], which involves setting up two adjacent windows in time and moving them along the A-scan. At each point on the trace, a sum of the absolute amplitudes for both the leading and following window were calculated. The ratio of these sums defines a characteristic amplitude function whose maximum value gives the time of flight of the ultrasonic pulse. One of the main considerations for image generation for NDT applications is the time taken to reconstruct the image. The reconstruction and fusion algorithms were implemented on a Sun Ultra Sparc workstation, enabling typical reconstruction times of less than a minute for each image, with the image fusion process being almost instantaneous. The transducers employed were cylindrical in shape but are considered to be point sources due to the transducer/object contact conditions and the nature of
Fig. 7. Specimens used to evaluate the performance of the image reconstruction and fuzzy logic fusion tools presented here were all cylindrical aluminum objects of 75 mm diameter and contained a number of representative defects. The defects considered here with their positions and dimensions displayed are: (a) 1.2 mm and 7 mm inclusion; (b) simulated 25×2 mm planar defect.
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the image reconstruction. That is, as the object is cylindrical and the transducer face flat, then the region of contact between the two can be considered to be a line. In addition, the frequency of the ultrasound used was 5 MHz, which had a wavelength of 1.2 mm in aluminum. This is small when compared to the object size of 75 mm. In addition, the reconstructed image is a 2-D slice of the object cross-section, so the line approximates to a point source in the reconstruction plane. The divergence within the object was measured to be ±35° for an aluminum cylinder of 75 mm diameter, providing good coverage of the aluminum samples.
5. Experimental results In order to validate the improvement in image quality obtained through fusing alternative images of a defect, data taken from the simulated flaws were reconstructed. All of the flaws were situated at a radius of 17.5 mm within aluminum cylinders of 75 mm diameter.
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For the specimen containing the 7 mm circular inclusion the first image reconstructed was the pulse echo reflection image, shown in Fig. 8(a). A-scans were captured at 72 equally spaced positions around the circumference of the cylindrical sample, giving a 5° angular separation between transmitter locations. The reconstructed image of the defect is nearly circular in shape, and has a diameter of approximately 7 mm; the actual defect boundary has been placed on the image for reference. The next image shown in Fig. 8(b) was generated using the pitch catch reflection algorithm. To obtain this, a pair of transducers set an angular distance of 65° apart were used, and the time of flight of the reflected pulses was determined for a transmitter separation of 5°. The boundary of the defect is shown in white and it can be seen that the boundary has not been reconstructed in its entirety. This is due to the lower amplitude signals, reflected from this part of the boundary caused by beam spreading in the far field, being swamped by the stronger reflections from the other side of the boundary where the incident ultrasonic energy is
Fig. 8. Reconstructed images of a 7 mm circular inclusion in an aluminum cylinder with actual flaw boundary marked: (a) pulse echo reflection tomography image reconstructed with a 5° angular transmitter separation; (b) pitch catch reflection tomography image reconstructed with a 5° angular transmitter separation and a 65° transmitter to receiver separation; (c) time-of-flight diffraction tomography image reconstructed with a 90° transmitter separation and a 10° receiver separation; and (d ) transmission tomography image reconstructed with a 20° transmitter separation and a 10° receiver separation.
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Fig. 9. Fused image of the 7 mm circular inclusion with flaw boundary included. The images fused were the pulse echo reflection tomography image, pitch catch reflection tomography image, time-of-flight diffraction tomography image and transmission tomography image.
stronger. The third image shown in Fig. 8(c) was reconstructed using the time-of-flight diffraction tomography algorithm. For this image, four transmit locations equally spaced around the object circumference were chosen. The ultrasonic energy scattered by the defect was then collected, over the circumference of the sample, at 10° intervals. The reconstructed image does not give a good indication of the flaw shape or orientation, the actual defect boundary being shown in white on the image. This can be explained by the fact that a strongly diffracted signal can only be obtained from the defect when the angle of incidence to the defect is favorable. In this case, a number of the diffracted pulses received were not of sufficient quality for the time-of-flight determination method to give an accurate time value, resulting in a deterioration of the image. The final image reconstructed is the transmission image, and is shown in Fig. 8(d ). A-scan data were taken with a transmitter separation of 20° and a 10° angular separation between the receiver locations. In this case, the resulting image gives a reasonably good indication of the defect size, shape and position. When the individual images had been reconstructed, they were fused together, as shown in Fig. 9. The resulting fused images demonstrate an improved indication of flaw size and shape, especially in the region where little information could be obtained from the two reflection images. In addition, there is a ‘hot’ spot on
the left-hand side of the defect boundary, originally from the pitch-catch reflection image, which corresponds to the region of the defect boundary illuminated by the most transmitter locations. It should be possible to reduce, if not remove, this artifact by normalization of the images prior to fusion. For the sample containing the simulated smaller inclusion, the same data acquisition system was used, except that no recognizable transmission image was obtainable due to the small defect size when compared to the transmitter beam width. The pulse-echo and pitch-catch reflection images are shown in Fig. 10(a) and (b), respectively, and the diffraction image is shown in Fig. 10(c). All three images clearly show a small defect, but there is a considerable amount of noise present in the images. It is also apparent that as well as coinciding at the reflector’s position, the arcs crowd together at neighbouring positions, thus introducing unwanted blurring [13]. The fusion of the three images is shown in Fig. 11, and it is apparent that there is improved characterization of the defect. It can be seen in the fused image that the majority of noise that was in the individual images has been removed, thus giving an improved indication of flaw size, orientation and position. Considering that the wavelength of the ultrasound compared to the flaw size of 1.2 mm is 1.28 mm in aluminum, at 5 MHz, then the image resolution obtained is good. The final defect to be evaluated was a simulated planar defect, a 2 mm wide, 25 mm long slot in the specimen shown in Fig. 7(b). The data acquisition system was the same as before, and the pulse-echo reflection image is shown in Fig. 12(a). This image clearly shows one end of the slot, but gives a poor image of the other, in terms of both the position and the representation of the end of the slot as a single point. This can be explained in terms of the data acquisition arrangement relative to the flaw orientation within the object. For a number of transmitter locations, the end point of the defect is effectively hidden from the transmitter by the body of the slot, and therefore, little information about that end point is obtainable. The pitch-catch reflection and diffraction images shown in Fig. 12(b) and (c), respectively, give improved images of both the defect end-points and the distance between the two points. If these three images alone are considered, then the specimen would be interpreted as containing two-point reflector type defects. The transmission image shown in Fig. 12(d ) clearly shows that the defect is planar in nature. The image gives a good indication of the defect orientation. However, it does not give a satisfactory indication of the defect length or width due to diffraction effects around the ends of the slot. This image could be improved by increasing the number of transmit and receive locations used to obtain data for the image reconstruction.
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Fig. 10. Reconstructed images of a 1.2 mm inclusion in an aluminum cylinder with the defect boundary shown: (a) pulse echo reflection tomography image reconstructed with a 5° angular transmitter separation; (b) pitch catch reflection tomography image reconstructed with a 5° angular transmitter separation and a 65° transmitter to receiver separation; (c) time-of-flight diffraction tomography image reconstructed with a 90° transmitter separation and a 10° receiver separation.
The fused image generated from the four images described above is given in Fig. 13. It clearly shows the end points of the slot, the distance between them being 25 mm. The body of the slot is poorly represented, as it does not extend to the end points as required for correct characterization of the defect, but it does give a good indication of the slot orientation, and improvement of the transmission image reconstruction would lead to improved imaging of the flaw body. Very little informa-
Fig. 11. Fused image of the 1.2 mm inclusion with the defect boundary included for clarity. The images fused were the pulse echo reflection tomography image, pitch catch reflection tomography image and timeof-flight diffraction tomography image. The image represents an area of 45 mm×45 mm.
tion about the width of the defect can be obtained from the fused image, but it does show considerable improvement over the transmission tomography image.
6. Conclusions and future work A flexible imaging system, based on the fusion of up to four tomographic images, has been presented. It uses the images reconstructed from time domain information to generate a single defect image. This approach demonstrates the potential for increasing the amount of information obtained about the defect under examination, where A-scan data are acquired using either a single transducer, or a pair of transducers mechanically scanned around the test specimen. In future, multielement arrays could be considered for data acquisition, thus obviating the need for mechanical scanning. Examples of images generated using all imaging methods have been presented for three simple simulated defects contained within aluminum cylinders. Although the samples tested were cylindrical in geometry, the image reconstruction algorithms presented here are independent of object geometry. To this end, it is intended to link the image reconstruction to a CAD model of the component to allow easier visualization of flaws with respect to the object geometry [14]. To increase the reliability of imaging methods, it is desirable to account for a single bounce before and/or after the flaw in the reconstruction algorithms, thus giving more information about the flaw for the same number of A-scans used presently, since indirectly reflected beams can be used to improve the image quality when all parts of the flaw cannot be directly isonified due to access restrictions. This involves using reflections from the backwall of the test specimen to obtain more detail about any defects embedded in the specimen. To
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Fig. 12. Reconstructed images of a 25 mm×2 mm slot in an aluminum cylinder with an actual flaw boundary shown: (a) pulse echo reflection tomography image reconstructed with a 5° angular transmitter separation; (b) pitch catch reflection tomography image reconstructed with a 5° angular transmitter separation and a 65° transmitter to receiver separation; (c) time-of-flight diffraction tomography image reconstructed with a 90° transmitter separation and a 10° receiver separation; and (d ) transmission tomography image reconstructed with a 20° transmitter separation and a 10° receiver separation.
achieve this, the geometry of the backwall must be known; if the backwall is a flat surface, then the backprojection is along circular arcs. However, if the backwall has a more complex geometry (i.e for the cylindrical
test specimens considered here), then the backprojection will be along more complex curves determined by the backwall geometry. The fact that the backwall geometry must be known is a drawback of this image enhancement
Fig. 13. Fused image of the simulated planar defect with the flaw boundary marked The images fused were the pulse echo reflection tomography image, pitch catch reflection tomography image, time-of-flight diffraction tomography image and transmission tomography image.
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method, but if the reconstruction is linked to a CAD model of the component, then this information will be available. Further work is progressing in this area.
Acknowledgements This work has been carried out under a Case studentship with a grant from the Engineering and Physical Sciences Research Council ( UK ) and Rolls-Royce PLC.
Appendix: Ostu thresholding method [7] This global thresholding technique is based on discriminant analysis. The thresholding operation is regarded as the partitioning of the pixels into two classes, C and C , (e.g., object and background ) at 0 1 gray level, t. That is, C ={0, 1,…, t) and C = 0 1 {t+1, t+2,…, l−1} where l is the number of levels in the grayscale image. Let s2 , s2 , and s2 be the withinW B T class, between class and total variance, respectively. An optimal threshold can be determined by minimizing one of the three possible criterion functions with respect to t: s2 s2 s2 l= B , g= B , k= T . s2 s2 s2 W T W Of the above three criterion functions, g is the simplest. Thus, the optimal threshold, T , is: c T =Arg Min g, c tµG where G={0, 1, 2,…, l−1} is a set of positive integers
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representing gray levels, where: l−1 l−1 s2 = ∑ (i−m )2p , m = ∑ ip , T T i T i i=0 i=0 t s2 =v v ( m m )2, v = ∑ p , v =1−v , B 0 1 0 1 0 i 1 0 l=0 m m −m t t , m = t , m =∑ ip . m = T 0 v t i 1 1−v i=0 0 0
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