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Quantification of gamma-ray Compton-scatter nondestructive testing
Applied Radiation and Isotopes 53 (2000) 541±546
www.elsevier.com/locate/apradiso
Quanti®cation of gamma-ray Compton-scatter nondestructive testing A.C. Ho, E.M.A. Hussein* Department of Mechanical Engineering, University of New Brunswick, PO Box 4400, Fredericton, NB, Canada E3B 5A3
Abstract A method is presented for quantifying information obtained from the indications of a Compton scattering nondestructive testing technique. This is achieved by formulating a measurement model, which provides a numerical estimate of the detector response for a given anomaly. Using the measured response function, the location of an anomaly, its size and density are obtained with the aid of the model. The process is demonstrated by quantifying indications obtained from experimental measurements for ¯aws arti®cially created in an aluminum block. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Nondestructive testing; Compton scattering; Measurement models
1. Introduction Radiography and tomography are now common forms of nondestructive testing (NDT) with radiation. Both methods rely on radiation transmission, requiring the source and the detection device to be placed at two opposite sides of the inspected object. However, there are situations in which access to both sides of the object is not possible, such as in extended or thick structures. Scattering techniques, particularly those based on Compton scattering of photons, have been emerging to deal with such situations, as evident by the 65 abstracts of work published between 1988 and 1994 (NDT&E, 1995). However, scattering measurements are modulated by the attenuation of radiation as it enters and leaves the inspected object. This makes
* Corresponding author. Tel.: +1-506-447-3105; fax: +1506-447-3380. E-mail address: [email protected] (E.M.A. Hussein).
it dicult to obtain quantitative information without a complete and complex imaging process; as was done by Prettyman et al. (1993) and Arendtsz and Hussein (1995). However, imaging is not necessary in many NDT applications where the objective is to ®nd and locate anomalies, which are typically limited within a small volume in an object with otherwise known features. Nevertheless, imaging provides quantitative information that is necessary in modern qualityassurance and monitoring programs that require documentation that is less subjective to personal interpretation, preferably in the form of speci®c numerical values. Most previous work on Compton Scattering NDT provided a quantitative signal indicating the nature of a detected anomaly. This work presents an approach to provide quantitative information regarding the location, size and density of a detected anomaly, that are more de®nitive and easier to document. We begin ®rst by a brief description of the NDT Compton Scatter method.
0969-8043/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 0 ) 0 0 2 1 3 - X
542
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
2. Compton-scatter NDT Compton scattering (CS) is a viable tool for inspecting industrial objects, since it is an interaction which is strongly dependent on the electron density of the scattering medium, and in turn, its mass density. A number of CS±NDT systems have been reported (NDT&E, 1995). In most techniques, a pencil beam of photons is employed to de®ne the path of the incident beam, while either a well-collimated or an open detector is used. With the former, the inspection volume is de®ned by the intersection of the ®eld-of-view of the incident beam with that of the detector's collimator, resulting in the inspection of one ``point'' at a time. When the detector is not fully collimated, an energy-sensitive detector can be used. With proper selection of the source energy, single-scatter photons can be made to dominate. Then, the energy of the detected once-scattered photons can be related to their angle-of-scattering using the well-known Compton scattering kinematics relationship: E y
E0 E0 1 1 ÿ cos y m0 c 2
1
where E0 is the incident photon energy, E(y ) is the energy of photons scattered by angle y and m0c 2 is the rest-mass energy of the electron (0.511 MeV). This relationship produces, in eect, a ``soft-collimation'' process, by virtue of the fact that each detected energy window corresponds to a particular direction of scattering. Thus, many ``points'' along the incident beam can be simultaneously inspected. This approach has been adopted by a number of workers (e.g., Anghaie et al., 1990; Jama and Hussein, 1998), and its con®guration is depicted schematically in Fig. 1. In order to avoid ambiguity when relating the energy to angle of scattering using Eq. (1), Jama and Hussein (1998) con®ned the detector to almost a point, using a wedgeshaped detector collimator. Therefore, more de®nitive
Fig. 1. A schematic of a wide-angle Compton-scatter inspection system.
information about anomaly detection, location, and sizing were obtained. The quanti®cation process developed here applies to the con®guration of Jama and Hussein (1998), but can be easily extended to other arrangements. A ``measurement model'' is formulated in the next section to provide a numerical estimate of the detector response for a given anomaly size. The model is then applied to quantify indications obtained from experimental results, to provide the size and density of a detected anomaly. The location of an anomaly is directly determined from the angle of scattering corresponding to its measured indication, with the aid of Eq. (1).
3. Measurement model In order to formulate a model simulating the CS process, scattering within an in®nitesimal volume, DV, around a point is considered, as schematically shown in Fig. 2. It is assumed that only single-scatter events contribute to the detector's response; multi-scattered photons suer more energy loss and can be excluded from the monitored energy range. The intensity of the photons scattered to the detector per unit source (the detector's response, S ) can be expressed as, guided by Fig. 2, as: x in p m S KS0 `r exp ÿ Sin r dx 2 2pR 0 2 exp ÿ
yout
0
Sout r dy
where K is a normalization constant that accounts for laboratory aspects, such as the source strength, detector eciency, system geometry, etc., S0 is the Compton scattering cross-section with respect to a reference material, typically the object being inspected, and r is the density at the inspected point relative to the reference material, Sin and Sout are the total cross-sections of the material present along the distances xin and yout, respectively (see Fig. 2), l is the width of DV along the incident beam path, p(m ) dm is the probability of scattering about angle cosine m within m2dm, with scattering in the azimuthal direction being isotropic, and R is the distance from the scattering point to the detector. The exponential terms in Eq. (2) account for the attenuation of photons as they travel toward the inspection point and away from it. The term S0 l represents the scattering rate per unit area within DV, normalized to that of the reference material. The scattering probability and the divergence of the scattered photons are accounted for in the term p(m )/2pR 2. The above model was veri®ed against Monte Carlo
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
simulations, reported by Ho (1999), and was shown to adequately represent the physical aspects of the problem. The measurement model of Eq. (2) enables the determination of the relative density of the inspected from the measurement, S, since all other parpoint, r, ameters in the model equation can be determined inde given S, was pendently. Simple iterative solution for r, readily implemented, both on a hand-held programable calculator and in a Fortran program. However, the peaking nature of the right-hand-side of Eq. (2), as it leads to two possible solutions. Fortuchanges with r, nately, one of the solutions results in an unrealistically which can be discarded. However, high value of r, starting with a physically appropriate initial guess for r led always to the correct solution, as was veri®ed by Ho (1999) in the solution of Eq. (2) using Monte Carlo simulated results. The application of the model, and the other aspects of the quanti®cation process, to experimentally measured data is discussed below. 4. Application to experiment data In NDT, the ®rst step is to determine whether an anomaly (usually a crack) is present or not. This is achieved in CS±NDT by observing whether an abrupt change (a reversed peak for a crack) occurs in the measured energy spectrum of the scattered photons (Jama and Hussein, 1998). This change is further elucidated by subtracting the measured spectrum from that corresponding to a ¯awless reference object. The shape of the obtained indication signal can also reveal information on the nature of the anomaly, e.g., a sharp crack or a smooth ¯aw. The second step is to determine the location of the detected anomaly. This is easily done in CS±NDT with the aid of Eq. (1), using
543
the energy corresponding to the indication peak to determine the angle of scattering and from geometry calculate the central location of the anomaly. Thirdly, one needs to determine the size of the anomaly, and this can be estimated from the width of the peak. Finally, in quantitative NDT, one needs to know the density of the material that occupies the anomaly, which is related to the height (strength) of the peak, and can be obtained by solving the measurement Before utilizing this model, one model, Eq. (2) for r: must obtain a value for the normalization constant, K, which relates the model to the experimental parameters. This constant was determined with the aid of small aluminum rods used to represent a scattering point in the path of the incident beam. The ratio between the measured indication spectrum for a scattering rod and that obtained using the measurement model of Eq. (2) provided an estimate of K. The above procedure was applied to the experimental results obtained by Jama (1997), who used a collimated 137Cs source and a high purity germanium detector con®ned with a wedge-shaped collimator. The results are reported in detail by Ho (1999). In this process, it was found necessary to introduce adjustment factors to account for the divergence of the incident beam, and the fact that some of the incident photons miss hitting the surface of a rod due to the divergence process. This section shows how the above NDT quanti®cation steps were applied to the experimental results obtained by Jama (1997) for arti®cially created ¯aws of dierent sizes, each representing a cylindrical void, drilled separately in 60 50 50 mm3 aluminum blocks. More applications are reported elsewhere (Ho, 1999). The experimentally obtained net indications (that is, the dierence between the measured signal
Fig. 2. A schematic of scattering at a point.
544
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
and that of the reference block) are shown in Fig. 3. Qualitatively, one can tell from the indications of Fig. 3 that the present anomalies have a density less than that of the reference material, given the negative count rate resulting from the subtraction process. The smooth nature of the reversed peaks indicates also that the ¯aws have a smooth surface; otherwise, a jagged indication would have been observed. One can also observe that the ¯aws have dierent sizes, as re¯ected by the change in the width of the reversed peaks. To quantify this size, determine the location of the ¯aw, and obtain an estimate of the density of the ¯aw material (which should have been zero), the procedures presented below were applied.
4.1. Location The energy corresponding to the bottom of the four reversed peaks of Fig. 3, were used in Eq. (1) to obtain the angle of scattering, which was found to be about 78.38 for the four ¯aws. This corresponded well with the actual location of the ¯aws, which were experimentally set by Jama (1997) to measure scattering at 77.58.
4.2. Size Fig. 3 shows an obvious increase in the width of the reversed peaks of the indications with increasing ¯aw size. The width of the anomaly can be represented by the parameter l in Eq. (2). However, obtaining a numerical value for this parameter requires the identi®cation of a proper measure of the peak width, since the width of the peak is also aected by the spread in the detector's response function caused by the incomplete energy deposition of photons. For simplicity, we adopted the well-known approach of full-width-at-halfmaximum (FWHM) as a measure of the peak width. This width provides two energy bounds in the indication spectrum, each of which corresponds to a dierent angle of scattering in accordance with Eq. (1). These angular bounds, along with the position of detector and angle of scattering, were used to geometrically calculate the width l. The obtained values are summarized in Table 1, compared with the actual diameter of the ¯aw. As the Table shows, the ¯aw size is overestimated. This is likely due to the application of the FWHM approach, which is usually used with symmetric peaks, to the slightly skewed peaks of the indications of Fig. 3. This skewness is caused by the
Fig. 3. Measured indications obtained by Jama (1997) for four void ¯aws, 1.58 mm (top curve), 3.23 mm (2nd top) 6.45 mm (2nd bottom) and 9.52 mm (bottom) in diameter, in an 60 50 50 mm3 aluminum block.
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
545
Table 1 Estimated width of ¯aws for indications of Fig. 3 Location of indication in Fig. 3
Estimated width (mm)
Actual diameter (mm)
Bottom 2nd Bottom 2nd Top Top
10.27 8.42 5.43 2.44
9.52 6.35 3.23 1.58
uneven attenuation of the incident photons within the area corresponding to the ¯aw in the reference block, which is used for obtaining the net indication. Nevertheless, the predicted ¯aw width is still indicative of the change in the ¯aw size. 4.3. Density Obviously the density of a voided ¯aw is zero. However, the indications of Fig. 3 do not directly indicate that, due to the spread of the indication peaks. In practice, it is also useful to estimate the ¯aw density. Determination of the ¯aw density, by solving directly using the measured detector response, is Eq. (2) for r, further complicated by the fact that the used indication is the result of subtracting the detector response for the reference specimen, S0, from that of the inspected specimen, S. However, after reversing the sign of the indication spectrum to obtain positive count rates, the relative density of the material in the ¯aw can be estimated from the following relationship: p m ` S0 ÿ S e1ÿ1 e3ÿ1 KS0 ` S exp ÿ S in out 2pR 2 2 r exp ÿSout r` ÿ exp ÿSin r` 3 where r0 is the mass density of the reference specimen and e1 and e3 are attenuation factors, respectively, of the incident radiation before reaching the ¯aw region and the scattered photons in their way to the detector, in both the reference and inspected specimens; all the other notations are as de®ned following Eq. (2). Eq. (3) is the result of subtracting the model of Eq. (2) when applied in the presence of a ¯aw of relative den from that applied to the reference specimen, sity r, and can be directly solved iteratively. For the indications of Fig. 3, the results shown in Table 2 were It should be noted that the detector reobtained for r: sponse values, S and S0, were obtained by integrating the ``negative'' counts under the reversed peaks of Fig. 3. As Table 2 shows, the density of the material within each ¯aw anomaly is quite small for the two largest ¯aws (bottom indications), but is not zero due to the
error in overestimating the ¯aw size. The latter error in the two smallest ¯aws is due to the signi®cant overestimation of the size as explained earlier. The above results show that the error in the ¯aw size has a strong in¯uence on the value of the estimated density. Ho (1999) further demonstrated this by utilizing the actual values of the ¯aw width (the diameter) in the solution of Eq. (3). The results were signi®cantly improved, but the estimated density for the two smallest ¯aws remained unsatisfactory. This was attributed to Jama's (1997) use of the same counting period for all ¯aw sizes, producing poorer counting statistics for the small ¯aws. Nevertheless, even with poor numerical values, one can still monitor progress in ¯aw propagation by comparing new numerical values for ¯aw size and density with old ones. 5. Conclusions An approach to quantifying indications obtained from Compton-scattering NDT system, which employed a collimated 137Cs gamma-ray source and a high-purity germanium detector, to examine ¯aws in a 60 50 50 mm3 aluminum block, was developed. Although the approach correctly determined the location of a ¯aw, it tended to overestimate its size, which in turn aected the obtained density of the material that occupies the ¯aw. This discrepancy is attributed to the use of the full-width-at-halfmaximum (FWHM) approach as a measure of the width of the slightly skewed indication peak, and in
Table 2 Relative density of ¯aw material estimated by solving Eq. (3) Relative density Location of indication in Fig. 3
Estimated
Actual
Bottom 2nd Bottom 2nd Top Top
0.103 0.229 0.25 0.843
0 0 0 0
546
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
turn the width of a ¯aw. In spite of the above dif®culties, the quanti®cation process of the Compton scatter NDT technique was reasonably successful. With some improvement in the processes of determining the ¯aw size, the quanti®cation process can be further improved. Therefore, future work should focus on replacing the FWHM method with a more adequate approach suitable for the skewed signals observed experimentally. Acknowledgements This work was supported by a grant to the second author from the Natural Sciences and Engineering Research Council of Canada. References Anghaie, S., Humphries, L.L., Diaz, N.J., 1990. Material characterization and ¯aw detection, sizing and location by
the dierential gamma scattering spectroscopy technique. Nuclear Technology 91, 361±387. Arendtsz, N.V., Hussein, E.M.A., 1995. Energy-spectral compton scatter imaging. IEEE Transactions on Nuclear Science 42, 2155±2172. Ho, A.C. 1999. Quanti®cation of gamma-ray Compton-scatter nondestructive testing. MScE Thesis, Mechanical Engineering, University of New Brunswick, Fredericton, Canada. Jama, H. 1997. Gamma-ray compton scatter nondestructive evaluation: determination of angles of scattering from the energy spectrum. MScE Thesis, Mechanical Engineering, University of New Brunswick, Fredericton, Canada. Jama, H.A., Hussein, E.M.A., 1998. Design aspects of a gamma-ray energy-spectral compton-scatter nondestructive testing method. Applied Radiation & Isotopes 50, 331± 342. NDT&E, 1995. NDT Abstracts: NDT using Compton scattering. NDT&E International 28, 189±195. Prettyman, T.H., Gardner, R.P., Russ, J.C., Verghese, K., 1993. A combined transmission and scattering tomographic approach to composition and density imaging. Applied Radiation and Isotopes 44, 1327±1341.
www.elsevier.com/locate/apradiso
Quanti®cation of gamma-ray Compton-scatter nondestructive testing A.C. Ho, E.M.A. Hussein* Department of Mechanical Engineering, University of New Brunswick, PO Box 4400, Fredericton, NB, Canada E3B 5A3
Abstract A method is presented for quantifying information obtained from the indications of a Compton scattering nondestructive testing technique. This is achieved by formulating a measurement model, which provides a numerical estimate of the detector response for a given anomaly. Using the measured response function, the location of an anomaly, its size and density are obtained with the aid of the model. The process is demonstrated by quantifying indications obtained from experimental measurements for ¯aws arti®cially created in an aluminum block. 7 2000 Elsevier Science Ltd. All rights reserved. Keywords: Nondestructive testing; Compton scattering; Measurement models
1. Introduction Radiography and tomography are now common forms of nondestructive testing (NDT) with radiation. Both methods rely on radiation transmission, requiring the source and the detection device to be placed at two opposite sides of the inspected object. However, there are situations in which access to both sides of the object is not possible, such as in extended or thick structures. Scattering techniques, particularly those based on Compton scattering of photons, have been emerging to deal with such situations, as evident by the 65 abstracts of work published between 1988 and 1994 (NDT&E, 1995). However, scattering measurements are modulated by the attenuation of radiation as it enters and leaves the inspected object. This makes
* Corresponding author. Tel.: +1-506-447-3105; fax: +1506-447-3380. E-mail address: [email protected] (E.M.A. Hussein).
it dicult to obtain quantitative information without a complete and complex imaging process; as was done by Prettyman et al. (1993) and Arendtsz and Hussein (1995). However, imaging is not necessary in many NDT applications where the objective is to ®nd and locate anomalies, which are typically limited within a small volume in an object with otherwise known features. Nevertheless, imaging provides quantitative information that is necessary in modern qualityassurance and monitoring programs that require documentation that is less subjective to personal interpretation, preferably in the form of speci®c numerical values. Most previous work on Compton Scattering NDT provided a quantitative signal indicating the nature of a detected anomaly. This work presents an approach to provide quantitative information regarding the location, size and density of a detected anomaly, that are more de®nitive and easier to document. We begin ®rst by a brief description of the NDT Compton Scatter method.
0969-8043/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 0 ) 0 0 2 1 3 - X
542
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
2. Compton-scatter NDT Compton scattering (CS) is a viable tool for inspecting industrial objects, since it is an interaction which is strongly dependent on the electron density of the scattering medium, and in turn, its mass density. A number of CS±NDT systems have been reported (NDT&E, 1995). In most techniques, a pencil beam of photons is employed to de®ne the path of the incident beam, while either a well-collimated or an open detector is used. With the former, the inspection volume is de®ned by the intersection of the ®eld-of-view of the incident beam with that of the detector's collimator, resulting in the inspection of one ``point'' at a time. When the detector is not fully collimated, an energy-sensitive detector can be used. With proper selection of the source energy, single-scatter photons can be made to dominate. Then, the energy of the detected once-scattered photons can be related to their angle-of-scattering using the well-known Compton scattering kinematics relationship: E y
E0 E0 1 1 ÿ cos y m0 c 2
1
where E0 is the incident photon energy, E(y ) is the energy of photons scattered by angle y and m0c 2 is the rest-mass energy of the electron (0.511 MeV). This relationship produces, in eect, a ``soft-collimation'' process, by virtue of the fact that each detected energy window corresponds to a particular direction of scattering. Thus, many ``points'' along the incident beam can be simultaneously inspected. This approach has been adopted by a number of workers (e.g., Anghaie et al., 1990; Jama and Hussein, 1998), and its con®guration is depicted schematically in Fig. 1. In order to avoid ambiguity when relating the energy to angle of scattering using Eq. (1), Jama and Hussein (1998) con®ned the detector to almost a point, using a wedgeshaped detector collimator. Therefore, more de®nitive
Fig. 1. A schematic of a wide-angle Compton-scatter inspection system.
information about anomaly detection, location, and sizing were obtained. The quanti®cation process developed here applies to the con®guration of Jama and Hussein (1998), but can be easily extended to other arrangements. A ``measurement model'' is formulated in the next section to provide a numerical estimate of the detector response for a given anomaly size. The model is then applied to quantify indications obtained from experimental results, to provide the size and density of a detected anomaly. The location of an anomaly is directly determined from the angle of scattering corresponding to its measured indication, with the aid of Eq. (1).
3. Measurement model In order to formulate a model simulating the CS process, scattering within an in®nitesimal volume, DV, around a point is considered, as schematically shown in Fig. 2. It is assumed that only single-scatter events contribute to the detector's response; multi-scattered photons suer more energy loss and can be excluded from the monitored energy range. The intensity of the photons scattered to the detector per unit source (the detector's response, S ) can be expressed as, guided by Fig. 2, as: x in p m S KS0 `r exp ÿ Sin r dx 2 2pR 0 2 exp ÿ
yout
0
Sout r dy
where K is a normalization constant that accounts for laboratory aspects, such as the source strength, detector eciency, system geometry, etc., S0 is the Compton scattering cross-section with respect to a reference material, typically the object being inspected, and r is the density at the inspected point relative to the reference material, Sin and Sout are the total cross-sections of the material present along the distances xin and yout, respectively (see Fig. 2), l is the width of DV along the incident beam path, p(m ) dm is the probability of scattering about angle cosine m within m2dm, with scattering in the azimuthal direction being isotropic, and R is the distance from the scattering point to the detector. The exponential terms in Eq. (2) account for the attenuation of photons as they travel toward the inspection point and away from it. The term S0 l represents the scattering rate per unit area within DV, normalized to that of the reference material. The scattering probability and the divergence of the scattered photons are accounted for in the term p(m )/2pR 2. The above model was veri®ed against Monte Carlo
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
simulations, reported by Ho (1999), and was shown to adequately represent the physical aspects of the problem. The measurement model of Eq. (2) enables the determination of the relative density of the inspected from the measurement, S, since all other parpoint, r, ameters in the model equation can be determined inde given S, was pendently. Simple iterative solution for r, readily implemented, both on a hand-held programable calculator and in a Fortran program. However, the peaking nature of the right-hand-side of Eq. (2), as it leads to two possible solutions. Fortuchanges with r, nately, one of the solutions results in an unrealistically which can be discarded. However, high value of r, starting with a physically appropriate initial guess for r led always to the correct solution, as was veri®ed by Ho (1999) in the solution of Eq. (2) using Monte Carlo simulated results. The application of the model, and the other aspects of the quanti®cation process, to experimentally measured data is discussed below. 4. Application to experiment data In NDT, the ®rst step is to determine whether an anomaly (usually a crack) is present or not. This is achieved in CS±NDT by observing whether an abrupt change (a reversed peak for a crack) occurs in the measured energy spectrum of the scattered photons (Jama and Hussein, 1998). This change is further elucidated by subtracting the measured spectrum from that corresponding to a ¯awless reference object. The shape of the obtained indication signal can also reveal information on the nature of the anomaly, e.g., a sharp crack or a smooth ¯aw. The second step is to determine the location of the detected anomaly. This is easily done in CS±NDT with the aid of Eq. (1), using
543
the energy corresponding to the indication peak to determine the angle of scattering and from geometry calculate the central location of the anomaly. Thirdly, one needs to determine the size of the anomaly, and this can be estimated from the width of the peak. Finally, in quantitative NDT, one needs to know the density of the material that occupies the anomaly, which is related to the height (strength) of the peak, and can be obtained by solving the measurement Before utilizing this model, one model, Eq. (2) for r: must obtain a value for the normalization constant, K, which relates the model to the experimental parameters. This constant was determined with the aid of small aluminum rods used to represent a scattering point in the path of the incident beam. The ratio between the measured indication spectrum for a scattering rod and that obtained using the measurement model of Eq. (2) provided an estimate of K. The above procedure was applied to the experimental results obtained by Jama (1997), who used a collimated 137Cs source and a high purity germanium detector con®ned with a wedge-shaped collimator. The results are reported in detail by Ho (1999). In this process, it was found necessary to introduce adjustment factors to account for the divergence of the incident beam, and the fact that some of the incident photons miss hitting the surface of a rod due to the divergence process. This section shows how the above NDT quanti®cation steps were applied to the experimental results obtained by Jama (1997) for arti®cially created ¯aws of dierent sizes, each representing a cylindrical void, drilled separately in 60 50 50 mm3 aluminum blocks. More applications are reported elsewhere (Ho, 1999). The experimentally obtained net indications (that is, the dierence between the measured signal
Fig. 2. A schematic of scattering at a point.
544
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
and that of the reference block) are shown in Fig. 3. Qualitatively, one can tell from the indications of Fig. 3 that the present anomalies have a density less than that of the reference material, given the negative count rate resulting from the subtraction process. The smooth nature of the reversed peaks indicates also that the ¯aws have a smooth surface; otherwise, a jagged indication would have been observed. One can also observe that the ¯aws have dierent sizes, as re¯ected by the change in the width of the reversed peaks. To quantify this size, determine the location of the ¯aw, and obtain an estimate of the density of the ¯aw material (which should have been zero), the procedures presented below were applied.
4.1. Location The energy corresponding to the bottom of the four reversed peaks of Fig. 3, were used in Eq. (1) to obtain the angle of scattering, which was found to be about 78.38 for the four ¯aws. This corresponded well with the actual location of the ¯aws, which were experimentally set by Jama (1997) to measure scattering at 77.58.
4.2. Size Fig. 3 shows an obvious increase in the width of the reversed peaks of the indications with increasing ¯aw size. The width of the anomaly can be represented by the parameter l in Eq. (2). However, obtaining a numerical value for this parameter requires the identi®cation of a proper measure of the peak width, since the width of the peak is also aected by the spread in the detector's response function caused by the incomplete energy deposition of photons. For simplicity, we adopted the well-known approach of full-width-at-halfmaximum (FWHM) as a measure of the peak width. This width provides two energy bounds in the indication spectrum, each of which corresponds to a dierent angle of scattering in accordance with Eq. (1). These angular bounds, along with the position of detector and angle of scattering, were used to geometrically calculate the width l. The obtained values are summarized in Table 1, compared with the actual diameter of the ¯aw. As the Table shows, the ¯aw size is overestimated. This is likely due to the application of the FWHM approach, which is usually used with symmetric peaks, to the slightly skewed peaks of the indications of Fig. 3. This skewness is caused by the
Fig. 3. Measured indications obtained by Jama (1997) for four void ¯aws, 1.58 mm (top curve), 3.23 mm (2nd top) 6.45 mm (2nd bottom) and 9.52 mm (bottom) in diameter, in an 60 50 50 mm3 aluminum block.
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
545
Table 1 Estimated width of ¯aws for indications of Fig. 3 Location of indication in Fig. 3
Estimated width (mm)
Actual diameter (mm)
Bottom 2nd Bottom 2nd Top Top
10.27 8.42 5.43 2.44
9.52 6.35 3.23 1.58
uneven attenuation of the incident photons within the area corresponding to the ¯aw in the reference block, which is used for obtaining the net indication. Nevertheless, the predicted ¯aw width is still indicative of the change in the ¯aw size. 4.3. Density Obviously the density of a voided ¯aw is zero. However, the indications of Fig. 3 do not directly indicate that, due to the spread of the indication peaks. In practice, it is also useful to estimate the ¯aw density. Determination of the ¯aw density, by solving directly using the measured detector response, is Eq. (2) for r, further complicated by the fact that the used indication is the result of subtracting the detector response for the reference specimen, S0, from that of the inspected specimen, S. However, after reversing the sign of the indication spectrum to obtain positive count rates, the relative density of the material in the ¯aw can be estimated from the following relationship: p m ` S0 ÿ S e1ÿ1 e3ÿ1 KS0 ` S exp ÿ S in out 2pR 2 2 r exp ÿSout r` ÿ exp ÿSin r` 3 where r0 is the mass density of the reference specimen and e1 and e3 are attenuation factors, respectively, of the incident radiation before reaching the ¯aw region and the scattered photons in their way to the detector, in both the reference and inspected specimens; all the other notations are as de®ned following Eq. (2). Eq. (3) is the result of subtracting the model of Eq. (2) when applied in the presence of a ¯aw of relative den from that applied to the reference specimen, sity r, and can be directly solved iteratively. For the indications of Fig. 3, the results shown in Table 2 were It should be noted that the detector reobtained for r: sponse values, S and S0, were obtained by integrating the ``negative'' counts under the reversed peaks of Fig. 3. As Table 2 shows, the density of the material within each ¯aw anomaly is quite small for the two largest ¯aws (bottom indications), but is not zero due to the
error in overestimating the ¯aw size. The latter error in the two smallest ¯aws is due to the signi®cant overestimation of the size as explained earlier. The above results show that the error in the ¯aw size has a strong in¯uence on the value of the estimated density. Ho (1999) further demonstrated this by utilizing the actual values of the ¯aw width (the diameter) in the solution of Eq. (3). The results were signi®cantly improved, but the estimated density for the two smallest ¯aws remained unsatisfactory. This was attributed to Jama's (1997) use of the same counting period for all ¯aw sizes, producing poorer counting statistics for the small ¯aws. Nevertheless, even with poor numerical values, one can still monitor progress in ¯aw propagation by comparing new numerical values for ¯aw size and density with old ones. 5. Conclusions An approach to quantifying indications obtained from Compton-scattering NDT system, which employed a collimated 137Cs gamma-ray source and a high-purity germanium detector, to examine ¯aws in a 60 50 50 mm3 aluminum block, was developed. Although the approach correctly determined the location of a ¯aw, it tended to overestimate its size, which in turn aected the obtained density of the material that occupies the ¯aw. This discrepancy is attributed to the use of the full-width-at-halfmaximum (FWHM) approach as a measure of the width of the slightly skewed indication peak, and in
Table 2 Relative density of ¯aw material estimated by solving Eq. (3) Relative density Location of indication in Fig. 3
Estimated
Actual
Bottom 2nd Bottom 2nd Top Top
0.103 0.229 0.25 0.843
0 0 0 0
546
A.C. Ho, E.M.A. Hussein / Applied Radiation and Isotopes 53 (2000) 541±546
turn the width of a ¯aw. In spite of the above dif®culties, the quanti®cation process of the Compton scatter NDT technique was reasonably successful. With some improvement in the processes of determining the ¯aw size, the quanti®cation process can be further improved. Therefore, future work should focus on replacing the FWHM method with a more adequate approach suitable for the skewed signals observed experimentally. Acknowledgements This work was supported by a grant to the second author from the Natural Sciences and Engineering Research Council of Canada. References Anghaie, S., Humphries, L.L., Diaz, N.J., 1990. Material characterization and ¯aw detection, sizing and location by
the dierential gamma scattering spectroscopy technique. Nuclear Technology 91, 361±387. Arendtsz, N.V., Hussein, E.M.A., 1995. Energy-spectral compton scatter imaging. IEEE Transactions on Nuclear Science 42, 2155±2172. Ho, A.C. 1999. Quanti®cation of gamma-ray Compton-scatter nondestructive testing. MScE Thesis, Mechanical Engineering, University of New Brunswick, Fredericton, Canada. Jama, H. 1997. Gamma-ray compton scatter nondestructive evaluation: determination of angles of scattering from the energy spectrum. MScE Thesis, Mechanical Engineering, University of New Brunswick, Fredericton, Canada. Jama, H.A., Hussein, E.M.A., 1998. Design aspects of a gamma-ray energy-spectral compton-scatter nondestructive testing method. Applied Radiation & Isotopes 50, 331± 342. NDT&E, 1995. NDT Abstracts: NDT using Compton scattering. NDT&E International 28, 189±195. Prettyman, T.H., Gardner, R.P., Russ, J.C., Verghese, K., 1993. A combined transmission and scattering tomographic approach to composition and density imaging. Applied Radiation and Isotopes 44, 1327±1341.