- Email: [email protected]
Scattering corrections in neutron radiography using point scattered functions
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341 www.elsevier.com/locate/nima
Scattering corrections in neutron radiography using point scattered functions N. Kardjilova,, F. de Beerb, R. Hassaneinc, E. Lehmannc, P. Vontobelc a
Department of Materials (SF3), Hahn-Meitner-Institut, Glienicker Str. 100, 14109 Berlin, Germany b NECSA, Pretoria, South Africa c Paul Scherrer Institute, Villigen, Switzerland Available online 25 February 2005
Abstract Scattered neutrons cause distortions and blurring in neutron radiography pictures taken at small distances between the investigated object and the detector. This defines one of the most significant problems in quantitative neutron radiography. The quantification of strong scattering materials such as hydrogenous materials—water, oil, plastic, etc.— with a high precision is very difficult due to the scattering effect in the radiography images. The scattering contribution in liquid test samples (H2O, D2O and a special type oil ISOPAR L) at different distances between the samples and the detector, the so-called Point Scattered Function (PScF), was calculated with the help of MCNP-4C Monte Carlo code. Corrections of real experimental data were performed using the calculated PScF. Some of the results as well as the correction algorithm will be presented. r 2005 Elsevier B.V. All rights reserved. PACS: 28.20Cz; 02.70Lq; 87.59Hp Keywords: Quantitative neutron radiography; Monte Carlo simulations; Scattering corrections
1. Introduction The digital processing of neutron radiography images gives the possibility for data quantification. In this case an exact relation between the measured neutron attenuation and the real macroscopic attenuation coefficient for every point of the Corresponding author. Tel.: +49 30 80622298;
fax: +49 30 80623094. E-mail address: [email protected] (N. Kardjilov).
sample is required. The assumption that the attenuation of the neutron beam through the sample is exponential I=I 0 ¼ expðtot d Þ
(1)
where I0 and I are the intensities of the beam before and after the transmission and Stot and d are the linear attenuation coefficient and the thickness of the sample, is valid only in an ideal case, where a monochromatic beam,
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.159
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
2. Analytical point scattered functions The scattering correction procedure was based on the simulation of the scattering component for different liquids at various distances from the detector using a Monte Carlo computation method. For this purpose the MCNP-4C code [3] was used. The reproducibility of the calculation of the scattering component, so-called Point Scattered Function (PScF), was tested by using different tallies (detector types). The comparison presented in Fig. 1 shows that the obtained behaviour of the scattering properties for a thin H2O layer of 3 mm is similar for all the used tallies. The observed drop in the central area of the PScF could be explained by uncertainties in the MCNP calculations for very narrow collision angles. This problem comes from the uncertainty of the MCNP code in case of using the Sða; bÞ treatment for processes of inelastic scattering from bounding materials like water [4].
Normalized intensity, (I/Io)
Water layer Thickness: 3 mm Distance sample-detector: 20 mm
Using F5 tally (point detector) Using F4 tally and a lattice structure Using F1 tally (ring detector)
1.2x10-5 1.0x10-5 8.0x10-6 6.0x10-6 4.0x10-6 2.0x10-6 0.0 -4
-2
0 2 Distance, cm
4
Fig. 1. Point scattering functions calculated by using different MCNP tally structures.
H2O Thickness: 3 mm; Distance sample-detector: 20 mm PScF(MCNP) Gauss fit
1.0x10-5
FWHM
5.0x10-6
Maximum
Normalized intensity (I/Io)
non-scattering sample and non-background contribution are assumed. In the real case these conditions are not fulfilled and in dependence on the sample material we have more or less deviation from the exponential attenuation law. Because of the high scattering cross-sections of hydrogen for thermal neutrons, the problem with the scattered neutrons at quantitative radiography investigations of hydrogenous materials (as PE, PMMA, oil, H2O, etc.) is not trivial. For these strong scattering materials the neutron beam attenuation is no longer exponential and a dependence of the macroscopic attenuation coefficient on the material thickness and on the distance between the sample and the detector appears. When quantitative radiography (2D) or tomography investigations (3D) are performed, some image restoration procedures for a correction of the scattering effect are required. An example for it is shown in Refs. [1,2] where point scattered functions were simulated by Monte Carlo code MCNP-4C. The aim of the current study is to show that the point scattered functions can be described analytically and implemented in user-friendly correction procedure.
337
0.0
-50
-25 0 25 Distance, [mm]
50
Data: W320PXPSF_B Model: Gauss Chi^2/DoF = 4.3361E-13 R^2 = 0.94382 6.6373E-7 ± 8.2038E-8 y0 xc -0.1329 ± 0.17469 w 33.72142 ± 0.59318 A 0.00033 ± 7.7766E-6
Fig. 2. Fitting of the calculated PScF by a Gauss function.
To overcome this problem we used an analytical description of the PScF by Gaussian functions. The shape of the Gauss function was chosen due to the good agreement at large collision angles (the wings of the scattering function). The central area is also adequately described by the Gauss function (see Fig. 2). For the analytical description the behaviour of the Gaussian maximum and FWHM were
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
338
investigated for different H2O thicknesses at a fixed distance between the sample and the detector of 20 mm as shown in Fig. 3. Analogically the Gaussian parameters were investigated for different sample-to-detector distances at a defined liquid thickness of 3 mm water (Fig. 4). The obtained behaviours could be fitted analytically by exponential or linear functions as shown in the figures. From these analytical descriptions it was possible to reconstruct the corresponding PScF without simulating it again by Monte Carlo H2O - sample-to-detector distance: 20 mm
Maximum FWHM 50
y= -1E-5 exp(-x/1.23) + 9.21E-6
8.0x10-6
48
7.0x10-6
46
-6
6.0x10
44 5.0x10-6
FWHM, [mm]
Maximum
9.0x10-6
y = 17.77 exp(-x/1.41) + 40.32
calculations. For this purpose an IDL routine was used which returns the 2D Gauss function by given FWHM and maximum input parameters (Fig. 5). The so-calculated Gauss functions were used for further corrections.
42
4.0x10-6 3.0x10-6
1
2 3 4 Layer thickness, [mm]
40
5
Fig. 3. Analytical description of the PScF functions by Gauss functions with correspondent maximum and FWHM for a defined sample-to-detector distance.
Maximum FWHM
H2O - layer thickness: 3 mm 8.0x10-5
y= 0.00019 exp(-x/6.00633) + 1.8879E-6
y = 5.7 + 1.83x
60
4.0x10-5
FWHM
Maximum
100 80
6.0x10-5
40 2.0x10-5 20 0.0 0 0
Fig. 5. Calculated 2D analytical PScF using the parameters listed in the figures above for a water layer with a thickness of 20 mm at a distance of 20 mm from the detector.
10 20 30 40 50 Sample-to-detector distance, [mm]
Fig. 4. Analytical description of the PScF functions by Gauss functions with correspondent maximum and FWHM for a defined layer thickness.
3. Results obtained Sets of experiments were performed at the neutron research reactor SAFARI 1 at NECSA, South Africa. In aluminum containers with different thickness, three types of liquids (H2O, D2O and oil) were radiographed with thermal neutrons at different distances to the detector. Images without sample in the beam (open beam images) and dark current images were used for normalization of the data. The recorded images were used in the scattering correction procedure. The main parameters of the radiography facility NRAD at the SAFARI 1 are its L/D ratio of 153 and the available thermal neutron flux at the sample position of 1.08 107 n/cm2 s. As a detection system, a standard CCD radiography configuration was used. The image obtained on the NE426 (6LiFZnS:Ag) scintillator was projected via a mirror and an optical lens
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
H2O - layer thickness: 2 mm sample-to-detector distance: 20 mm 1.2
before the correction after the correction
sample-to-detector distance: 20 mm 30 mm 50 mm
H2O - layer thickness: 3 mm before the correction
Normalized intensity, I/Io
1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4
0.50 0.43 0.37
0.3 0
200
400 Pixel
600
800
sample-to-detector distance: 20 mm 30 mm 50 mm
H2O - layer thickness: 3 mm after the correction 1.1 Normalized intensity, I/Io
system to a CCD camera (Andor DV-434) with a 1024(H) 1024(V) pixel array and 13 13 mm pixel size. The dynamic range of the camera is 16 bit. The corrections were performed as a subtraction of the analytical calculated Gauss shaped PScF from all the pixels in the sample area. An example for this is shown in Fig. 6. It can be seen that after the correction procedure the build-up effect due to scattered neutrons is not present in the intensity profile (Fig. 6). The correction method was used to determine quantitatively the measured beam attenuation for a defined liquid thickness at different distances between the sample and the detector. For this purpose a water layer with a thickness of 3 mm was used. From the profiles presented in Fig. 7, before and after the correction procedure, it could be seen that before the correction the attenuation level cannot be defined as unique. After the correction, the attenuation can be determined with a good precision of approx. 3% statistical error. The same correction procedure was performed for different thicknesses of D2O and oil layers radiographed at various distances to the detector. From the obtained images the linear macroscopic attenuation coefficients Stot (see Eq. (1)) were calculated and compared for the cases before and
339
1.0 0.9 0.8 0.7 0.6 0.5 0.4
0.35 + 0.01
0.3 0
200
400 Pixel
600
800
Fig. 7. Intensity profiles for a defined water layer at different distances from the detector before and after the correction procedure.
Normalized intensity, I/Io
1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0
200
400 600 Pixel
800
1000
Fig. 6. Intensity profiles for a 2 mm water layer at a distance 20 mm from the detector before and after the correction procedure.
after the correction procedure. The results are shown in Fig. 8. As seen from Fig. 8 the distance dependence of the calculated attenuation coefficient for the three liquids can be minimized using the scattering correction procedure as described above. In this way a higher accuracy at the determination of the corresponding attenuation coefficient of a few percentage is achieved. The contribution of the liquid thickness to the fluctuation of the attenuation coefficient at a fixed distance to the detector was also investigated and the comparison of the data obtained before and
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
340
Before the correction After the correction
H2O - layer thickness: 3 mm Attenuation coefficient Σ, [cm-1]
4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0
2
3
4
5
after the correction procedure for two liquids (H2O and oil) is presented in Fig. 9. It can be seen that the application of scattering corrections using analytical calculated PScF reduces considerably the error at the determination of the corresponding attenuation coefficient. The relative errors after the corrections calculated from the data shown in Fig. 9 vary between 3 and 4% for different layer thicknesses, which is much lower than the error before the corrections getting values more than 10%. This means that the use of this kind of corrections can help to improve the
Distance sample-detector, [cm]
Before the corrections After the corrections
Distance sample-detector: 20 mm
Attenuation coefficient Σ, [cm-1]
5.0 Attenuation coefficient Σ, [cm-1]
5
Before the correction After the correction
Oil - layer thickness: 3 mm
4.5 4.0 3.5 3.0 2.5 2.0 2
Σ = 4.26 ± 0.16 cm-1
4
3
2
3 4 5 Distance sample-detector, [cm]
0.1
0.2
0.3
0.4
0.5
Oil layer thickness, [cm] D2O - layer thickness: 3 mm
Before the correction After the correction
Distance sample-detector: 20 mm
4.0
0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40
2
3
4
5
Distance sample-detector, [cm]
Fig. 8. Calculated attenuation coefficients before and after the scattering corrections for three liquids (H2O, oil and D2O) with a thickness of 3 mm radiographed at different distances to the detector.
Attenuation cofficient Σ, [cm-1]
Attenuation coefficient Σ, [cm-1]
0.80
Before the corrections After the corrections
Σ = 3.53 + 0.14 cm-1
3.5
3.0
2.5
2.0 0.1
0.2 0.3 0.4 H2O layer thickness, [cm]
0.5
Fig. 9. Calculated attenuation coefficients for two liquids (H2O and oil) with different thicknesses radiographed at a fixed distance of 20 mm to the detector before and after the scattering corrections.
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
accuracy of the quantitative neutron radiography investigations of hydrogenous materials.
4. Conclusion The use of scattering corrections in neutron radiography images helps to eliminate the build-up effect caused by the incoherent scattering in the sample typical for all hydrogenous materials. For this purpose point scattered functions were described analytically by Gauss functions for three liquids (water, heavy water and oil). The parameters of the Gauss functions (maximum value and FWHM) were investigated in dependence of the thickness of the liquid layers and the distance between the layer and the detector. The so-defined scattering functions will be implemented in a userfriendly software for scattering corrections in radiography images of simple sample geometries (slabs, cylinders and so on). For the future, an attempt to extend the correction method for arbitrary sample geometries will be made.
341
Acknowledgements This research project has been supported by the International Atomic Energy Agency under the Co-ordinated Research Project in ‘‘Development of improved sources and imaging systems for neutron radiography’’ (F1-RC-925): IAEA Research Contract no 12455/R0/RBF. References [1] N. Kardjilov, E. Lehmann, P. Vontobel, Appl. Phys. A 74 (Suppl.) (2002) S228. [2] N. Kardjilov, F. de Beer, M. Middleton, E. Lehmann, B. Schillinger, P. Vontobel, Corrections for scattered neutrons in quantitative neutron radiography, Proceedings of the Seventh World Conference on Neutron Radiography, 2002. [3] J. Briesmeister (Ed.), MCNP—a General Monte Carlo NParticle Transport Code, Version 4B, Los Alamos National Lab., Los Alamos, 1996. [4] D.E. Cullen, L.F. Hansen, E.M. Lent, E.F. Plechaty, Thermal scattering law data: implementation and testing using the Monte Carlo neutron transport codes COG, MCNP and TART, report of Lawrence Livermore National Laboratory, UCRL-ID-153656, May 17, 2003.
Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341 www.elsevier.com/locate/nima
Scattering corrections in neutron radiography using point scattered functions N. Kardjilova,, F. de Beerb, R. Hassaneinc, E. Lehmannc, P. Vontobelc a
Department of Materials (SF3), Hahn-Meitner-Institut, Glienicker Str. 100, 14109 Berlin, Germany b NECSA, Pretoria, South Africa c Paul Scherrer Institute, Villigen, Switzerland Available online 25 February 2005
Abstract Scattered neutrons cause distortions and blurring in neutron radiography pictures taken at small distances between the investigated object and the detector. This defines one of the most significant problems in quantitative neutron radiography. The quantification of strong scattering materials such as hydrogenous materials—water, oil, plastic, etc.— with a high precision is very difficult due to the scattering effect in the radiography images. The scattering contribution in liquid test samples (H2O, D2O and a special type oil ISOPAR L) at different distances between the samples and the detector, the so-called Point Scattered Function (PScF), was calculated with the help of MCNP-4C Monte Carlo code. Corrections of real experimental data were performed using the calculated PScF. Some of the results as well as the correction algorithm will be presented. r 2005 Elsevier B.V. All rights reserved. PACS: 28.20Cz; 02.70Lq; 87.59Hp Keywords: Quantitative neutron radiography; Monte Carlo simulations; Scattering corrections
1. Introduction The digital processing of neutron radiography images gives the possibility for data quantification. In this case an exact relation between the measured neutron attenuation and the real macroscopic attenuation coefficient for every point of the Corresponding author. Tel.: +49 30 80622298;
fax: +49 30 80623094. E-mail address: [email protected] (N. Kardjilov).
sample is required. The assumption that the attenuation of the neutron beam through the sample is exponential I=I 0 ¼ expðtot d Þ
(1)
where I0 and I are the intensities of the beam before and after the transmission and Stot and d are the linear attenuation coefficient and the thickness of the sample, is valid only in an ideal case, where a monochromatic beam,
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.159
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
2. Analytical point scattered functions The scattering correction procedure was based on the simulation of the scattering component for different liquids at various distances from the detector using a Monte Carlo computation method. For this purpose the MCNP-4C code [3] was used. The reproducibility of the calculation of the scattering component, so-called Point Scattered Function (PScF), was tested by using different tallies (detector types). The comparison presented in Fig. 1 shows that the obtained behaviour of the scattering properties for a thin H2O layer of 3 mm is similar for all the used tallies. The observed drop in the central area of the PScF could be explained by uncertainties in the MCNP calculations for very narrow collision angles. This problem comes from the uncertainty of the MCNP code in case of using the Sða; bÞ treatment for processes of inelastic scattering from bounding materials like water [4].
Normalized intensity, (I/Io)
Water layer Thickness: 3 mm Distance sample-detector: 20 mm
Using F5 tally (point detector) Using F4 tally and a lattice structure Using F1 tally (ring detector)
1.2x10-5 1.0x10-5 8.0x10-6 6.0x10-6 4.0x10-6 2.0x10-6 0.0 -4
-2
0 2 Distance, cm
4
Fig. 1. Point scattering functions calculated by using different MCNP tally structures.
H2O Thickness: 3 mm; Distance sample-detector: 20 mm PScF(MCNP) Gauss fit
1.0x10-5
FWHM
5.0x10-6
Maximum
Normalized intensity (I/Io)
non-scattering sample and non-background contribution are assumed. In the real case these conditions are not fulfilled and in dependence on the sample material we have more or less deviation from the exponential attenuation law. Because of the high scattering cross-sections of hydrogen for thermal neutrons, the problem with the scattered neutrons at quantitative radiography investigations of hydrogenous materials (as PE, PMMA, oil, H2O, etc.) is not trivial. For these strong scattering materials the neutron beam attenuation is no longer exponential and a dependence of the macroscopic attenuation coefficient on the material thickness and on the distance between the sample and the detector appears. When quantitative radiography (2D) or tomography investigations (3D) are performed, some image restoration procedures for a correction of the scattering effect are required. An example for it is shown in Refs. [1,2] where point scattered functions were simulated by Monte Carlo code MCNP-4C. The aim of the current study is to show that the point scattered functions can be described analytically and implemented in user-friendly correction procedure.
337
0.0
-50
-25 0 25 Distance, [mm]
50
Data: W320PXPSF_B Model: Gauss Chi^2/DoF = 4.3361E-13 R^2 = 0.94382 6.6373E-7 ± 8.2038E-8 y0 xc -0.1329 ± 0.17469 w 33.72142 ± 0.59318 A 0.00033 ± 7.7766E-6
Fig. 2. Fitting of the calculated PScF by a Gauss function.
To overcome this problem we used an analytical description of the PScF by Gaussian functions. The shape of the Gauss function was chosen due to the good agreement at large collision angles (the wings of the scattering function). The central area is also adequately described by the Gauss function (see Fig. 2). For the analytical description the behaviour of the Gaussian maximum and FWHM were
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
338
investigated for different H2O thicknesses at a fixed distance between the sample and the detector of 20 mm as shown in Fig. 3. Analogically the Gaussian parameters were investigated for different sample-to-detector distances at a defined liquid thickness of 3 mm water (Fig. 4). The obtained behaviours could be fitted analytically by exponential or linear functions as shown in the figures. From these analytical descriptions it was possible to reconstruct the corresponding PScF without simulating it again by Monte Carlo H2O - sample-to-detector distance: 20 mm
Maximum FWHM 50
y= -1E-5 exp(-x/1.23) + 9.21E-6
8.0x10-6
48
7.0x10-6
46
-6
6.0x10
44 5.0x10-6
FWHM, [mm]
Maximum
9.0x10-6
y = 17.77 exp(-x/1.41) + 40.32
calculations. For this purpose an IDL routine was used which returns the 2D Gauss function by given FWHM and maximum input parameters (Fig. 5). The so-calculated Gauss functions were used for further corrections.
42
4.0x10-6 3.0x10-6
1
2 3 4 Layer thickness, [mm]
40
5
Fig. 3. Analytical description of the PScF functions by Gauss functions with correspondent maximum and FWHM for a defined sample-to-detector distance.
Maximum FWHM
H2O - layer thickness: 3 mm 8.0x10-5
y= 0.00019 exp(-x/6.00633) + 1.8879E-6
y = 5.7 + 1.83x
60
4.0x10-5
FWHM
Maximum
100 80
6.0x10-5
40 2.0x10-5 20 0.0 0 0
Fig. 5. Calculated 2D analytical PScF using the parameters listed in the figures above for a water layer with a thickness of 20 mm at a distance of 20 mm from the detector.
10 20 30 40 50 Sample-to-detector distance, [mm]
Fig. 4. Analytical description of the PScF functions by Gauss functions with correspondent maximum and FWHM for a defined layer thickness.
3. Results obtained Sets of experiments were performed at the neutron research reactor SAFARI 1 at NECSA, South Africa. In aluminum containers with different thickness, three types of liquids (H2O, D2O and oil) were radiographed with thermal neutrons at different distances to the detector. Images without sample in the beam (open beam images) and dark current images were used for normalization of the data. The recorded images were used in the scattering correction procedure. The main parameters of the radiography facility NRAD at the SAFARI 1 are its L/D ratio of 153 and the available thermal neutron flux at the sample position of 1.08 107 n/cm2 s. As a detection system, a standard CCD radiography configuration was used. The image obtained on the NE426 (6LiFZnS:Ag) scintillator was projected via a mirror and an optical lens
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
H2O - layer thickness: 2 mm sample-to-detector distance: 20 mm 1.2
before the correction after the correction
sample-to-detector distance: 20 mm 30 mm 50 mm
H2O - layer thickness: 3 mm before the correction
Normalized intensity, I/Io
1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4
0.50 0.43 0.37
0.3 0
200
400 Pixel
600
800
sample-to-detector distance: 20 mm 30 mm 50 mm
H2O - layer thickness: 3 mm after the correction 1.1 Normalized intensity, I/Io
system to a CCD camera (Andor DV-434) with a 1024(H) 1024(V) pixel array and 13 13 mm pixel size. The dynamic range of the camera is 16 bit. The corrections were performed as a subtraction of the analytical calculated Gauss shaped PScF from all the pixels in the sample area. An example for this is shown in Fig. 6. It can be seen that after the correction procedure the build-up effect due to scattered neutrons is not present in the intensity profile (Fig. 6). The correction method was used to determine quantitatively the measured beam attenuation for a defined liquid thickness at different distances between the sample and the detector. For this purpose a water layer with a thickness of 3 mm was used. From the profiles presented in Fig. 7, before and after the correction procedure, it could be seen that before the correction the attenuation level cannot be defined as unique. After the correction, the attenuation can be determined with a good precision of approx. 3% statistical error. The same correction procedure was performed for different thicknesses of D2O and oil layers radiographed at various distances to the detector. From the obtained images the linear macroscopic attenuation coefficients Stot (see Eq. (1)) were calculated and compared for the cases before and
339
1.0 0.9 0.8 0.7 0.6 0.5 0.4
0.35 + 0.01
0.3 0
200
400 Pixel
600
800
Fig. 7. Intensity profiles for a defined water layer at different distances from the detector before and after the correction procedure.
Normalized intensity, I/Io
1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0
200
400 600 Pixel
800
1000
Fig. 6. Intensity profiles for a 2 mm water layer at a distance 20 mm from the detector before and after the correction procedure.
after the correction procedure. The results are shown in Fig. 8. As seen from Fig. 8 the distance dependence of the calculated attenuation coefficient for the three liquids can be minimized using the scattering correction procedure as described above. In this way a higher accuracy at the determination of the corresponding attenuation coefficient of a few percentage is achieved. The contribution of the liquid thickness to the fluctuation of the attenuation coefficient at a fixed distance to the detector was also investigated and the comparison of the data obtained before and
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
340
Before the correction After the correction
H2O - layer thickness: 3 mm Attenuation coefficient Σ, [cm-1]
4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0
2
3
4
5
after the correction procedure for two liquids (H2O and oil) is presented in Fig. 9. It can be seen that the application of scattering corrections using analytical calculated PScF reduces considerably the error at the determination of the corresponding attenuation coefficient. The relative errors after the corrections calculated from the data shown in Fig. 9 vary between 3 and 4% for different layer thicknesses, which is much lower than the error before the corrections getting values more than 10%. This means that the use of this kind of corrections can help to improve the
Distance sample-detector, [cm]
Before the corrections After the corrections
Distance sample-detector: 20 mm
Attenuation coefficient Σ, [cm-1]
5.0 Attenuation coefficient Σ, [cm-1]
5
Before the correction After the correction
Oil - layer thickness: 3 mm
4.5 4.0 3.5 3.0 2.5 2.0 2
Σ = 4.26 ± 0.16 cm-1
4
3
2
3 4 5 Distance sample-detector, [cm]
0.1
0.2
0.3
0.4
0.5
Oil layer thickness, [cm] D2O - layer thickness: 3 mm
Before the correction After the correction
Distance sample-detector: 20 mm
4.0
0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40
2
3
4
5
Distance sample-detector, [cm]
Fig. 8. Calculated attenuation coefficients before and after the scattering corrections for three liquids (H2O, oil and D2O) with a thickness of 3 mm radiographed at different distances to the detector.
Attenuation cofficient Σ, [cm-1]
Attenuation coefficient Σ, [cm-1]
0.80
Before the corrections After the corrections
Σ = 3.53 + 0.14 cm-1
3.5
3.0
2.5
2.0 0.1
0.2 0.3 0.4 H2O layer thickness, [cm]
0.5
Fig. 9. Calculated attenuation coefficients for two liquids (H2O and oil) with different thicknesses radiographed at a fixed distance of 20 mm to the detector before and after the scattering corrections.
ARTICLE IN PRESS N. Kardjilov et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 336–341
accuracy of the quantitative neutron radiography investigations of hydrogenous materials.
4. Conclusion The use of scattering corrections in neutron radiography images helps to eliminate the build-up effect caused by the incoherent scattering in the sample typical for all hydrogenous materials. For this purpose point scattered functions were described analytically by Gauss functions for three liquids (water, heavy water and oil). The parameters of the Gauss functions (maximum value and FWHM) were investigated in dependence of the thickness of the liquid layers and the distance between the layer and the detector. The so-defined scattering functions will be implemented in a userfriendly software for scattering corrections in radiography images of simple sample geometries (slabs, cylinders and so on). For the future, an attempt to extend the correction method for arbitrary sample geometries will be made.
341
Acknowledgements This research project has been supported by the International Atomic Energy Agency under the Co-ordinated Research Project in ‘‘Development of improved sources and imaging systems for neutron radiography’’ (F1-RC-925): IAEA Research Contract no 12455/R0/RBF. References [1] N. Kardjilov, E. Lehmann, P. Vontobel, Appl. Phys. A 74 (Suppl.) (2002) S228. [2] N. Kardjilov, F. de Beer, M. Middleton, E. Lehmann, B. Schillinger, P. Vontobel, Corrections for scattered neutrons in quantitative neutron radiography, Proceedings of the Seventh World Conference on Neutron Radiography, 2002. [3] J. Briesmeister (Ed.), MCNP—a General Monte Carlo NParticle Transport Code, Version 4B, Los Alamos National Lab., Los Alamos, 1996. [4] D.E. Cullen, L.F. Hansen, E.M. Lent, E.F. Plechaty, Thermal scattering law data: implementation and testing using the Monte Carlo neutron transport codes COG, MCNP and TART, report of Lawrence Livermore National Laboratory, UCRL-ID-153656, May 17, 2003.