- Email: [email protected]
Mapping elemental distributions of heavy elements using tunable gamma-ray beams
Nuclear Instruments and Methods in Physics Research B 149 (1999) 141±146
Mapping elemental distributions of heavy elements using tunable gamma-ray beams Th. Materna b
a,*
, J. Jolie a, W. Mondelaers
b
a Institute of Physics, University of Fribourg, P erolles, CH-1700 Fribourg, Switzerland Vakgroep Subatomaire en Stralingsfysica, Universiteit Gent, Proeftuinstraat 86, B-9000 Gent, Belgium
Received 14 July 1998
Abstract A non-destructive analysis of the distribution of heavy elements in samples can be performed using tunable gammaray sources. By scanning a sample using photons having two energies, one just below and one just above the K-edge of the element under study, the reconstructed distribution becomes only sensitive to this element. Here we show that the distribution of a sample containing several heavy elements can be reconstructed element by element. We also study how far the method can be made quantitative. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 07.85.Yk; 87.59.Fm Keywords: Gamma-ray source; Tomography; Linear electron accelerator
1. Introduction For four years, a tunable gamma-ray source has been under development at the 15 MeV electron LINAC facility from the university of Gent [1±3]. The source delivers monochromatic photons with energies that can be selected between 50 keV and 1 MeV. Therefore, it allows various experiments on heavy elements, such as absorption studies, inelastic scattering or tomographies. Since element sensitive tomography can be of interest in the ®eld of geology or even in nuclear waste stor-
* Corresponding author. Tel.: ++41 26 300 91 02; fax: ++41 26 300 97 47; e-mail: [email protected]
age, some experiments on samples containing only uranium were performed [4]. In the present work, the possibility of selectively viewing dierent heavy elements inside a sample is tested. For instance, we present two-dimensional tomographies of an arti®cial sample that contains uranium, bismuth and lead. These elements have similar atomic numbers (ZPb 82, ZBi 83 and ZU 92), so that one element can easily be hidden by the others. Subsequently, as sensitive tomographies enable the estimation of the concentrations, we analyse a sample containing four well-de®ned concentrations of bismuth. The next section reviews brie¯y the concept of elemental tomography. Sections 3 and 4 describes the samples used in this study and the tunable gamma-ray source. The experimental
0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 6 2 0 - X
142
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
procedure is explained in Section 5. The tomographic reconstruction method used is presented in Section 6. Then, Section 7 shows results and provides a quantitative study of concentrations. Finally, the conclusion can be found in Section 8. 2. Concept of element-sensitive tomography In classical tomography, one uses the monoenergetic photons from a radioactive source or a polychromatic beam obtained from an X-ray facility. From the analysis of the transmission through the sample, one can deduce the distribution of the elements. However, the identi®cation can be arduous when several elements are present having similar concentrations and attenuation coecients. Element-sensitive tomography is based on a well-known phenomenon. The absorption curve of each element presents a speci®c discontinuity when photons get enough energy to ionise the inner electron shell of the atoms. The energy of the edge depends on the selected element. To view a particular element, one can measure the transmissions with two beams, one just below and one just above the energy of the discontinuity (EK ) [5]. Lambert law is used to de®ne the projection p(E): Z I E l E; s ds; 1 p E ÿ ln I0 E path where l E; s is the attenuation coecient along the path of the beam. I0 E and I(E) are the intensities before and after the transmission through the sample. Due to the positive discontinuity of the attenuation, the dierence Dp p EK eÿ p EK ÿ e is positive in the presence of the element. It is small and negative for other elements. The projections, Dp, are then used to reconstruct the distribution of the selected element inside the sample. This will be explained in Section 6. 3. Description of the samples The arti®cial samples are 10-mm-diameter and 5-cm-long aluminium cylinders with four 2-mmdiameter holes. For the ®rst experiment (an ele-
ment-sensitive study), two holes are ®lled with uranyl nitrate (concentration of uranium: 1 and 0.5 g/cm3 ). The third one is ®lled with a mixture of bismuth chloride (concentration of bismuth 1 g/cm3 ) and the last one contains a copper wire wrapped in lead (concentration of lead 2.5 g/ cm3 ). For the second experiment (a quantitative study of concentrations), the four holes are ®lled with dierent mixture of bismuth chloride: qA 2.00 g/cm3 , qB 1.24 g/cm3 , qC 0.50 g/cm3 and qD 0.15 g/cm3 . The given concentrations are the concentration of bismuth inside the mixture. 4. The tunable gamma-ray source The source used provides energies above 50 keV, around the K-edges of many heavy elements. With our choice of the elements, for the ®rst experiment only ®ve energies are required due to the proximity of the K-edge of bismuth and lead: EK (Pb) 88.0 keV, EK (Bi) 90.5 keV and EK (U) 115.5 keV. The concentrations were also limited so that the maximal beam attenuation I/I0 is in the order of 1/50. Element-sensitive tomography needs two photon beams with energies around the edge of each element under consideration. To obtain those, a tunable source must be used. The one installed at the University of Ghent is illustrated in Fig. 1. At ®rst, an electron linear accelerator (1) delivers high intensity (max. 2 mA) low-energy pulsed beams of electrons (max. 15 MeV). Next, magnets de¯ect these electrons towards a Ta/C target (2) in order to obtain photons by the Bremsstrahlung eect. As these photons have a wide energy spectrum (50 keV±15 MeV), the target can be considered as a white gamma-ray source. A Si-crystal (3) cylindrically bent to a radius of 10.65 m and collimators (4±5) are placed behind it. During the transmission in the crystal, the photons are diracted following the Bragg rules and due to the bending, they are focused on particular positions depending on their energies. The collection of these positions forms an arc of a circle of 10.65 m diameter. To select the desired energy, a vertical tungsten collimator (6) called the Rowland slit can be moved on a small part of that circle using a rotation±translation table (8). Finally, a 76 cm3
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
143
Fig. 1. Set-up installed at the Ghent electron linear accelerator to produce tunable monochromatic gamma-ray beams. Numbers are explained in the text.
Ge-detector (7) counts the monochromatic photons. For a complete explanation of the concept and operation of this source, we refer the reader to our previous papers [1±3]. Fig. 2 shows the spectrum of a beam used to detect uranium. It was obtained with 10 MeV electrons pulsed at 2000 Hz to a mean intensity of 160 lA. As shown, the source does not deliver pure mono-energetic photons but also all the orders allowed by the diraction rules [1]. The photon peak used has energy of 114.5 keV with a bandwidth of about 120 eV and its intensity is approximately 33 ph/s cm2 . Since the background was relatively large (the peaks intensity-to-background ratio, Ipeaks /Ibackground , < 18%), the saturation in our detector limited the electron
intensity chosen. It is noteworthy that the source is still under development and does not yet provide its optimal beam intensity. The very last developments show that the background can still be decreased and that the monochromatic beam intensity is greatly enhanced by choosing other crystals. New values for the photon beam intensity are about 100 ph/s cm2 lA with the ratio Ipeaks /Ibackground > 80%. With a mean electron beam intensity of 1 mA that can be produced by the accelerator and that can be handled by an optimised bremsstrahlung target, a photon beam intensity of 1 ´ 105 ph/s cm2 can be expected. Full exploitation of these improvements requires other detectors as the Ge-detector used for this experiment.
Fig. 2. Typical spectrum of a photon beam used to detect uranium. We used the peak at 114.5 keV to measure the attenuation through the sample.
144
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
5. Experimental procedure The sample was mounted on a translation±rotation table (9) placed in front of the Rowland slit. At ®rst, the right energy was selected by moving the Rowland slit and turning the crystal. Then, using a 1-mm-wide 3-cm-high beam, the transmission through the sample was measured. It was done for twelve horizontal positions hm (m 0±11) that covered the whole sample width. The sample was then rotated by an angle of 40° and the horizontal scan was repeated. On the whole, this scan was performed for nine dierent orientations (angles hi , i 0±8) of the sample. With a beam intensity of about 33 ph/s cm2 , each measurement p(hi , hm ) took 4 min to have good statistics. Thus, a single-energy tomography took more than 7 h. With the new improvements this duration can be reduced to a few minutes. Five energies were used for the ®rst experiment: 114.5 and 116.5 keV to detect uranium, then 87, 89.2 and 91.7 keV for lead and bismuth. Only the last two energies were used to detect and quantify the bismuth in the second experiment.
image, the attenuation is the sum of the projections Dp* for which the pixel had contributed during the transmission of the beam, interpolated at the pixel position: 2p X Dl r; u Dp hi ; hc r cos u ÿ hi : 3 Td i Here, T is the number of orientations, d is the beam width, r and u are the polar coordinates of the pixel, calculated from the centre of the image; hc is the horizontal position of the rotation axis. The last step aims to determine the concentration distribution. For each pixel, we calculate: q
A Dl ; NA Dr
Dr r EK e ÿ r EK ÿ e;
4
where NA is the Avogadro number; A the atomic number of the element and Dr, the tabulated absorption cross-section dierence [7]. Only positive values of Dl are considered in this last equation because only these are related to the selected element. 7. Results and quantitative study
6. Reconstruction method A previous paper explained how to reconstruct the elemental distribution in a sample from the measured projections [4]. The method, with some changes, has been used to obtain the concentration distribution. It is a fast direct procedure that can be summarised in three steps. First, each Dp projection is sharpened using the abs function as ®lter [6]. The result, which is an approximation, can be expressed in terms of the following convolution: X Dp hi ; hm Dp hi ; hm ÿ ; 2 Dp hi ; hm 4 p2 n ÿ m2 n nÿmodd
where hi and hm have been de®ned above. In this study, we used Dp instead of the ratio of intensity at the two energies, I(EK ) e)/I(EK + e), chosen in our previous work [4] to be in better agreement with the mathematical explanation of this method [6]. The second step is designed to obtain the Dl attenuation distribution where Dl l EK e ÿl EK ÿ e. For each pixel of the reconstructed
Fig. 3 illustrates the reconstruction method for the sample containing uranium, bismuth and lead. Except for some artefacts in the case of uranium, the elemental distribution matches very well the sample and it shows no distortions that could result from the presence of the other elements. Fig. 4 shows the reconstruction result for the sample containing four dierent concentrations of bismuth. The hole with the lower concentration does not appear. Its distribution is hardly distinguished from the artefacts. Therefore, this concentration has to be below the detection threshold attained. The concentrations of the elements inside the holes are estimated using the distribution pattern. The values calculated are tabulated against the real concentrations in Table 1. Discrepancies are below 20% except for the low-concentration hole. The limited number of projections, 108, decreases the quality of the reconstruction process. In order to sort out the in¯uence of the number of projections, we simulated distributions of the same shape and size; then, we calculated the projections and
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
145
Fig. 3. The sample used to verify the elemental sensitivity of the method (left). Four holes were drilled in an aluminium cylinder of 10mm-diameter. Two holes were ®lled with uranyl nitrate, the third one contained bismuth and the last one contained lead. Besides are shown three reconstruction patterns resulting of the tomography of each element.
reconstructed the distribution using the method described above. The ratio between the calculated and the initial concentrations was used as a corrective factor. The ®nal values given in Table 1 show discrepancies of the order of 10%. Since the statistical errors of the measured data were about 10%, no other corrections have been applied.
8. Conclusion In brief, the present study shows that, by using the tunable gamma source installed in Ghent, it is possible to map an element-speci®c distribution of a sample containing dierent heavy elements with similar absorption coecients. Despite the low
Fig. 4. Reconstruction result for the sample used to test the quantitative possibilities of the method. For this experiment, well-de®ned concentrations of bismuth were placed in the four holes of the aluminium cylinder. Three peaks can clearly be seen. The fourth one is hardly distinguished from the artifacts. Positions and full widths at half maximum of the peaks agree with the positions and sizes of the holes. The concentration of bismuth is calculated with the peak intensity.
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Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
Table 1 Concentrations of bismuth in the second sample Original concentrations (g/cm3 ) Hole Hole Hole Hole
A B C D
2.00 1.24 0.50 0.15
Calculated from reconstruction (g/cm3 )
Corrected with simulations (g/cm3 )
2.3 1.3 0.60 (0.20)
1.9 1.1 0.50 (0.16)
Calculated values are compared to original values.
beam intensity used for these experiments, the method leads to useful images; indeed, the distribution of an element does not show distortions that could be due to the presence of the other comparable elements in the neighbourhood. With regard to the second experiment, it is concluded that this method allows to determine the concentrations of the elements inside the sample with a good approximation. Further improvements on the values of the concentration can be achieved by taking more projections of the sample; a correction using simulations would then not be necessary. Finally, better results could be obtained more rapidly by using a more powerful source. But, the conclusions presented above will remain valid. As stated, a quantitative element-sensitive tomography can be performed on a small-scale electron linac facility. Therefore the use of the scarce beam-time at a synchrotron radiation facility is not prerequisite for this type of experiments.
Acknowledgements The authors would like to thank M. Bertschy and N. Warr for their help. This research is supported by the Swiss National Science Foundation, the Flemish Fund for Scienti®c Research (FWOVlaanderen) and by the Research Board of the Gent University. References [1] J. Jolie, M. Bertschy, Nucl. Instr. and Meth. B 95 (1995) 431. [2] M. Bertschy, J. Jolie, W. Mondelaers, Nucl. Instr. and Meth. B 95 (1995) 437. [3] J. Jolie, M. Bertschy, Th. Materna, N. Stritt, AIP Conf. Proc. CP 392 (1997) 1235. [4] M. Bertschy, J. Jolie, W. Mondelaers, Appl. Phys. A 62 (1996) 437. [5] L. Grodzins, Nucl. Instr. and Meth. 206 (1983) 547. [6] G.T. Herman, Image Reconstruction from Projections, Academic Press, New York, 1980. [7] E. Storm, H.I. Israel, Nucl. Data Tables A 7 (6) (1970) 565.
Mapping elemental distributions of heavy elements using tunable gamma-ray beams Th. Materna b
a,*
, J. Jolie a, W. Mondelaers
b
a Institute of Physics, University of Fribourg, P erolles, CH-1700 Fribourg, Switzerland Vakgroep Subatomaire en Stralingsfysica, Universiteit Gent, Proeftuinstraat 86, B-9000 Gent, Belgium
Received 14 July 1998
Abstract A non-destructive analysis of the distribution of heavy elements in samples can be performed using tunable gammaray sources. By scanning a sample using photons having two energies, one just below and one just above the K-edge of the element under study, the reconstructed distribution becomes only sensitive to this element. Here we show that the distribution of a sample containing several heavy elements can be reconstructed element by element. We also study how far the method can be made quantitative. Ó 1999 Elsevier Science B.V. All rights reserved. PACS: 07.85.Yk; 87.59.Fm Keywords: Gamma-ray source; Tomography; Linear electron accelerator
1. Introduction For four years, a tunable gamma-ray source has been under development at the 15 MeV electron LINAC facility from the university of Gent [1±3]. The source delivers monochromatic photons with energies that can be selected between 50 keV and 1 MeV. Therefore, it allows various experiments on heavy elements, such as absorption studies, inelastic scattering or tomographies. Since element sensitive tomography can be of interest in the ®eld of geology or even in nuclear waste stor-
* Corresponding author. Tel.: ++41 26 300 91 02; fax: ++41 26 300 97 47; e-mail: [email protected]
age, some experiments on samples containing only uranium were performed [4]. In the present work, the possibility of selectively viewing dierent heavy elements inside a sample is tested. For instance, we present two-dimensional tomographies of an arti®cial sample that contains uranium, bismuth and lead. These elements have similar atomic numbers (ZPb 82, ZBi 83 and ZU 92), so that one element can easily be hidden by the others. Subsequently, as sensitive tomographies enable the estimation of the concentrations, we analyse a sample containing four well-de®ned concentrations of bismuth. The next section reviews brie¯y the concept of elemental tomography. Sections 3 and 4 describes the samples used in this study and the tunable gamma-ray source. The experimental
0168-583X/98/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 8 ) 0 0 6 2 0 - X
142
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
procedure is explained in Section 5. The tomographic reconstruction method used is presented in Section 6. Then, Section 7 shows results and provides a quantitative study of concentrations. Finally, the conclusion can be found in Section 8. 2. Concept of element-sensitive tomography In classical tomography, one uses the monoenergetic photons from a radioactive source or a polychromatic beam obtained from an X-ray facility. From the analysis of the transmission through the sample, one can deduce the distribution of the elements. However, the identi®cation can be arduous when several elements are present having similar concentrations and attenuation coecients. Element-sensitive tomography is based on a well-known phenomenon. The absorption curve of each element presents a speci®c discontinuity when photons get enough energy to ionise the inner electron shell of the atoms. The energy of the edge depends on the selected element. To view a particular element, one can measure the transmissions with two beams, one just below and one just above the energy of the discontinuity (EK ) [5]. Lambert law is used to de®ne the projection p(E): Z I E l E; s ds; 1 p E ÿ ln I0 E path where l E; s is the attenuation coecient along the path of the beam. I0 E and I(E) are the intensities before and after the transmission through the sample. Due to the positive discontinuity of the attenuation, the dierence Dp p EK eÿ p EK ÿ e is positive in the presence of the element. It is small and negative for other elements. The projections, Dp, are then used to reconstruct the distribution of the selected element inside the sample. This will be explained in Section 6. 3. Description of the samples The arti®cial samples are 10-mm-diameter and 5-cm-long aluminium cylinders with four 2-mmdiameter holes. For the ®rst experiment (an ele-
ment-sensitive study), two holes are ®lled with uranyl nitrate (concentration of uranium: 1 and 0.5 g/cm3 ). The third one is ®lled with a mixture of bismuth chloride (concentration of bismuth 1 g/cm3 ) and the last one contains a copper wire wrapped in lead (concentration of lead 2.5 g/ cm3 ). For the second experiment (a quantitative study of concentrations), the four holes are ®lled with dierent mixture of bismuth chloride: qA 2.00 g/cm3 , qB 1.24 g/cm3 , qC 0.50 g/cm3 and qD 0.15 g/cm3 . The given concentrations are the concentration of bismuth inside the mixture. 4. The tunable gamma-ray source The source used provides energies above 50 keV, around the K-edges of many heavy elements. With our choice of the elements, for the ®rst experiment only ®ve energies are required due to the proximity of the K-edge of bismuth and lead: EK (Pb) 88.0 keV, EK (Bi) 90.5 keV and EK (U) 115.5 keV. The concentrations were also limited so that the maximal beam attenuation I/I0 is in the order of 1/50. Element-sensitive tomography needs two photon beams with energies around the edge of each element under consideration. To obtain those, a tunable source must be used. The one installed at the University of Ghent is illustrated in Fig. 1. At ®rst, an electron linear accelerator (1) delivers high intensity (max. 2 mA) low-energy pulsed beams of electrons (max. 15 MeV). Next, magnets de¯ect these electrons towards a Ta/C target (2) in order to obtain photons by the Bremsstrahlung eect. As these photons have a wide energy spectrum (50 keV±15 MeV), the target can be considered as a white gamma-ray source. A Si-crystal (3) cylindrically bent to a radius of 10.65 m and collimators (4±5) are placed behind it. During the transmission in the crystal, the photons are diracted following the Bragg rules and due to the bending, they are focused on particular positions depending on their energies. The collection of these positions forms an arc of a circle of 10.65 m diameter. To select the desired energy, a vertical tungsten collimator (6) called the Rowland slit can be moved on a small part of that circle using a rotation±translation table (8). Finally, a 76 cm3
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
143
Fig. 1. Set-up installed at the Ghent electron linear accelerator to produce tunable monochromatic gamma-ray beams. Numbers are explained in the text.
Ge-detector (7) counts the monochromatic photons. For a complete explanation of the concept and operation of this source, we refer the reader to our previous papers [1±3]. Fig. 2 shows the spectrum of a beam used to detect uranium. It was obtained with 10 MeV electrons pulsed at 2000 Hz to a mean intensity of 160 lA. As shown, the source does not deliver pure mono-energetic photons but also all the orders allowed by the diraction rules [1]. The photon peak used has energy of 114.5 keV with a bandwidth of about 120 eV and its intensity is approximately 33 ph/s cm2 . Since the background was relatively large (the peaks intensity-to-background ratio, Ipeaks /Ibackground , < 18%), the saturation in our detector limited the electron
intensity chosen. It is noteworthy that the source is still under development and does not yet provide its optimal beam intensity. The very last developments show that the background can still be decreased and that the monochromatic beam intensity is greatly enhanced by choosing other crystals. New values for the photon beam intensity are about 100 ph/s cm2 lA with the ratio Ipeaks /Ibackground > 80%. With a mean electron beam intensity of 1 mA that can be produced by the accelerator and that can be handled by an optimised bremsstrahlung target, a photon beam intensity of 1 ´ 105 ph/s cm2 can be expected. Full exploitation of these improvements requires other detectors as the Ge-detector used for this experiment.
Fig. 2. Typical spectrum of a photon beam used to detect uranium. We used the peak at 114.5 keV to measure the attenuation through the sample.
144
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
5. Experimental procedure The sample was mounted on a translation±rotation table (9) placed in front of the Rowland slit. At ®rst, the right energy was selected by moving the Rowland slit and turning the crystal. Then, using a 1-mm-wide 3-cm-high beam, the transmission through the sample was measured. It was done for twelve horizontal positions hm (m 0±11) that covered the whole sample width. The sample was then rotated by an angle of 40° and the horizontal scan was repeated. On the whole, this scan was performed for nine dierent orientations (angles hi , i 0±8) of the sample. With a beam intensity of about 33 ph/s cm2 , each measurement p(hi , hm ) took 4 min to have good statistics. Thus, a single-energy tomography took more than 7 h. With the new improvements this duration can be reduced to a few minutes. Five energies were used for the ®rst experiment: 114.5 and 116.5 keV to detect uranium, then 87, 89.2 and 91.7 keV for lead and bismuth. Only the last two energies were used to detect and quantify the bismuth in the second experiment.
image, the attenuation is the sum of the projections Dp* for which the pixel had contributed during the transmission of the beam, interpolated at the pixel position: 2p X Dl r; u Dp hi ; hc r cos u ÿ hi : 3 Td i Here, T is the number of orientations, d is the beam width, r and u are the polar coordinates of the pixel, calculated from the centre of the image; hc is the horizontal position of the rotation axis. The last step aims to determine the concentration distribution. For each pixel, we calculate: q
A Dl ; NA Dr
Dr r EK e ÿ r EK ÿ e;
4
where NA is the Avogadro number; A the atomic number of the element and Dr, the tabulated absorption cross-section dierence [7]. Only positive values of Dl are considered in this last equation because only these are related to the selected element. 7. Results and quantitative study
6. Reconstruction method A previous paper explained how to reconstruct the elemental distribution in a sample from the measured projections [4]. The method, with some changes, has been used to obtain the concentration distribution. It is a fast direct procedure that can be summarised in three steps. First, each Dp projection is sharpened using the abs function as ®lter [6]. The result, which is an approximation, can be expressed in terms of the following convolution: X Dp hi ; hm Dp hi ; hm ÿ ; 2 Dp hi ; hm 4 p2 n ÿ m2 n nÿmodd
where hi and hm have been de®ned above. In this study, we used Dp instead of the ratio of intensity at the two energies, I(EK ) e)/I(EK + e), chosen in our previous work [4] to be in better agreement with the mathematical explanation of this method [6]. The second step is designed to obtain the Dl attenuation distribution where Dl l EK e ÿl EK ÿ e. For each pixel of the reconstructed
Fig. 3 illustrates the reconstruction method for the sample containing uranium, bismuth and lead. Except for some artefacts in the case of uranium, the elemental distribution matches very well the sample and it shows no distortions that could result from the presence of the other elements. Fig. 4 shows the reconstruction result for the sample containing four dierent concentrations of bismuth. The hole with the lower concentration does not appear. Its distribution is hardly distinguished from the artefacts. Therefore, this concentration has to be below the detection threshold attained. The concentrations of the elements inside the holes are estimated using the distribution pattern. The values calculated are tabulated against the real concentrations in Table 1. Discrepancies are below 20% except for the low-concentration hole. The limited number of projections, 108, decreases the quality of the reconstruction process. In order to sort out the in¯uence of the number of projections, we simulated distributions of the same shape and size; then, we calculated the projections and
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
145
Fig. 3. The sample used to verify the elemental sensitivity of the method (left). Four holes were drilled in an aluminium cylinder of 10mm-diameter. Two holes were ®lled with uranyl nitrate, the third one contained bismuth and the last one contained lead. Besides are shown three reconstruction patterns resulting of the tomography of each element.
reconstructed the distribution using the method described above. The ratio between the calculated and the initial concentrations was used as a corrective factor. The ®nal values given in Table 1 show discrepancies of the order of 10%. Since the statistical errors of the measured data were about 10%, no other corrections have been applied.
8. Conclusion In brief, the present study shows that, by using the tunable gamma source installed in Ghent, it is possible to map an element-speci®c distribution of a sample containing dierent heavy elements with similar absorption coecients. Despite the low
Fig. 4. Reconstruction result for the sample used to test the quantitative possibilities of the method. For this experiment, well-de®ned concentrations of bismuth were placed in the four holes of the aluminium cylinder. Three peaks can clearly be seen. The fourth one is hardly distinguished from the artifacts. Positions and full widths at half maximum of the peaks agree with the positions and sizes of the holes. The concentration of bismuth is calculated with the peak intensity.
146
Th. Materna et al. / Nucl. Instr. and Meth. in Phys. Res. B 149 (1999) 141±146
Table 1 Concentrations of bismuth in the second sample Original concentrations (g/cm3 ) Hole Hole Hole Hole
A B C D
2.00 1.24 0.50 0.15
Calculated from reconstruction (g/cm3 )
Corrected with simulations (g/cm3 )
2.3 1.3 0.60 (0.20)
1.9 1.1 0.50 (0.16)
Calculated values are compared to original values.
beam intensity used for these experiments, the method leads to useful images; indeed, the distribution of an element does not show distortions that could be due to the presence of the other comparable elements in the neighbourhood. With regard to the second experiment, it is concluded that this method allows to determine the concentrations of the elements inside the sample with a good approximation. Further improvements on the values of the concentration can be achieved by taking more projections of the sample; a correction using simulations would then not be necessary. Finally, better results could be obtained more rapidly by using a more powerful source. But, the conclusions presented above will remain valid. As stated, a quantitative element-sensitive tomography can be performed on a small-scale electron linac facility. Therefore the use of the scarce beam-time at a synchrotron radiation facility is not prerequisite for this type of experiments.
Acknowledgements The authors would like to thank M. Bertschy and N. Warr for their help. This research is supported by the Swiss National Science Foundation, the Flemish Fund for Scienti®c Research (FWOVlaanderen) and by the Research Board of the Gent University. References [1] J. Jolie, M. Bertschy, Nucl. Instr. and Meth. B 95 (1995) 431. [2] M. Bertschy, J. Jolie, W. Mondelaers, Nucl. Instr. and Meth. B 95 (1995) 437. [3] J. Jolie, M. Bertschy, Th. Materna, N. Stritt, AIP Conf. Proc. CP 392 (1997) 1235. [4] M. Bertschy, J. Jolie, W. Mondelaers, Appl. Phys. A 62 (1996) 437. [5] L. Grodzins, Nucl. Instr. and Meth. 206 (1983) 547. [6] G.T. Herman, Image Reconstruction from Projections, Academic Press, New York, 1980. [7] E. Storm, H.I. Israel, Nucl. Data Tables A 7 (6) (1970) 565.