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Flaw detection by spatially coded backscatter radiography
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Applied Radiation and Isotopes 65 (2007) 189–198 www.elsevier.com/locate/apradiso
Flaw detection by spatially coded backscatter radiography Sivakumar Thangavelu, Esam M.A. Hussein Laboratory for Threat Material Detection, Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada Received 27 June 2006; received in revised form 4 August 2006; accepted 14 August 2006
Abstract Backscatter imaging is useful for inspecting structures that are accessible only from one side. However, indications provided by scattered radiation are typically weak, convoluted and difficult to interpret. This paper explores the use of the coded aperture technique to detect flaws using gamma-ray backscatter imaging. The viability of this approach is demonstrated with indications obtained from Monte Carlo simulations of radiation scattering measurements. The results show that, with a 2 mm wide beam of 137Cs photons, flaws as small as 1.5 mm in width can be detected using this technique. Indications of changes in flaw size, location, multiplicity and density were also observable. In addition, it is possible to quantify, from the decoded indications, the flaw location and its size. r 2006 Elsevier Ltd. All rights reserved. PACS: 87.59.Hp; 25.20.Dc; 78.70.g Keywords: Digital radiography; Compton backscattering; Coded aperture
1. Introduction Conventional radiography relies on monitoring radiation transmitted through an object from one end to another. Such access to two opposite sides is not always readily available. Moreover, conventional radiography cannot be used to inspect objects that are too thick to allow sufficient amount of transmitted radiation to register a useful image. Therefore, structures such as airframes, bridges, pressure vessels, floors, layered structures, etc., do not benefit from traditional radiographic imaging. Ultrasonic inspection can be utilized in some cases, but the need for direct contact and coupling and the strong dispersion of sound waves in the presence of interfaces limit its application. The scattering of X-rays and gamma-rays offers an attractive alternative to conventional imaging technology, as it allows inspection from one side of an object and also provides density-dependent indications as in transmission radiography. However, indications from scattered radiation are not as straightforward to be Corresponding author. Tel.: +1 506 447 3105; fax: +1 506 453 5025.
E-mail address: [email protected] (E.M.A. Hussein). 0969-8043/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2006.08.008
geometrically back-projected to deduce geometric and density indications, as in the case with radiation transmission. Although effort has been made to devise systems to facilitate the extraction of useful indications from scattered radiation, as discussed by Lawson (2002), and more recently by Banerjee and Dunn (2005), the convoluted indication makes scatter radiography quite difficult. The obscurity of scatter indications is to some extent similar to that encountered in astronomical imaging of space objects using photons of energy above 10 keV, where it is common to register weak indications that are overwhelmed by interferences. It is therefore worth considering some of the image extraction methods employed in astronomical imaging. One of those is the coded aperture technique that has been used in astronomy for number of years (Caroli et al., 1987). The same technique has also been used more recently in medical imaging (Accorsi et al., 2001; Zhang et al., 1999), to detect contraband in luggage from neutron-induced activation (Zhang and Lanza, 1999), and to observe gamma-ray sources (Rennie, 2006). In addition, coded aperture has also been utilized in imaging emissions from low-intensity gamma-ray sources (Smith et al., 2001; Woodring et al.,
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1999). To the authors’ knowledge, the coded aperture approach has not been considered before for use with scattered radiation to detect flaws; except in the case of detecting concealed large objects, such as landmines (Faust and Rothschild, 2003). Prior to experimental application of the coded aperture method to radiographic imaging with scattered radiation, it is vital to demonstrate its feasibility using numerical simulations. This is the objective of the work presented here, which begins with a summary of the difficulties of imaging with scattered radiation and a brief introduction to the coded aperture concept. 2. Background 2.1. Scatter imaging Backscatter imaging involves directing a radiation source towards an object and recording on the same side radiation scattered off the object. To avoid direct exposure of the radiation receiver (a film or a radiographic plate), a shielding material is placed in between the source and the receiver. Note that, unlike in transmission radiography, where only one image can be acquired with each radiation exposure, more than one record can be simultaneously obtained in scatter imaging at different directions. However, scatter imaging is disadvantaged by the fact that an anomaly in the object can leave an imprint at more than one location on the receiver. These indicators are difficult to trace back, since the radiation causing them would have encountered many changes in direction before reaching the detector. Nevertheless, by using radiation collimation and/ or energy discrimination, only once-scattered events can be recorded, which greatly simplifies the imaging process by geometrically relating the recorded signal to the position of scattering; as shown by Hussein (2003, Chapter 7). This comes however at a much reduced signal, since the probability of radiation encountering a single collision is quite low. Allowing the detection of multi-scattered photons increases the strength of the recorded signal, but at the same time completely dilutes the position (location of scattering) information provided by single scattering. However, as in photography, where the light source is widely spread, a ‘‘camera’’ may be used to project an image of the strength of the scattered radiation, to reflect the spatial and material features of the scattering medium. 2.2. Coded aperture imaging Unlike light, radiation cannot be focused with a lens, unless it has a very low energy where its use is limited to surface imaging of lattice structures. Radiation scattered from deep within an object can however be localized with the aid of a pinhole camera (Lawson, 2002), where an anomaly can be detected and its direction identified by the change in the intensity of its projected image as the camera scans the object. However, indications obtained from a
pinhole are quite weak, since only a small portion of the signal induced by the anomaly can reach the camera. Of course, a larger pinhole can be used to strengthen the detected signal, but this will come at the expense of reduced definition of directionality. Even if an acceptable signal is attained, only the direction of the anomaly can be determined (along the lines connecting the edges of the projected indication to those of the pinhole). Nevertheless, if a number of images are obtained at different pinhole locations, the intersection of all the determined directions defines the position of the anomaly. This approach, however, does not overcome the inherent problem of the weakness of the indication. In astrophysics, where astronomical X-rays are used to image the sky, the problem of a weak signal is overcome by employing multiple pinholes arranged in a particular fashion into a plate (In’t Zand, 2006). This concept is known as coded aperture, since in effect the recorded indication is ‘‘encoded’’ by the mask pattern. A numerical algorithm is then applied to ‘‘decode’’ the recorded indication, hence determine the location and the brightness of an astronomical object. Radiation projected through the mask creates a pattern, P, on the detector, which is related to the spatial distribution of the object’s radiation intensity, represented via a matrix O by (Accorsi, 2001) O A ¼ P,
(1)
where A is a matrix representing the mask pattern and is the correlation operator. In other words, the mask ‘‘encodes’’ the radiation signal before it is recorded by the detector. It should be noted that Eq. (1) is exactly true when the object is very far away from the mask and the detector, i.e. for far fields. To recover the features of the original radiation source from the projected data, the recorded signal must be decoded. This is done with the aid of a decoding matrix, G, which is such that A G ¼ d,
(2)
where d is the Dirac delta function. The reconstructed ^ is recovered from the projection, P, by image, O, ^ ¼ P G ¼ ðO AÞ G ¼ O ðA GÞ, O
(3)
where is the convolution operator, and the proof of the last step of Eq. (3) is given by Accorsi (2001). Substituting ^ ¼ O d ¼ O, i.e. the Eq. (2) into Eq. (3) leads to: O reconstructed image resembles exactly the object. This perfect matching is obtained if, and only if, Eq. (2) is satisfied. A random mask pattern would not satisfy Eq. (2), and would result in a point-response function which is not a d function. However, a mask pattern can be devised to satisfy Eq. (2), as in the case of a mask formed from uniformly redundant arrays, the so-called URA mask pattern. In addition, the mask pattern, A, should be chosen to minimize the propagation of noise. In this work, a mask pattern based on modified uniformly redundant arrays (MURA) was chosen, as it was deemed to be suitable for near-field projections, such as those associated with
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radiation emerging from nearby objects (Accorsi, 2001; Faust and Rothschild, 2003). MURA consists of cyclically shifted uniform patterns, with 50% open positions. It has decoding coefficients, G, that are modified from URA, so that the decoded indication is completely independent of noise (Gottesman and Fenimore, 1989). In astronomical imaging, the imaged object is at a very large distance from the mask and the detector. However, in near-field imaging, the object-to-mask distance must be known, in order to be able to scale the decoding array to match the dimensions of the projected pattern. Therefore, some plane in the object, parallel to the mask and the detector, needs to be designated as the focal plane.
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Test object
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Source Shielding Mask
2.3. Concept In inspecting an object for the presence of flaws using radiation scattering, a flaw would reduce the intensity of the scattered radiation by the removal of material that would have caused radiation to scatter. If the scattered radiation is viewed as a radiation source, in the same manner the skylight is a source of photons, a flaw can be viewed as a ‘‘negative source’’; unlike light emission that presents a positive source with elevated light intensity. Indications imprinted by a flaw, like those of a faraway astronomical photon source, are quite feeble and would be buried in an overwhelming background caused by the scattering of radiation from all over the scattering medium. Employing the coded aperture technique may enable the detection of weak indications produced by the flaw, even in the presence of a high background. It is conceived here that a detector in the form of a radiographic plate is to be used to detect backscattered radiation from an object. A mask is to be placed in between the object and the detector, as shown in Fig. 1. Radiation scattered within the object will be seen by the detector as a secondary widespread source, provided of course that radiation from the primary source is blocked from reaching the detector. Then each point on the object that scatters radiation towards the detector will be viewed by certain pixels on the radiographic plate, due to radiation passing through open holes in the mask. Therefore, points in the object corresponding to a flaw will affect many detector pixels in a correlated manner. This correlated signal on subsequent decoding should indicate the presence of the flaw and its spatial location, in spite of the uncorrelated scattering emerging from other flawless points in the object. In order to demonstrate the feasibility of this concept, Monte Carlo simulations were conducted with a geometric setup as depicted in Fig. 1. Monte Carlo simulations with the MCNP code (X-5 Monte Carlo Team, 2003) provide faithful representation of the physical interaction processes without being hindered by practical interference and difficulty. While proving the feasibility of the concept with such simulations is not necessarily affirmative of its practicability, a technique that is not functionally demonstrable with simulations is most likely not viable. Monte
Detector (Radiographic plate) Fig. 1. Geometric setup for coded backscatter radiography (the checkboard mask pattern shown here is simply symbolic of the presence of a mask and is not the actual one simulated in this work).
Carlo simulations also enable the testing of the numerical tools necessary for the decoding process. 2.4. Simulation setup A 2 mm wide well collimated beam of photons emerging from a 137Cs source, which emits 662 keV photons, was directed towards an aluminum block (60 60 60 mm3 ) containing spherical holes of various sizes simulating flaws. This was the same source type and width proposed by Jama and Hussein (1999) for optimal detection of flaws using energy-spectral measurements of scattered radiation. The source beam is assumed to scan the object progressively to cover a wide area. Note that a wider beam could have been used, but that will come at the expense of reduced contrast. A 33 33 MURA mask pattern formed by replicating a basic 17 17 MURA pattern, 2 2 times, was simulated, with each pixel being 1 1 mm2 in area. The mask was 4 mm in thickness, made of tungsten (19; 100 kg=m3 density) to block at least 78% of the incident radiation (Thangavelu, 2006). A MURA mask can be manufactured using photolithographic etching techniques (Cherry et al., 1999). The radiographic detector was considered to consist of a 70 70 mm2 radiographic plate divided into 70 70 equal pixels. For simplification, the detector was assumed to have a 100% efficiency, i.e. each photon passing through it was recorded. Sufficient number of source particles were tracked in the Monte Carlo simulations to provide a relative standard deviation of less than 1% (it varied typically from 0.3% to 0.75% at a detector pixel). Let us consider the plane passing through the center of the aluminum block (parallel to the radiographic film), at a depth of 30 mm in the object, as the focal plane of the
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system. For a detector located at 400 mm (axial object-todetector distance) from the focal plane, and a mask-todetector axial distance of 200 mm, a 66 66 mm2 field-ofview (FoV) at the focal plane is seen by the detector. Then, each pixel on the mask will be magnified by a factor of two. At this object-to-detector distance, the projection of a single mask pixel on the detector would cover 2 2 detector pixels. Therefore, the sampling ratio, a, (defined as the number of detector pixels covered by the projection of a single mask pixel) is equal to two. In order to achieve a perfect reconstruction, the value of a should be an integer. Obviously, the object-to-detector distance varies at different planes in the object. The projected data, therefore, encodes information from all planes in the object. However, only one depth at a time can be reconstructed perfectly, since each projected plane is associated with a different value of a. Integer values of a, for all depths in the object, can be ensued by accordingly changing the objectto-detector distance, or when possible by altering the detector’s pixel size (Thangavelu, 2006).
2.5. Decoding For the geometry shown in Fig. 1, the projection data, P, in Eq. (1) was calculated from Monte Carlo simulations. The flux recorded at each detector pixel was formulated into a matrix, P, which was fed into a decoding algorithm that performed the correlation: P G, where G is a predetermined decoding matrix for the employed MURA mask (Gottesman and Fenimore, 1989). In this work, the decoding algorithm reported in the thesis of Accorsi (2001) was employed. A 33 33 MURA pattern was utilized. This pattern was formulated by a 2 2 mosaic of a basic 17 17 MURA mask pattern; the A and G matrix for which are graphically shown in Fig. 2. Note that the 2 2 arrangement produces a 33 33 array, since one row and
one column are removed to avoid the aliasing problem (the projection of two object points on the same detector point). 3. Flaw indicators Below we present results that demonstrate the detectability and localization of single and multiple flaws from coded radiographic indications. In addition, the technique’s ability to detect changes in flaw size and density is also illustrated. 3.1. Single flaw Let us consider a 1.5 mm spherical flaw located at the center of the focal plane of the aluminum block of Fig. 1. Monte Carlo results for the detector flux are shown in Fig. 3(a). This is the ‘‘difference indication’’, i.e. the signal for the object with flaw minus the signal obtained for a flawless reference object. The combined Monte Carlo statistical error for this difference indications was in the range of 0.42–1.07% fractional standard deviation per pixel. Nevertheless, the detected signal is quite diffused and there is no obvious indication for the presence of the flaw. The decoded indication for the same difference indication is shown in Fig. 3(b). One can see clearly that the presence of a flaw is reflected by a strong dip in the decoded indication, caused by the removal of radiation that would have otherwise been scattered to the detector. Moreover, the flaw’s dip is immediately followed by a peak; the same trend was observed in the energy coded indication reported by Jama and Hussein (1999). The presence of the peak is due to the increase in the photon flux in the region directly downstream of the flaw caused by the lack of radiation attenuation within the flaw region. The position of the dip identifying a flaw on the indication corresponds to the flaw position on the focal plane. It should be noted that with a 2 mm wide beam, the 1.5 mm flaw was the smallest
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Fig. 2. A graphic representation of the encoding array, A, and the decoding array, G, for a 17 17 MURA. For A: ‘‘white’’ designates an open pixel, and ‘‘black’’ an opaque one. For G : ‘‘white’’ refers to a þ1 value, and ‘‘grey’’ to a value of 1.
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Fig. 3. Raw difference indication and corresponding decoded indication for a 1.5 mm spherical flaw. The horizontal axes in this and subsequent graphs refer to image pixels.
observable flaw size. Statistical analysis (Thangavelu, 2006) showed that this flaw size was still detectable even with the extreme combination of statistical bounding within one standard deviation, i.e. when taking the difference between the high statistical bound of the signal for an object containing the flaw and that of the lowest bound of the flawless object. Small flaws result in much weaker indications that were difficult to descramble. A smaller beam size will allow the detection of smaller flaws: with an infinitesimally single-ray pencil beam, a flaw as small as 0.5 mm in size was detectable (Thangavelu, 2006).
3.2. Size To examine the effect of flaw size on the decoded indication, simulations were also conducted for 2, 4, 6 and 8 mm diameter spherical flaws located at the center of the aluminum block. The results are shown in Fig. 4. As one would expect, the flaw size affects the magnitude and the width of the dip associated with the flaw. The indications shown in Fig. 4 suggest that one may be able to quantify the flaw size. It is obvious from Fig. 4 that the width and the magnitude of the dip increase with the flaw size. Increasing the size of the flaw removes more radiation that would have otherwise been scattered to the detector, and therefore the magnitude of the dip deepens with the increase in flaw size. But the depth of the dip also changes with the flaw location, as a flaw located closer to the radiation source will remove more radiation than a flaw farther away. However, this effect can be accounted for, once the flaw location is determined.
3.3. Location The position of the dip in the decoded image indicates the location of the flaw. In order to verify this, two locations of a 2 mm diameter flaw were considered, at distances of 11.18 and 44.72 mm along the source beam, measured from its point of entry. The decoded indications for these two cases are shown in Fig. 5. These flaws were considered one at a time, with the focal plane passing by the flaw location for best clarity. The change in the flaw location is reflected in the decoded indication by the change in the position of the dip. It should be kept in mind that these two flaw positions are determined by the position of the dip and the direction of the incident radiation beam, as explained further in Section 4.1. The simultaneous presence of more than one flaw along the beam path can also be detected, as shown in Fig. 6. Two flaws of size 2 mm and 3 mm located 22.36 mm and 33.50 mm, respectively, along the source beam path were considered. In this case, the focal plane was associated with the location of one of the flaws, the 3 mm flaw. Instead of seeing a single dip for a single flaw, one observes multiple dips, the position and width of such dips represent the corresponding flaw location and size, respectively. The lower magnitude of the dip for the 3 mm flaw is due to attenuation and divergence of the radiation source, since that flaw exists deeper in the object. 3.4. Density A flaw could be due to a complete removal of material, resulting in an internal void, or it can be the result of
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Fig. 4. Decoded indications for different flaw sizes; notice the change of magnitude in the vertical axes.
reduction of material density due to corrosion or erosion, or the migration of some foreign material. A flaw can also be the result of an undesirable inclusion of a higher density material. Such flaws can be caused by either material failure or manufacturing deficiencies. Although corrosion and erosion are usually encountered at the material surface and spread over a wide area, for theoretical determination of this technique’s ability, we considered localized flaws within an object. Within the object of Fig. 1, a uniform aluminum block of density 2700 kg=m3 , the density of a 2 mm flaw at the center of the object was changed from
zero (for void) to 11; 400 kg=m3 . The decoded difference indications are shown in Fig. 7. It is obvious that when the flaw is a void, a strong dip appears, while an inclusion with slightly lower density than that of the surrounding material produces a dip with a much lower magnitude than that for the void. On the other hand, for an inclusion with higher density than the object’s material, the decoded indication becomes a peak. One can also note that the sharp peak of an inclusion is followed by a sharp dip, due to the reduced radiation intensity induced by the inclusion.
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Fig. 5. Decoded indications for two different flaw locations.
4.1. Flaw Location
Fig. 6. Decoded indication for two flaws (2 mm and 3 mm) located along the same source beam.
4. Quantification The results presented above showed that the coded aperture technique could resolve the presence of a flaw, and changes in its size and location. However, in many applications, it is desirable to obtain quantitative information about the flaw location and its size. Since the coded aperture technique involves numerical data, it lends itself to further processing to determine other relevant quantifiable parameters.
As Fig. 1 shows, a narrow beam is used to scan the object. A detected flaw indication would then correspond to a flaw along the incident beam. Flaw localization is therefore concerned with determining the depth of the detected flaw along the incident beam. This is obtained by finding the intersection of the focal plane with the incident source beam. Consequently, it is crucial to determine the focal plane. By decoding the measurements at different hypothetical planes across the examined object, one can find the plane that provides the sharpest dip, which in turn defines the focal plane. The sharpest dip is the one that corresponds to the maximum dip magnitude, and minimum spurious sidelobes. Once the focal plane is determined, the location of the flaw can be further confirmed by the position of the dip on the decoded indication. The decoded indication can be scaled to the object space by knowing the FoV. For example, at a depth of 30 mm in the object, the FoV of the system is 66 66 mm2 , and the size of each image pixel is approximately 1 1 mm2 . The pixels corresponding to the dip in the decoded indication would then locate the flaw in the object. This procedure was adopted for the 2 mm wide flaw located at different depths in the object and the results obtained are shown in Table 1. The scaling process and the other statistical uncertainties with the obtained indications resulted in some error in determining the flaw location, as the results of Table 1 show. 4.2. Flaw size As Fig. 4 showed, the width of a flaw dip increases with the flaw size. To measure the width of the flaw dip, one can
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Fig. 7. Decoded indications for different flaw densities (r); note the change of magnitude in the vertical axes.
Table 1 Estimated depths (along beam path) for flaw located at different locations along an incident beam Estimated depth (mm)
Actual depth (mm)
13.34 23.7 35.77 47.29
11.18 22.36 33.50 44.72
utilize its full-width-at-half-maximum (FWHM). However, to relate the value of the FWHM to the flaw size, some calibration method is required. This calibration can be done by recording the scatter indication from an isolated rod (called here a scatterer) of known size, preferably made of the same material as the inspected object. The scatterer provides a ‘‘positive’’ source that increases the scattering signal, unlike a flaw which reduces the signal strength. However, a scatterer provides a clean signal
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5. Conclusions
Fig. 8. Decoded indication for a 2 mm diameter aluminum rod.
This work demonstrated, at least conceptually, that the coded aperture technique, originally developed for far-field imaging of weak point sources, is applicable to the nearfield (radiation emanating from nearby) problem of oneside scatter imaging. This technique was assessed using independent data obtained from Monte Carlo simulations, with a well-collimated 2 mm wide beam extracted from a 137 Cs isotopic source made incident on a 60 60 60 mm3 aluminum block with simulated flaws. A 33 33 MURA mask along with a digitizable radiographic plate were assumed to be used. It was shown that flaws as small as 1.5 mm in size were resolvable with this technique. Changes in flaw size, location and density were detectable, and the presence of multiple flaws was discernible. Methods were presented to quantify the flaw location and size. The promising results of this numerical study should encourage further exploitation of the coded aperture technique to overcome the problems of weak and diffused indications associated with single-side scatter radiography. Acknowledgments
Table 2 Estimated flaw size for the indications of Fig. 4 Estimated width (mm)
Actual width (mm)
1.75 3.25 5.25 7.25
2.0 4.0 6.0 8.0
This work was supported by grants to the second author from the New Brunswick Innovation Foundation (NBIF) and Natural Sciences and Engineering Research Council of Canada (NSERC). References
free from the influence of surrounding material, and in effect resembles on the limit (i.e. at zero radius) a point source. Fig. 8 gives the decoded indication obtained for a 2 mm wide aluminum scatterer, giving a calculated FWHM of 8.5 mm on a particular indication scale. Repeating this process for scatterers of various known sizes and extrapolating the results to a point source, one obtains the system’s point spread function, which was found to have a FWHM of 6.75 mm in this indication scale (Thangavelu, 2006). Note that this value does not correspond to the system’s resolution, since it was measured on an arbitrary scale. By subtracting the FWHM for the point source from that of the dip of a flaw of unknown size, one can estimate the flaws size (i.e. the equivalent diameter if the flaw were spherical). Applying this procedure for the indications of Fig. 4, the estimated flaw size was obtained and reported in Table 2 versus the actual size. One can see that in all cases, this approach slightly underestimates the actual flaw size. The discrepancy between the actual and estimated values is beyond what can be attributed to statistical error and the propagation of error during decoding, and is likely due to the application of FWHM to an non-symmetrical distribution. Nevertheless, one can deduce a reasonable estimate of the flaw size.
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Applied Radiation and Isotopes 65 (2007) 189–198 www.elsevier.com/locate/apradiso
Flaw detection by spatially coded backscatter radiography Sivakumar Thangavelu, Esam M.A. Hussein Laboratory for Threat Material Detection, Department of Mechanical Engineering, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada Received 27 June 2006; received in revised form 4 August 2006; accepted 14 August 2006
Abstract Backscatter imaging is useful for inspecting structures that are accessible only from one side. However, indications provided by scattered radiation are typically weak, convoluted and difficult to interpret. This paper explores the use of the coded aperture technique to detect flaws using gamma-ray backscatter imaging. The viability of this approach is demonstrated with indications obtained from Monte Carlo simulations of radiation scattering measurements. The results show that, with a 2 mm wide beam of 137Cs photons, flaws as small as 1.5 mm in width can be detected using this technique. Indications of changes in flaw size, location, multiplicity and density were also observable. In addition, it is possible to quantify, from the decoded indications, the flaw location and its size. r 2006 Elsevier Ltd. All rights reserved. PACS: 87.59.Hp; 25.20.Dc; 78.70.g Keywords: Digital radiography; Compton backscattering; Coded aperture
1. Introduction Conventional radiography relies on monitoring radiation transmitted through an object from one end to another. Such access to two opposite sides is not always readily available. Moreover, conventional radiography cannot be used to inspect objects that are too thick to allow sufficient amount of transmitted radiation to register a useful image. Therefore, structures such as airframes, bridges, pressure vessels, floors, layered structures, etc., do not benefit from traditional radiographic imaging. Ultrasonic inspection can be utilized in some cases, but the need for direct contact and coupling and the strong dispersion of sound waves in the presence of interfaces limit its application. The scattering of X-rays and gamma-rays offers an attractive alternative to conventional imaging technology, as it allows inspection from one side of an object and also provides density-dependent indications as in transmission radiography. However, indications from scattered radiation are not as straightforward to be Corresponding author. Tel.: +1 506 447 3105; fax: +1 506 453 5025.
E-mail address: [email protected] (E.M.A. Hussein). 0969-8043/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2006.08.008
geometrically back-projected to deduce geometric and density indications, as in the case with radiation transmission. Although effort has been made to devise systems to facilitate the extraction of useful indications from scattered radiation, as discussed by Lawson (2002), and more recently by Banerjee and Dunn (2005), the convoluted indication makes scatter radiography quite difficult. The obscurity of scatter indications is to some extent similar to that encountered in astronomical imaging of space objects using photons of energy above 10 keV, where it is common to register weak indications that are overwhelmed by interferences. It is therefore worth considering some of the image extraction methods employed in astronomical imaging. One of those is the coded aperture technique that has been used in astronomy for number of years (Caroli et al., 1987). The same technique has also been used more recently in medical imaging (Accorsi et al., 2001; Zhang et al., 1999), to detect contraband in luggage from neutron-induced activation (Zhang and Lanza, 1999), and to observe gamma-ray sources (Rennie, 2006). In addition, coded aperture has also been utilized in imaging emissions from low-intensity gamma-ray sources (Smith et al., 2001; Woodring et al.,
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1999). To the authors’ knowledge, the coded aperture approach has not been considered before for use with scattered radiation to detect flaws; except in the case of detecting concealed large objects, such as landmines (Faust and Rothschild, 2003). Prior to experimental application of the coded aperture method to radiographic imaging with scattered radiation, it is vital to demonstrate its feasibility using numerical simulations. This is the objective of the work presented here, which begins with a summary of the difficulties of imaging with scattered radiation and a brief introduction to the coded aperture concept. 2. Background 2.1. Scatter imaging Backscatter imaging involves directing a radiation source towards an object and recording on the same side radiation scattered off the object. To avoid direct exposure of the radiation receiver (a film or a radiographic plate), a shielding material is placed in between the source and the receiver. Note that, unlike in transmission radiography, where only one image can be acquired with each radiation exposure, more than one record can be simultaneously obtained in scatter imaging at different directions. However, scatter imaging is disadvantaged by the fact that an anomaly in the object can leave an imprint at more than one location on the receiver. These indicators are difficult to trace back, since the radiation causing them would have encountered many changes in direction before reaching the detector. Nevertheless, by using radiation collimation and/ or energy discrimination, only once-scattered events can be recorded, which greatly simplifies the imaging process by geometrically relating the recorded signal to the position of scattering; as shown by Hussein (2003, Chapter 7). This comes however at a much reduced signal, since the probability of radiation encountering a single collision is quite low. Allowing the detection of multi-scattered photons increases the strength of the recorded signal, but at the same time completely dilutes the position (location of scattering) information provided by single scattering. However, as in photography, where the light source is widely spread, a ‘‘camera’’ may be used to project an image of the strength of the scattered radiation, to reflect the spatial and material features of the scattering medium. 2.2. Coded aperture imaging Unlike light, radiation cannot be focused with a lens, unless it has a very low energy where its use is limited to surface imaging of lattice structures. Radiation scattered from deep within an object can however be localized with the aid of a pinhole camera (Lawson, 2002), where an anomaly can be detected and its direction identified by the change in the intensity of its projected image as the camera scans the object. However, indications obtained from a
pinhole are quite weak, since only a small portion of the signal induced by the anomaly can reach the camera. Of course, a larger pinhole can be used to strengthen the detected signal, but this will come at the expense of reduced definition of directionality. Even if an acceptable signal is attained, only the direction of the anomaly can be determined (along the lines connecting the edges of the projected indication to those of the pinhole). Nevertheless, if a number of images are obtained at different pinhole locations, the intersection of all the determined directions defines the position of the anomaly. This approach, however, does not overcome the inherent problem of the weakness of the indication. In astrophysics, where astronomical X-rays are used to image the sky, the problem of a weak signal is overcome by employing multiple pinholes arranged in a particular fashion into a plate (In’t Zand, 2006). This concept is known as coded aperture, since in effect the recorded indication is ‘‘encoded’’ by the mask pattern. A numerical algorithm is then applied to ‘‘decode’’ the recorded indication, hence determine the location and the brightness of an astronomical object. Radiation projected through the mask creates a pattern, P, on the detector, which is related to the spatial distribution of the object’s radiation intensity, represented via a matrix O by (Accorsi, 2001) O A ¼ P,
(1)
where A is a matrix representing the mask pattern and is the correlation operator. In other words, the mask ‘‘encodes’’ the radiation signal before it is recorded by the detector. It should be noted that Eq. (1) is exactly true when the object is very far away from the mask and the detector, i.e. for far fields. To recover the features of the original radiation source from the projected data, the recorded signal must be decoded. This is done with the aid of a decoding matrix, G, which is such that A G ¼ d,
(2)
where d is the Dirac delta function. The reconstructed ^ is recovered from the projection, P, by image, O, ^ ¼ P G ¼ ðO AÞ G ¼ O ðA GÞ, O
(3)
where is the convolution operator, and the proof of the last step of Eq. (3) is given by Accorsi (2001). Substituting ^ ¼ O d ¼ O, i.e. the Eq. (2) into Eq. (3) leads to: O reconstructed image resembles exactly the object. This perfect matching is obtained if, and only if, Eq. (2) is satisfied. A random mask pattern would not satisfy Eq. (2), and would result in a point-response function which is not a d function. However, a mask pattern can be devised to satisfy Eq. (2), as in the case of a mask formed from uniformly redundant arrays, the so-called URA mask pattern. In addition, the mask pattern, A, should be chosen to minimize the propagation of noise. In this work, a mask pattern based on modified uniformly redundant arrays (MURA) was chosen, as it was deemed to be suitable for near-field projections, such as those associated with
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radiation emerging from nearby objects (Accorsi, 2001; Faust and Rothschild, 2003). MURA consists of cyclically shifted uniform patterns, with 50% open positions. It has decoding coefficients, G, that are modified from URA, so that the decoded indication is completely independent of noise (Gottesman and Fenimore, 1989). In astronomical imaging, the imaged object is at a very large distance from the mask and the detector. However, in near-field imaging, the object-to-mask distance must be known, in order to be able to scale the decoding array to match the dimensions of the projected pattern. Therefore, some plane in the object, parallel to the mask and the detector, needs to be designated as the focal plane.
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2.3. Concept In inspecting an object for the presence of flaws using radiation scattering, a flaw would reduce the intensity of the scattered radiation by the removal of material that would have caused radiation to scatter. If the scattered radiation is viewed as a radiation source, in the same manner the skylight is a source of photons, a flaw can be viewed as a ‘‘negative source’’; unlike light emission that presents a positive source with elevated light intensity. Indications imprinted by a flaw, like those of a faraway astronomical photon source, are quite feeble and would be buried in an overwhelming background caused by the scattering of radiation from all over the scattering medium. Employing the coded aperture technique may enable the detection of weak indications produced by the flaw, even in the presence of a high background. It is conceived here that a detector in the form of a radiographic plate is to be used to detect backscattered radiation from an object. A mask is to be placed in between the object and the detector, as shown in Fig. 1. Radiation scattered within the object will be seen by the detector as a secondary widespread source, provided of course that radiation from the primary source is blocked from reaching the detector. Then each point on the object that scatters radiation towards the detector will be viewed by certain pixels on the radiographic plate, due to radiation passing through open holes in the mask. Therefore, points in the object corresponding to a flaw will affect many detector pixels in a correlated manner. This correlated signal on subsequent decoding should indicate the presence of the flaw and its spatial location, in spite of the uncorrelated scattering emerging from other flawless points in the object. In order to demonstrate the feasibility of this concept, Monte Carlo simulations were conducted with a geometric setup as depicted in Fig. 1. Monte Carlo simulations with the MCNP code (X-5 Monte Carlo Team, 2003) provide faithful representation of the physical interaction processes without being hindered by practical interference and difficulty. While proving the feasibility of the concept with such simulations is not necessarily affirmative of its practicability, a technique that is not functionally demonstrable with simulations is most likely not viable. Monte
Detector (Radiographic plate) Fig. 1. Geometric setup for coded backscatter radiography (the checkboard mask pattern shown here is simply symbolic of the presence of a mask and is not the actual one simulated in this work).
Carlo simulations also enable the testing of the numerical tools necessary for the decoding process. 2.4. Simulation setup A 2 mm wide well collimated beam of photons emerging from a 137Cs source, which emits 662 keV photons, was directed towards an aluminum block (60 60 60 mm3 ) containing spherical holes of various sizes simulating flaws. This was the same source type and width proposed by Jama and Hussein (1999) for optimal detection of flaws using energy-spectral measurements of scattered radiation. The source beam is assumed to scan the object progressively to cover a wide area. Note that a wider beam could have been used, but that will come at the expense of reduced contrast. A 33 33 MURA mask pattern formed by replicating a basic 17 17 MURA pattern, 2 2 times, was simulated, with each pixel being 1 1 mm2 in area. The mask was 4 mm in thickness, made of tungsten (19; 100 kg=m3 density) to block at least 78% of the incident radiation (Thangavelu, 2006). A MURA mask can be manufactured using photolithographic etching techniques (Cherry et al., 1999). The radiographic detector was considered to consist of a 70 70 mm2 radiographic plate divided into 70 70 equal pixels. For simplification, the detector was assumed to have a 100% efficiency, i.e. each photon passing through it was recorded. Sufficient number of source particles were tracked in the Monte Carlo simulations to provide a relative standard deviation of less than 1% (it varied typically from 0.3% to 0.75% at a detector pixel). Let us consider the plane passing through the center of the aluminum block (parallel to the radiographic film), at a depth of 30 mm in the object, as the focal plane of the
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system. For a detector located at 400 mm (axial object-todetector distance) from the focal plane, and a mask-todetector axial distance of 200 mm, a 66 66 mm2 field-ofview (FoV) at the focal plane is seen by the detector. Then, each pixel on the mask will be magnified by a factor of two. At this object-to-detector distance, the projection of a single mask pixel on the detector would cover 2 2 detector pixels. Therefore, the sampling ratio, a, (defined as the number of detector pixels covered by the projection of a single mask pixel) is equal to two. In order to achieve a perfect reconstruction, the value of a should be an integer. Obviously, the object-to-detector distance varies at different planes in the object. The projected data, therefore, encodes information from all planes in the object. However, only one depth at a time can be reconstructed perfectly, since each projected plane is associated with a different value of a. Integer values of a, for all depths in the object, can be ensued by accordingly changing the objectto-detector distance, or when possible by altering the detector’s pixel size (Thangavelu, 2006).
2.5. Decoding For the geometry shown in Fig. 1, the projection data, P, in Eq. (1) was calculated from Monte Carlo simulations. The flux recorded at each detector pixel was formulated into a matrix, P, which was fed into a decoding algorithm that performed the correlation: P G, where G is a predetermined decoding matrix for the employed MURA mask (Gottesman and Fenimore, 1989). In this work, the decoding algorithm reported in the thesis of Accorsi (2001) was employed. A 33 33 MURA pattern was utilized. This pattern was formulated by a 2 2 mosaic of a basic 17 17 MURA mask pattern; the A and G matrix for which are graphically shown in Fig. 2. Note that the 2 2 arrangement produces a 33 33 array, since one row and
one column are removed to avoid the aliasing problem (the projection of two object points on the same detector point). 3. Flaw indicators Below we present results that demonstrate the detectability and localization of single and multiple flaws from coded radiographic indications. In addition, the technique’s ability to detect changes in flaw size and density is also illustrated. 3.1. Single flaw Let us consider a 1.5 mm spherical flaw located at the center of the focal plane of the aluminum block of Fig. 1. Monte Carlo results for the detector flux are shown in Fig. 3(a). This is the ‘‘difference indication’’, i.e. the signal for the object with flaw minus the signal obtained for a flawless reference object. The combined Monte Carlo statistical error for this difference indications was in the range of 0.42–1.07% fractional standard deviation per pixel. Nevertheless, the detected signal is quite diffused and there is no obvious indication for the presence of the flaw. The decoded indication for the same difference indication is shown in Fig. 3(b). One can see clearly that the presence of a flaw is reflected by a strong dip in the decoded indication, caused by the removal of radiation that would have otherwise been scattered to the detector. Moreover, the flaw’s dip is immediately followed by a peak; the same trend was observed in the energy coded indication reported by Jama and Hussein (1999). The presence of the peak is due to the increase in the photon flux in the region directly downstream of the flaw caused by the lack of radiation attenuation within the flaw region. The position of the dip identifying a flaw on the indication corresponds to the flaw position on the focal plane. It should be noted that with a 2 mm wide beam, the 1.5 mm flaw was the smallest
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Fig. 2. A graphic representation of the encoding array, A, and the decoding array, G, for a 17 17 MURA. For A: ‘‘white’’ designates an open pixel, and ‘‘black’’ an opaque one. For G : ‘‘white’’ refers to a þ1 value, and ‘‘grey’’ to a value of 1.
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Fig. 3. Raw difference indication and corresponding decoded indication for a 1.5 mm spherical flaw. The horizontal axes in this and subsequent graphs refer to image pixels.
observable flaw size. Statistical analysis (Thangavelu, 2006) showed that this flaw size was still detectable even with the extreme combination of statistical bounding within one standard deviation, i.e. when taking the difference between the high statistical bound of the signal for an object containing the flaw and that of the lowest bound of the flawless object. Small flaws result in much weaker indications that were difficult to descramble. A smaller beam size will allow the detection of smaller flaws: with an infinitesimally single-ray pencil beam, a flaw as small as 0.5 mm in size was detectable (Thangavelu, 2006).
3.2. Size To examine the effect of flaw size on the decoded indication, simulations were also conducted for 2, 4, 6 and 8 mm diameter spherical flaws located at the center of the aluminum block. The results are shown in Fig. 4. As one would expect, the flaw size affects the magnitude and the width of the dip associated with the flaw. The indications shown in Fig. 4 suggest that one may be able to quantify the flaw size. It is obvious from Fig. 4 that the width and the magnitude of the dip increase with the flaw size. Increasing the size of the flaw removes more radiation that would have otherwise been scattered to the detector, and therefore the magnitude of the dip deepens with the increase in flaw size. But the depth of the dip also changes with the flaw location, as a flaw located closer to the radiation source will remove more radiation than a flaw farther away. However, this effect can be accounted for, once the flaw location is determined.
3.3. Location The position of the dip in the decoded image indicates the location of the flaw. In order to verify this, two locations of a 2 mm diameter flaw were considered, at distances of 11.18 and 44.72 mm along the source beam, measured from its point of entry. The decoded indications for these two cases are shown in Fig. 5. These flaws were considered one at a time, with the focal plane passing by the flaw location for best clarity. The change in the flaw location is reflected in the decoded indication by the change in the position of the dip. It should be kept in mind that these two flaw positions are determined by the position of the dip and the direction of the incident radiation beam, as explained further in Section 4.1. The simultaneous presence of more than one flaw along the beam path can also be detected, as shown in Fig. 6. Two flaws of size 2 mm and 3 mm located 22.36 mm and 33.50 mm, respectively, along the source beam path were considered. In this case, the focal plane was associated with the location of one of the flaws, the 3 mm flaw. Instead of seeing a single dip for a single flaw, one observes multiple dips, the position and width of such dips represent the corresponding flaw location and size, respectively. The lower magnitude of the dip for the 3 mm flaw is due to attenuation and divergence of the radiation source, since that flaw exists deeper in the object. 3.4. Density A flaw could be due to a complete removal of material, resulting in an internal void, or it can be the result of
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Fig. 4. Decoded indications for different flaw sizes; notice the change of magnitude in the vertical axes.
reduction of material density due to corrosion or erosion, or the migration of some foreign material. A flaw can also be the result of an undesirable inclusion of a higher density material. Such flaws can be caused by either material failure or manufacturing deficiencies. Although corrosion and erosion are usually encountered at the material surface and spread over a wide area, for theoretical determination of this technique’s ability, we considered localized flaws within an object. Within the object of Fig. 1, a uniform aluminum block of density 2700 kg=m3 , the density of a 2 mm flaw at the center of the object was changed from
zero (for void) to 11; 400 kg=m3 . The decoded difference indications are shown in Fig. 7. It is obvious that when the flaw is a void, a strong dip appears, while an inclusion with slightly lower density than that of the surrounding material produces a dip with a much lower magnitude than that for the void. On the other hand, for an inclusion with higher density than the object’s material, the decoded indication becomes a peak. One can also note that the sharp peak of an inclusion is followed by a sharp dip, due to the reduced radiation intensity induced by the inclusion.
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Fig. 5. Decoded indications for two different flaw locations.
4.1. Flaw Location
Fig. 6. Decoded indication for two flaws (2 mm and 3 mm) located along the same source beam.
4. Quantification The results presented above showed that the coded aperture technique could resolve the presence of a flaw, and changes in its size and location. However, in many applications, it is desirable to obtain quantitative information about the flaw location and its size. Since the coded aperture technique involves numerical data, it lends itself to further processing to determine other relevant quantifiable parameters.
As Fig. 1 shows, a narrow beam is used to scan the object. A detected flaw indication would then correspond to a flaw along the incident beam. Flaw localization is therefore concerned with determining the depth of the detected flaw along the incident beam. This is obtained by finding the intersection of the focal plane with the incident source beam. Consequently, it is crucial to determine the focal plane. By decoding the measurements at different hypothetical planes across the examined object, one can find the plane that provides the sharpest dip, which in turn defines the focal plane. The sharpest dip is the one that corresponds to the maximum dip magnitude, and minimum spurious sidelobes. Once the focal plane is determined, the location of the flaw can be further confirmed by the position of the dip on the decoded indication. The decoded indication can be scaled to the object space by knowing the FoV. For example, at a depth of 30 mm in the object, the FoV of the system is 66 66 mm2 , and the size of each image pixel is approximately 1 1 mm2 . The pixels corresponding to the dip in the decoded indication would then locate the flaw in the object. This procedure was adopted for the 2 mm wide flaw located at different depths in the object and the results obtained are shown in Table 1. The scaling process and the other statistical uncertainties with the obtained indications resulted in some error in determining the flaw location, as the results of Table 1 show. 4.2. Flaw size As Fig. 4 showed, the width of a flaw dip increases with the flaw size. To measure the width of the flaw dip, one can
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Fig. 7. Decoded indications for different flaw densities (r); note the change of magnitude in the vertical axes.
Table 1 Estimated depths (along beam path) for flaw located at different locations along an incident beam Estimated depth (mm)
Actual depth (mm)
13.34 23.7 35.77 47.29
11.18 22.36 33.50 44.72
utilize its full-width-at-half-maximum (FWHM). However, to relate the value of the FWHM to the flaw size, some calibration method is required. This calibration can be done by recording the scatter indication from an isolated rod (called here a scatterer) of known size, preferably made of the same material as the inspected object. The scatterer provides a ‘‘positive’’ source that increases the scattering signal, unlike a flaw which reduces the signal strength. However, a scatterer provides a clean signal
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5. Conclusions
Fig. 8. Decoded indication for a 2 mm diameter aluminum rod.
This work demonstrated, at least conceptually, that the coded aperture technique, originally developed for far-field imaging of weak point sources, is applicable to the nearfield (radiation emanating from nearby) problem of oneside scatter imaging. This technique was assessed using independent data obtained from Monte Carlo simulations, with a well-collimated 2 mm wide beam extracted from a 137 Cs isotopic source made incident on a 60 60 60 mm3 aluminum block with simulated flaws. A 33 33 MURA mask along with a digitizable radiographic plate were assumed to be used. It was shown that flaws as small as 1.5 mm in size were resolvable with this technique. Changes in flaw size, location and density were detectable, and the presence of multiple flaws was discernible. Methods were presented to quantify the flaw location and size. The promising results of this numerical study should encourage further exploitation of the coded aperture technique to overcome the problems of weak and diffused indications associated with single-side scatter radiography. Acknowledgments
Table 2 Estimated flaw size for the indications of Fig. 4 Estimated width (mm)
Actual width (mm)
1.75 3.25 5.25 7.25
2.0 4.0 6.0 8.0
This work was supported by grants to the second author from the New Brunswick Innovation Foundation (NBIF) and Natural Sciences and Engineering Research Council of Canada (NSERC). References
free from the influence of surrounding material, and in effect resembles on the limit (i.e. at zero radius) a point source. Fig. 8 gives the decoded indication obtained for a 2 mm wide aluminum scatterer, giving a calculated FWHM of 8.5 mm on a particular indication scale. Repeating this process for scatterers of various known sizes and extrapolating the results to a point source, one obtains the system’s point spread function, which was found to have a FWHM of 6.75 mm in this indication scale (Thangavelu, 2006). Note that this value does not correspond to the system’s resolution, since it was measured on an arbitrary scale. By subtracting the FWHM for the point source from that of the dip of a flaw of unknown size, one can estimate the flaws size (i.e. the equivalent diameter if the flaw were spherical). Applying this procedure for the indications of Fig. 4, the estimated flaw size was obtained and reported in Table 2 versus the actual size. One can see that in all cases, this approach slightly underestimates the actual flaw size. The discrepancy between the actual and estimated values is beyond what can be attributed to statistical error and the propagation of error during decoding, and is likely due to the application of FWHM to an non-symmetrical distribution. Nevertheless, one can deduce a reasonable estimate of the flaw size.
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