The Pennsylvania State University. The Graduate School. Department of Mechanical and Nuclear Engineering

Transcription

1 The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering ERROR CORRECTIONS FOR QUANTITATIVE THERMAL NEUTRON COMPUTED TOMOGRAPHY A Dissertation in Nuclear Engineering by Liang Shi 2010 Liang Shi Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy December 2010

2 The dissertation of Liang Shi was reviewed and approved* by the following: Jack Brenizer J. Lee Everett Professor of Mechanical and Nuclear Engineering Dissertation Advisor Chair of Committee Kenan Ünlü Director of the Radiation Science and Engineering Center Professor of Nuclear Engineering Matthew Mench Professor and Condra Chair of Excellence in Energy Conversion and Storage Department of Mechanical, Aerospace and Biomedical Engineering University of Tennessee Knoxville Adjunct Faculty at Pennsylvania State University, University Park William Higgins Distinguished Professor of Electrical Engineering Arthur Motta Professor of Nuclear Engineering and Materials Science and Engineering Chair of Nuclear Engineering *Signatures are on file in the Graduate School

3 iii ABSTRACT A state-of-the art, two mirror reflection, combination of a Li-6 scintillation screen and a cooled CCD camera high spatial resolution neutron radioscopy imaging system was designed and developed in the RSEC at Penn State. Radiation shielding was applied to the imaging system to achieve a higher spatial resolution. Modulation Transfer Function (MTF) analysis shows that a spatial resolution of 116 microns was achieved. The imaging system was successfully applied for diagnostic measurements of hydrogen fuel cells. A quantitative neutron computed tomography NCT model was developed which confirmed the fundamental computed tomography theory. The model justified the partial volume neutron computed tomography water/ice mass evaluation technique which was designed and tested by Heller. The evaluation results of the water/ice mass using the NCT method was very close to the theoretical value. Sample and background neutron scattering effects were considered as one of the errors that influenced the accuracy of the quantitative measurement using the NCT method. The neutron scattering effect induced cupping artifacts that also contributed to the error in the measurement of water/ice mass using NCT. One method was developed to reduce the cupping artifacts in the reconstruction slice of the water/ice column. The geometric unsharpness,u g, was demonstrated as the predominant source of error for the accuracy of the 3-D water/ice mass evaluation technique. A unique method was established to reduce the divergence neutron beam associated geometric unsharpness U g. Compared to the de-convolution algorithm used in de-blurring the

4 iv image projection, the method has the advantage of minimizing the unsharpness while keeping the degree of cupping through the water column the same. For the 3-D water/ice mass evaluation purpose, this method is a better choice for the water quantification technique error correction.

5 v TABLE OF CONTENTS LIST OF FIGURES... viii LIST OF TABLES... xvii NOMENCLATURE... xix ACKNOWLEDGEMENTS... xxii Chapter 1 INTRODUCTION Neutron Physics Neutron Source Neutron Interaction with Materials Neutron Detection Neutron Imaging Technique Physics and Mathematics of Neutron Radioscopy Neutron Imaging Detectors Neutron Computed Tomography Motivation and Statement of Research Objectives Chapter 2 NEUTRON IMAGING SYSTEM DESIGN Overall Design Strategy Upper Portion of the Imaging System Lower Portion of the Imaging System Adjunct Component Lower Portion Radiation Shielding Design Shielding Strategy Shielding Materials Spatial Resolution Modulation Transfer Function Theory for the Neutron Imaging System Experimental Measurement and Results Summary Chapter 3 QUANTITATIVE NEUTRON COMPUTED TOMOGRAPHY MODEL DESIGN Determination of Effective Thermal Neutron Macroscopic Cross Sections of the Selected Materials for the Thremal Neutron Imaging System Experiment Setup and Measurement Method... 51

6 vi Measurement Results and Discussion Determination of total Thermal Neutron Macroscopic Cross Sections of different Densities P.E. foams Chapter 4 SIMULATION AND EXPERIMENTAL VALIDATION OF THE QUANTITATIVE NEUTRON COMPUTED TOMOGRAPHY MODEL D Thermal Neutron Radioscopy Projection Model Analytical Simulation of the 2-D Thermal Neutron Radioscopy Projections Simulation Results and Discussion Experiment Validation of the Model Measurement Results and Discussion Initial Water/Ice Mas Evaluation Result Using Neutron Computed Tomography Technique D NCT Water/Ice Mass Evaluation Theory Experiment Setup for 3-D NCT Water/Ice Mass Evaluation D NCT Water/Ice Mass Evaluation Results and Discussion Chapter 5 ERROR CORRECTION AND ANALYSIS METHODS FOR QUANTITATIVE NEUTRON COMPUTED TOMOGRAPHY Neutron Scattering Effects Background Neutron Scattering Correction Method Cupping Artifacts and Beam Hardening Cupping Artifacts and Neutron Scattering Proposed Experiment Setup for Neutron Scattering Induced Cupping Artifacts Reduction Measurement Results and Discussion Geometric Unsharpness U g Evaluation and Correction Method for Neutron Computed Tomography System in RSEC Geometric Unsharpness U g for Neutron Radioscopy Imaging True Magnification M and Magnification m for the Neutron Radioscopy System Proposed Geometric Unsharpness U g Correction Method for 3-D NCT Water/Ice Mass Evaluation Work Meaurement Results and Discussion Chapter 6 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK Conclusions Suggestions for Future Work BIBLIOGRAPHY

7 Appendix A Plots for Other Materials Attenuation Measurement Results Appendix B Demonstraction of Various Measurement Results Due to Experimental Setup Change Appendix C Linear Attenuation Plots for the Materials under different Experimental Conditions and with the Background Neutron Scattering Correction Method vii

8 viii LIST OF FIGURES Figure 1.1: Various types of neutron interactions with matter Figure 1.2: A comparison of neutron and 100KeV, 600KeV X-rays mass attenuation coefficients versus atomic number Figure 1.3: Neutron radioscopy imaging system Figure 1.4: Projection data geometry in neutron computed tomography (a) parallel beam geometry (b) fan beam geometry Figure 2.1: The schematic diagram of the neutron imaging system Figure 2.2: Front view of the upper thermal neutron imaging component, with a 28 cm 28 cm field of view Figure 2.3: Front view of the first surface mirror without scintillation screen Figure 2.4: Inner structure of the adjunct portion of the imaging system Figure 2.5: A separate structure was used for stacking different shielding materials Figure 2.6: Inner structure of lower portion of the thermal neutron imaging system...34 Figure 2.7: Lead bricks were placed around the lower portion of the imaging system as the first layer of shielding materials to absorb gamma photons Figure 2.8: BORAL were placed around outside the lead bricks as the second layer of the shielding material to absorb thermal neutrons Figure 2.9: Flex Boron Sheet were placed around outside the BORAL plates as the third layer of shielding material to absorb thermal neutrons Figure 2.10: Normalized knife-edge intensity data for the neutron imaging system. The dash line represents the curve fit result to the experimental measured data Figure 2.11: The neutron imaging system impulse response function derived from the gadolinium knife edge Figure 2.12: Modulation transfer function for the neutron imaging system Figure 3.1: Flow chart of the experimental and theoretical thermal neutron computed tomography model. (a).direct experimental thermal neutron

9 ix computed tomography data acquisition and (b). indirect simulated thermal neutron computed tomography data acquisition, which needs geometry and material attenuation property of the object Figure 3.2: Blank beam shot image of the entire scintillation screen. The red arrows mark individual Position is where the metal samples were tested Figure 3.3: Linear attenuation property of aluminum sample step wedge at Position 1 of the scintillation screen Figure 3.4: Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 1 of the scintillation screen Figure 3.5: Linear attenuation property of aluminum sample step wedge at Position 2 of the scintillation screen Figure 3.6: Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 2 of the scintillation screen Figure 3.7: Linear attenuation property of aluminum sample step wedge at Position 3 of the scintillation screen Figure 3.8: Corresponding calculated effective total thermal neutron macroscopic cross sections of aluminum versus step wedge thickness at Position 3 of the scintillation screen Figure 3.9: Linear attenuation property of aluminum sample step wedge at Position 4a of the scintillation screen Figure 3.10: Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 4a of the scintillation screen Figure 3.11: Linear attenuation property of aluminum sample step wedge at Position 4d of the scintillation screen Figure 3.12: Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 4d of the scintillation screen Figure 3.13: Linear attenuation property of aluminum sample step wedge at Position 5 of the scintillation screen

10 x Figure 3.14: Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 5 of the scintillation screen Figure 3.15: First recorded 2-D neutron radioscopy image for different density P.E foams after beam and power normalization Figure 3.16: Second recorded 2-D neutron radioscopy image for different density P.E foams after beam and power normalization Figure 3.17: Third recorded 2-D neutron radioscopy image for the 0.333g/cm 3 P.E. foams after beam and power normalization Figure 3.18: Linear attenuation property of the P.E foam with a density of g/cm Figure 3.19: Corresponding calculated effective total thermal neutron macroscopic cross section for the P.E foam of g/cm 3 versus thickness Figure 3.20: Linear attenuation property of the P.E foam with a density of 0.04g/cm Figure 3.21: Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of 0.04g/cm 3 versus thickness Figure 3.22: Linear attenuation property of the P.E foam with a density of 0.05g/cm Figure 3.23: Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of 0.05g/cm 3 versus thickness Figure 3.24: Linear attenuation property of the P.E foam with a density of 0.125g/cm Figure 3.25: Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of 0.125g/cm 3 versus thickness Figure 3.26: Linear attenuation property of the P.E foam with a density of 0.2g/cm Figure 3.27: Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of 0.2g/cm 3 versus thickness Figure 3.28: Linear attenuation property of the P.E foam with a density of 0.333g/cm

11 xi Figure 3.29: Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of 0.333g/cm 3 versus thickness Figure 3.30: Linear relationship between the total thermal neutron macroscopic cross sections and the densities for selected P.E foams Figure 4.1: Linear relationship between the calculated total thermal neutron macroscopic cross sections of the P.E foams at 4.68mm and the density Figure 4.2: Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the /cm 3 P.E foam) Figure 4.3: The corresponding cross-sectional reconstruction result for the first density section (0.0286g/cm 3 ) of the object. The location of this crosssectional slice is indicated by the horizontal red-line in Figure Figure 4.4: Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the 0.04g/cm 3 P.E foam) Figure 4.5: The corresponding cross-sectional reconstruction result for the second density section (0.04g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure Figure 4.6: Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the 0.05/cm 3 P.E foam) Figure 4.7: The corresponding cross-sectional reconstruction result for the third density section (0.05g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure Figure 4.8: Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the 0.125/cm 3 P.E foam) Figure 4.9: The corresponding cross-sectional reconstruction result for the fourth density section (0.125g/cm 3 ) of the object. The location of this crosssectional slice is indicated by the horizontal red-line in Figure Figure 4.10: Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the 0.2/cm 3 P.E foam) Figure 4.11: The corresponding cross-sectional reconstruction result for the fifth density section (0.2g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure Figure 4.12: Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the 0.333/cm 3 P.E foam)

12 Figure 4.13: The corresponding cross-sectional reconstruction result for the sixth density section (0.333g/cm 3 ) of the object. The location of this crosssectional slice is indicated by the horizontal red-line in Figure Figure 4.14: Linear relationship between voxel gray values and the corresponding total macroscopic cross sections for each density P.E foams Figure 4.15: Top view of the designed object which was used for the NCT model Figure 4.16: Thermal neutron computed tomography experiment setup to validate the simulation model Figure 4.17: Experimental measurement result of NCT projection data. The redline indicates the location of the first density section (0.0286g/cm 3 ) of P.E foam Figure 4.18: The corresponding cross-sectional reconstruction result for the first density section (0.0286g/cm 3 ) of the object. The location of this crosssectional slice is indicated by the horizontal red-line in Figure Figure 4.19: Experimental measurement result of NCT projection data. The redline indicates the location of the second density section (0.04g/cm 3 ) of P.E foam Figure 4.20: The corresponding cross-sectional reconstruction result for the second density section (0.04g/cm 3 ) of the object. The location of this crosssectional slice is indicated by the horizontal red-line in Figure Figure 4.21: Experimental measurement result of NCT projection data. The redline indicates the location of the third density section (0.05g/cm 3 ) of P.E foam Figure 4.22: The corresponding cross-sectional reconstruction result for the third density section (0.05g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure Figure 4.23: Experimental measurement result of NCT projection data. The redline indicates the location of the fourth density section (0.125g/cm 3 ) of P.E foam Figure 4.24: The corresponding cross-sectional reconstruction result for the fourth density section (0.125g/cm 3 ) of the object. The location of this crosssectional slice is indicated by the horizontal red-line in Figure Figure 4.25: Experimental measurement result of NCT projection data. The redline indicates the location of the fifth density section (0.2g/cm 3 ) of P.E foam xii

13 Figure 4.26: The corresponding cross-sectional reconstruction result for the fifth density section (0.2g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure Figure 4.27: Experimental measurement result of NCT projection data. The redline indicates the location of the sixth density section (0.333g/cm 3 ) of P.E foam Figure 4.28: The corresponding cross-sectional reconstruction result for the sixth density section (0.333g/cm 3 ) of the object. The location of this crosssectional slice is indicated by the horizontal red-line in Figure Figure 4.29: Comparison plot of average voxel gray values versus densities of different density P.E foams from experiment measurement and simulation result Figure 4.30: Comparison plot of average voxel gray values versus corresponding total thermal neutron macroscopic cross sections for different density P.E foams from experiment and simulation result Figure 4.31: The aluminum cylinder teste sample for 3-D NCT water/ice mass evaluation experiment and its dimensions Figure 4.32: A 3-Dimensional NCT reconstruction result of water column with diameter of 3.988mm Figure 5.1: Experimental setup for testing the impact of backscattered neutrons on the scintillation screen of NCT facility at RSEC. The moving BORAL plate was moving uniformly at step size of 20mm from left to right side of the scintilaltion screen Figure 5.2: The recorded neutron beam intensity in the shielded open beam area when the BORAL shielding plate moved from left to right side of the scintillation screen Figure 5.3: The recorded neutron beam intensity in the selected area behind the shielding area (Backscattered component) when the BORAL shielding plate moved from left to right side of the scintillation screen Figure 5.4: The measured effective macroscopic cross sction of copper as BORAL plate moving from left to right side of the scintillation screen Figure 5.5: The measured effective macroscopic cross section of iron as BORAL plate moving from left to right side of the scintillation screen xiii

14 Figure 5.6: The measured effective macroscopic cross section of lead as the BORAL plate moving from left to right side of the scintillation screen Figure 5.7: The surrounding area of sample materials are completely covered by BORAL plates and were put directly against the scintillation screen Figure 5.8: Experiment setup with opaque paper behind scintillation screen which was used to shielding light photons. The center cut in the opaque paper has the exactly same spatial location as where the sample was measured in front of the scintillation screen Figure 5.9: The linear attenuation property of aluminum step wedge after background neutron scattering correction. The scattering correction (shield), direct measurement results and the theoretical value were also plot in the same figure Figure 5.10: The linear attenuation property of copper step wedge after background neutron scattering correction. The scattering correction (shield), direct measurement results and the theoretical value were also plot in the same figure Figure 5.11: The linear attenuation property of iron step wedge after background neutron scattering correction. The scattering correction (shield), direct measurement results and the theoretical value were also plot in the same figure Figure 5.12: The linear attenuation property of lead step wedge after background neutron scattering correction. The scattering correction (shield), direct measurement results and the theoretical value were also plot in the same figure Figure 5.13: Cross-sectional reconstruction results of the 3.988mm diameter water column when the object-to-detector distance is 0mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen Figure 5.14: The corresponding voxel gray values across the 3.988mm diameter water column Figure 5.15: Cross-sectional reconstruction results of the 3.988mm diameter water column when the object-to-detector distance is 35mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen Figure 5.16: The corresponding voxel gray values across the 3.988mm diameter water column xiv

15 Figure 5.17: Cross-sectional reconstruction results of the 3.988mm diameter water column when the object-to-detector distance is 70mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen Figure 5.18: The corresponding voxel gray values across the 3.988mm diameter water column Figure 5.19: Cross-sectional reconstruction results of the 3.988mm diameter water column when the object-to-detector distance is 105mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen Figure 5.20: The corresponding voxel gray values across the 3.988mm diameter water column Figure 5.21: Cross-sectional reconstruction results of the 3.988mm diameter water column when the object-to-detector distance is 140mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen Figure 5.22: The corresponding voxel gray values across the 3.988mm diameter water column Figure 5.23: Magnitude of the cupping versus object-to-detector distance for 3.988mm cavity diameter sample Figure 5.24: The normalized line profile of the test object with 3.988mm diameter cavity in the center for the object-to-detector distance of 140mm using MCNP and neutron attenuation law Figure 5.25: The corresponding 3.988mm diameter water column voxel gray value in the reconstruction slices from the radioscopy images of the test object generated by MCNP and ideally method. The object-to-detector distance is 140mm Figure 5.26: Illustration of geometric unshaprness in X-rays imaging inspection setup Figure 5.27: The magnified in normalized 2-D neutron radioscopy image of the 3.988mm diameter water column with object-to-detector distance of 140mm. The blurred edge of water column due to the geometric unsharpness U g is indicated in the image Figure 5.28: The line profile of the voxel gray values through the center of the 3.98mm diameter water column with object-to-detector distance of 140mm. xv

16 Note the edges of the profile are bended outward, which is caused by geometric unsharpness U g Figure 5.29: Illustration of a magnified image produced from a point source (a) and from a finite area source (b) Figure 5.30: The line profile of the normalized voxel gray values through the center of a 3.988mm diameter water column cross sectional slice that was reconstructed from experimental projection data. The un-sharp outline due to geometric unsharpness U g and geometric magnification M is indicated by the black line. The ideal voxel gray values under the magnified condition are indicated by the red line Figure 5.31:Top view of the 3-D NCT water/ice mass evaluation experiment setup before increasing effective L/D ratio to reduce geometric unsharpness U g Figure 5.32:Top view of the 3-D NCT water/ice mass evaluation experiment setup after increasing effective L/D ratio to reduce geometric unsharpness U g Figure 5.33: The geometry needed for the width of wooden spacer calculation Figure 5.34: Front view of the BORAL shielding structure including wooden spacer and its dimensions Figure 5.35: Experiment setup for the geometric unsharpness U g reduction Figure 5.36: The 3.988mm diameter water column reconstruction stack averaged from slices 200 to 450. (a) without BORAL shielding plates and (b) with BORAL shielding plates Figure 5.37: The comparison of the normalized voxel gray values for the 3.988mm diameter water column reconstruction stack averaged from slices 200 to 450 with and without BORAL shielding plates in place xvi

17 xvii LIST OF TABLES Table 1.1: Types of neutron sources Table 1.2: Lists of nuclear reaction used for neutron imaging detector Table 3.1: Comparison of the reported and experiment determined total macroscopic cross sections of the materials using the imaging facility Table 3.2: Calculated total thermal neutron macroscopic cross sections of the selected P.E foams Table 4.1: The mean free path of the metals calculated from the determined total thermal neutron macroscopic cross sections for the imaging system Table 4.2: The mean free path of different densities P.E foams calculated from the determined total thermal neutron macroscopic cross sections for the imaging system Table 4.3: Calculated total thermal neutron macroscopic cross sections of different density P.E foams at thickness of 4.68mm Table 4.4: The average voxel gray value of each density P.E foam in the simulated cross sectional slice and the corresponding thermal neutron macroscopic cross section of thickness 4.68mm which is stacked from top to bottom in the object Table 4.5: The measured gamma radiation dose at the position of CCD sensor before and after BORAL shielding plates were placed in front of the scintillation screen Table 4.6: Experimental and simulation results of voxel gray values for aluminum and different density P.E foams of the designed test object Table 4.7: Results of Liquid and Ice phase water mass analysis Table 5.1: The ratio of backscattered component and opean beam gray value measured from the experiment setup Table 5.2: Comparison of the reported and experiment determined total macroscopic cross sections of the materials with BORAL shielding plates in front of the scintillation screen using the imaging faciltiy Table 5.3: The measured total macroscopic cross sections of the materials for the open beam condition and the opaque paper behind the scintillation screen

18 Table 5.4: Comparison of the reported and the determined total macroscopic cross sections of the materials with the background neutron scattering correction method using Eq. (5.4) Table 5.5: Experimental and simulation results of voxel gray values for aluminum and different density P.E foams after background neutron scattering correction method for the designed test object Table 5.6: A list of the calculated χ c from the experiment at different object-todetector distances xviii

19 xix NOMENCLATURE Acronyms CCD RSEC MTF NCT TRIGA ASTM MCP MCNP NIST CBP FBP ART MART Charged-Coupled Device Radiation Science and Engineering Center Modulation Transfer Function Neutron Computed Tomography Training Research Isotope Production Generation Atomics American Society of Materials and Testing Micro Channel Plate Monte Carlo N-Particle Transport National Institute of Standards and Technology Convolution Back Projection Filtered Back Projection Algebraic Reconstruction Technique Modified Algebraic Reconstruction Technique Parameters Units k Boltzman constant m 2 kg s 2 K 1 E Energy of the neutron flux ev T Temperature of the media K (Kelvin) b Cross sectional area of nucleus cm 2 β System resolution parameter cm -1 x Coordinate of the knife edge cm x 0 x coordinate of the knife edge center cm x i i th spatial coordinate cm f i Luminance value of the i th location unitless θ Beam divergence angle º (degree) u System frequency cm -1 f N Fraction of information passed through the unitless system between zero and Nyquist frequency x Coordinate of the knife edge cm x Sample spacing of the system cm t Total neutron macroscopic cross section of the mm -1 material for the imaging system I sample Intensity gray level value of the sample material unitless I darkcurrent Intensity of the dark-current image unitless I 0 Intensity of blank beam image unitless t Each step thickness of tested material mm

20 xx G dry Pixel gray value of aluminum in the image unitless C Gain of the imaging system unitless G offset Pixel gray value from CCD charge build up unitless o Incoming neutron flux neutrons/cm 2 s Σ Al Total macroscopic cross section of aluminum mm -1 t Al Thickness of aluminum mm Σ water Total macroscopic cross section of water mm -1 t water Thickness of water mm G wet Pixel gray value of the aluminum with water unitless filled in the cavity G F Voxel gray value of water in a fully fulfilled unitless voxel G P Voxel gray value of water in a partially fulfilled unitless voxel ς t Total microscopic cross section of water barns ρ P Density of water in the partially fulfilled voxel g/cm 3 ρ F Density of water in the fully fulfilled voxel g/cm 3 A g Avagadro s number mol -1 M Molecular weight of water g mol -1 V P Volume of partially fulfilled with water mm 3 V F Volume of fully fulfilled with water mm 3 m F Water mass in fully fulfilled voxels g m p Water mass in partially fulfilled voxels g R s Pixel mapping of the imaging system mm/pixel f bgscat Black body scaled factor unitless Ф x, y Measured intensity of the sample radioscopy unitless image at the pixel location (x, y) Ф x, y bb Measured intensity of the black body radioscopy unitless image at the pixel location (x, y) χ c Degree of the cupping artifacts unitless U g Geometric Unsharpness mm a/f Ratio of the distance between source aperture to unitless the object and the diameter of the inlet source for X-rays imaging b Object-to-detector distance for X-rays imaging mm L/D Reactor collimation ratio unitless L Object to detector distance for neutron imaging mm D Diameter of the neutron inlet aperture mm M True Magnification of the neutron imaging system mm

21 xxi m Geometric magnification of the neutron imaging unitless system d Diameter of the object mm I The magnified size of the sample object mm new U g Geometric unsharpness with the shielding plate mm

22 xxii ACKNOWLEDGEMENTS I am indebted to Dr. Jack Brenizer for his continued support and patient for this research over last five years, whose invaluable support and encouragement stimulated me to explore my own ideas freely throughout this research project. He was very patient with his students and dedicated with the research, since beginning of this research, no matter how busy his weekly schedule is, he would always come to the reactor facility to have a research meeting with me and check my research progress every Wednesday to make sure that I am on the right track. He would always give me clues to the problems that I have from the research. Without his inspiration and encouragement, I would not progress so far. I would like to extend my gratitude to my dissertation committee, Dr. Kenan Ünlü, Dr. Matthew Mench and Dr. William Higgins, for their suggestions and comments while serving on my committee. I would like to thank Dr. Cory Trivelpiece for his time and assistance with the editing and reviewing of this dissertation and for his helpful suggestions. I would like to express my gratitude to Ronald L. Eaken Jr, who has been working with me throughout the research project. Beginning from development of the imaging system, every time after I designed the objects that need to be built for the research, he would always try to understand exactly what I need and would do his best to machine them for me. I would also like to extend my gratitude to the staff in Radiation Science and Engineering Center at Pennsylvania State University, University Park, who put a lot

23 xxiii of time and patient for scheduling the reactor beam time for neutron tomography research work. I also wish to thank the United State Department of Energy, whose award of the Innovations and Enhancements for a Consortium of Big-10 University Research and Training Reactors grant made this research possible. Last, special gratitude will go to my beloved parents, who not only gave me my life and raised me, but also gave me consistent love and moral support, which is an incredible source of strength for me to pursue doctorate degree in the U.S.

24 xxiv DEDICATION 献给我敬爱的父母和所有关心及给于我帮助的亲人和朋友

25 Chapter 1 1 INTRODUCTION Compared to X rays, neutrons can penetrate deeper into most materials by orders of magnitude. For X rays, electromagnetic interactions depend on the number of electrons present in the target materials. Since the neutrons have no electric charge and are not affected by the orbital electrons, there is no such correlation for neutrons [1]. Thin layers of light materials, such as hydrogenous materials, can significantly attenuate neutrons, but are hardly detected by X rays for the same thickness. Compared to water, aluminum is nearly transparent to neutrons, but greatly attenuates X rays because of its higher atomic number. The transmitted neutron intensity varies after passing through different elements due to absorption and scattering interactions. By detecting the transmitted, twodimensional neutron intensity, the inner structure of the object can be observed. This technique is called neutron imaging. There are two common types of neutron imaging techniques, neutron radiography and neutron radioscopy. Neutron radiography is the technique that captures the static images on a permanent recording medium, such as film [2]. With the more advanced technology of electronic imaging systems, especially through a digital video with computers and CCD camera, a new real-time form of neutron radiography was developed. This new technique is known as neutron radioscopy [2]. Thus, neutron radioscopy is very well suited for time-dependent processes, such as visualization of fluid inside a fuel cell. In addition to this merit, neutron radioscopy also allows the researchers to perform digital image processing, which provides enhanced

26 2 detail and more precise quantitative and qualitative information on the investigated objects [2]. Depending on the neutron source energy, neutron imaging can be generally categorized as fast neutron imaging and thermal neutron imaging [3]. Note that the characteristic gamma rays stimulated by neutrons may also be measured to investigate certain specific materials. The thermal neutrons produce prompt capture gamma-rays followed by delayed gamma-ray emissions from longer-lived activated nuclei, whereas fast neutrons generate prompt gamma-rays through inelastic scattering. Fast neutrons are preferred for drug and explosives interrogation indicative elements such as carbon, nitrogen, oxygen, and hydrogen because of the relatively strong and specific prompt gamma-ray stimulated from these elements [4]. In reality, contraband detection applications such as large cargo inspection, often look at gamma-ray based elemental signatures rather than use imaging due to low detection sensitivity [5], slow speed equipment complexity and high cost associated with the imaging method [6]. The research work for neutron imaging can be dated back to late 1940 s. Extensive research work was not conducted until 1960 s and 1970 s after research reactors became commonly available in universities world-wide. Due to a lack of portable neutron sources that provide high neutron flux, neutron imaging lagged behind x-ray imaging in some advanced research areas such as development of high resolution detector systems. Among the variety of neutron imaging detectors, the scintillations screen coupled with a charged couple device (CCD) is commonly used because it provides a high dynamic range of spatial resolution and digitized high quality images. Since semiconductor technology can manufacture CCD pixels as small as several

27 3 microns, the limiting factor for the system spatial resolution is the scintillation screen itself. Part of the motivation and framework of this dissertation is to develop a high spatial resolution thermal neutron imaging/tomography system by using a 6 Li doped scintillation screen and a cooled CCD camera [7], that can be utilized for applications such as water/ice quantification of the fuel cell and to keep up with the latest industrial neutron imaging application. 1.1 Neutron Physics Neutron Source The neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton. Neutrons are usually found in atomic nuclei. The nuclei of most atoms consist of protons and neutrons bound together by the strong force. The number of protons in a nucleus is equal to the atomic number and defines the type of element. The number of neutrons determines the isotope of an element. Free neutrons do not exist in nature due to the short-lived mean lifetime of 885.7s. Because of this reason, neutrons can be obtained only from nuclear disintegrations, nuclear reactions, and high energy reactions (such as in cosmic radiation showers or accelerator collisions). Based on its energy, a neutron is mainly categorized into the following five categories. Cold neutron (below 0.01eV ) Thermal neutron (0.01 to 0.03eV) Epithermal neutron (0.03 to 10,000eV) Fast neutron (10keV to 20MeV) Relativistic (>20MeV)

28 4 Table 1.1 lists the neutron sources that are used in neutron imaging, Table1.1. Types of neutron sources [13]. For spontaneous fission of 252 Cf, the spectrum is peaked between 0.5 and 1 MeV, although a significant yield of neutrons extends to as high as 8 or 10 MeV [1]. When some of the heavy atomic nuclei capture a neutron, they will split into several smaller fragments, or fission products. Two or three neutrons are also emitted simultaneously. This process is called fission and is the fundamental physical principle underlying a nuclear reactor. Most of the research reactors in the world provide thermal neutrons. Thermal neutrons are usually used for neutron imaging because most materials exhibit higher attenuation for low energy neutrons. After the production of neutrons by fission reaction, the neutrons usually have higher kinetic energy (approximately peaks at 2MeV). These neutrons must have slowed down by scattering process in a moderator in order to

29 5 reach the thermal energy range. Heavy water (D 2 O) and graphite are often used as a moderator because of the relatively large scattering cross section and the small absorption cross section of deuterium atom. The fission neutrons usually reach the thermal energy state after a few scattering interactions with deuterium atoms. At room temperature, the thermal neutron energy spectrum usually yields an average energy of ev and with a velocity of 2200m/s [8]. When the neutron energy reaches the thermal energy range, the neutrons are collimated and directed towards the sample and detector. The neutron source in the Radiation Science and Engineering Center (RSEC) at Pennsylvania State University, University Park is a 1MW TRIGA research reactor that supplies a well thermalized neutron beam [41]. The neutron beam at the imaging plane is approximately 30 cm in diameter with a L/D ratio of 150 (as measured using ASTM 803) [9], where L is the length of collimator and D is the diameter of aperture, which corresponds to a divergence half angle of approximately 1.4 º [10]. The energy distribution of the moderated thermal neutrons is the Maxwell- Boltzman energy spectrum [11], which is described by the following equation, Ф 0 E de E E exp de, E < E kt kt t (1. 1) where k is the Boltzman constant, E is the energy of the neutrons, Ф 0 E is the neutron flux at the energy of E, and T is the temperature of the media. The neutron beam consists of moderated thermal neutrons, neutrons still in the moderation process, and neutrons that are in the epithermal region of the spectrum and is described by the following equation, Ф 0 E de de, E E t E E epi (1. 2)

30 6 The direction in which the scattered neutrons are moving is approximately isotropic after the moderation process, the beam is collimated so that only neutrons that pass through a predetermined solid-angle reach the sample object, therefore, the beam is assumed to be a nearly parallel beam for most neutron imaging applications if the length of the collimator (L) is long compared to the inlet aperture diameter (D). An α-beryllium source is used in laboratory work with weak intensities. This type of neutron source is unattractive for high quality neutron imaging because of the low neutron flux and the accompanying gamma-rays. The (d, n) and (p, n) reactions are frequently used in accelerator-based facilities to produce fast neutrons for detecting elements associated with contraband materials such as carbon, nitrogen, oxygen, and hydrogen. Californium-252 is often used as a portable fission isotropic neutron source especially used in neutron imaging applications that require a high neutron flux [12] Neutron Interactions with Materials Since neutrons are free of electrical charge, they can penetrate into material, pass through the atomic electron cloud and interact with the nucleus. A neutron may have many types of interactions with a nucleus. Figure 1.1 shows the types of interactions and their cross sections. Each category of interaction in the figure consists of all those linked below it. The total cross section, σ t, expresses the probability of any interaction taking place. An interaction may be one of the major types: scattering or absorption. When a neutron is scattered by a nucleus, its speed and direction change but the nucleus is left with the same number of protons and neutrons it had before the interaction. The nucleus will have some recoil velocity and it may be left in an excited state that will lead to the

31 7 eventual release of radiation. When a neutron is absorbed by a nucleus, a wide of radiations can be emitted or fission can be induced. Figure 1.1.Various types of neutron interactions with matter [13]. Scattering events can be subdivided into elastic and inelastic scattering. In elastic scattering, the total kinetic energy of the neutron and nucleus is unchanged by the interaction. During the interaction, a fraction of the neutron s kinetic energy is transferred to the nucleus. Inelastic scattering is similar to elastic scattering except that the nucleus undergoes an internal rearrangement into an excited state from which it eventually releases radiation. The total kinetic energy of the outgoing neutron and nucleus is less than the kinetic energy of the incoming neutron, part of the original kinetic energy is used to place the nucleus into the excited state. It is worth noting that hydrogen nucleus does not have excited states, so only elastic scattering can occur for this case. In general, scattering moderates or reduces the energy of neutrons and provides the basis for some neutron detectors.

32 8 Instead of being scattered by a nucleus, the neutron may be absorbed or captured. A variety of emissions may follow. The nucleus may rearrange its internal structure and release one or more gamma rays. Charged particles may also be emitted. The more common ones are protons, deuterons, and alpha particles. The nucleus may also rid itself of excess neutrons. The emission of only one neutron is indistinguishable from a scattering event; if more than one neutron is emitted, the number of neutrons now moving through the material is more than the number present before the interaction and the number is said to have been multiplied. Finally a fission event may occur, producing to two or more fission fragments and more neutrons. Each interaction takes place with a certain probability, and the cross section is used to describe this probability. The elastic cross section is usually the physical cross sectional area of a nucleus. A typical value of this area for a heavy nucleus is approximately cm 2. A different unit area is used in order to avoid the inconvenience of working with such small numbers. The barn, denoted by the symbol b, is defined to be cm 2. Thermal neutron interaction cross sections usually range between and 1000 b and they are also function of the neutron energy. The probability of each interaction event is independent from one to the other so the total cross section is the summation of all the interaction events probabilities. Neutron attenuation through bulk materials using the macroscopic cross section, which is similar to the mass attenuation coefficient defined for X rays as the multiplication of the total cross section with the inverse density of the material. Figure 1.2 shows the comparison of thermal neutron mass attenuation coefficients and X-ray mass attenuation coefficients versus atomic numbers. It can be observed that, as

33 9 compared to X rays, thermal neutrons can be highly attenuated by light nuclei such as hydrogen, lithium, boron and nitrogen. They can also penetrate heavy nuclei such as uranium and plutonium. It can be also seen that the thermal neutron attenuation coefficient shows no correlation with the atomic number, but the X-ray mass attenuation coefficient is relatively a smooth curve through over most of the region of atomic number. This feature makes neutrons capable of detecting elements or isotopes that X rays cannot easily detect. Figure 1.2: A comparison of neutron and 100 KeV, 600 KeV X-ray mass attenuation coefficients versus atomic number [13] Neutron Detection Mechanisms for detecting neutrons in matter are based on indirect methods. The neutron has no electric charge, therefore, an intermediate medium and a nuclear reaction are

34 10 needed to convert neutrons into charged particles for measurement. The process of neutron detection begins when neutrons interacting with various nuclei and initiating the release of one or more charged particles. The electrical signals produced by the charged particles can then be processed by the detection system. Table 1.2 lists the nuclear reactions that commonly used for neutron detection. Lithium, boron and gadolinium are good candidates for thermal neutron imaging because of their high thermal cross section. The 28 Si (n, p) 28 Al reaction is a good potential candidate for fast neutron imaging [13]. Table 1.2. Lists of nuclear reaction used for neutron imaging detector [13]. 1.2 Neutron Imaging Technique Physics and Mathematics of Neutron Radioscopy A conventional neutron radioscopy system consists of a nearly parallel neutron beam (either a thermal or cold neutron beam) and a detector system as illustrated in Figure 1.3

35 11 Figure 1.3. Neutron radioscopy imaging system [7]. When the neutron beam passes through the object, the thickness and the composition of the object attenuate the beam by scattering neutrons from their flight path or absorbing them. Neutrons that successfully pass through the object then impact the detector. In radioscopy, the detector is a scintillations screen / image intensifier where a neutron beam is converted to light photons and amplified and then recorded by a CCD camera. In radiography, the detector is a converter screen and radiographic film which is placed inside a light-tight cassette. Both radiography and radioscopy produce gray scale images after digitization, with the variations in neutron beam attenuation causing the differing shades of gray. Therefore, each shade of gray in the resulting image is indicative of the attenuation properties of the object. As described above, the attenuated neutron flux is dependent on a geometric mapping of the element s location, the thickness of the object and is detected by a neutron detector. It can be seen as a plane detector consisting of many sensor units, each of these function as a small neutron integration device to record the transmitted neutrons. Assuming that an object with thickness x is between a neutron source and a detector, the

36 12 collimated incoming neutron flux is Ф 0, the macroscopic absorption cross section of the object is a and the scattering macroscopic cross section is s. Therefore, the total macroscopic cross section is a + s. Then the un-collided transmitted neutron flux can be written as: t Ф unc x = Ф 0 exp( a x + s x dx) 0 (1. 3) If the object is homogenous in composition, Equation (1.3) can be reduced to Ф unc x = Ф 0 ex p a + s x (1. 4) Equation (1.4) is used to calculate the un-collided neutron flux and it represents those neutrons that have traversed their trajectory in the material without any interaction. This part of the effective neutron flux contributes to neutron imaging. However, in reality, the total neutron flux to reach the detector consists of neutrons that are scattered from other positions in the object and from the ambient environment. Therefore, the total neutron flux arriving at a single sensor detector unit is: Ф total x = Ф unc x + Ф scat x (1. 5) Ф scat x is a degradation factor relevant to the desired spatial resolution. For those materials known to have significant scattering cross sections (such as copper, stainless steel, lead, nickel, hydrogenous compounds and silicon), the buildup of scattered neutrons in the detector position is significant, therefore, the spatial resolution of imaging objects with a dominate scattering cross section is degraded Neutron Imaging Detectors Film has been used in neutron imaging field as a detection tool for many years. Although a good spatial resolution has been achieved with the film detection method, the demand

37 13 for new detection systems with more flexible applicability, especially with respect to spatial resolution, dynamic range and quantitative information from the images has been increased. Therefore, developing new types of neutron detectors is one of the most active areas in neutron imaging technology field. The basic physics of film, image plates and scintillation screens with CCD camera is discussed in the following sections, as these systems are primarily used in current neutron imaging facilities around the world. Film Detection System Film was mostly used in early neutron radiography work, and it has dominated in the neutron imaging detector field for decades because of its unmatchable spatial resolution of 20 μm. The film method can be used in either direct or indirect methods [14, 15]. For indirect method, thin foils of either dysprosium or indium are used. After being exposed for a sufficiently long time, the thin foils are removed from the beam and placed in close contact with the image recorder and the decay radiation emitted (low energy electrons) transfers the activation image to the image recorder. In this method, the image recorder is film, and subsequent development of the film yields a neutron radiography image. The direct method differs from the above principle in that the film (image recorder) is placed in the beam with the conversion screen made of thin gadolinium metal foil. The foil absorbs neutrons and emits low energy internal conversion and Auger electrons. These electrons expose the film s emulsion, after which the film must be developed. Converter screens of this type are usually 25 μm thick and are either gadolinium foils laminated to aluminum or vapor deposited gadolinium on aluminum for ease of handling. Vacuum cassettes are used to ensure good contact between the

38 14 converter and image recorder, which is vital in reducing image blur. The resolution of this converter-image recorder combination is 10 to 20 μm. Image Plates Image plates are well known in the field of X-ray imaging, but the use of imaging plates in neutron imaging is relatively new. Image Plates (IPs) have inherent advantages as compared to other imaging detectors, such as [16]: No accumulation of intrinsic dark signals during the exposure, No limitation in the count or dose rate, A high dynamic range in dose of more than 8 orders of magnitude, High efficiency, and No principle limitation of the detection area. The neutron sensitive IPs are made up of a thin phosphor layer consisting of a mixture of a storage phosphor, neutron converter and organic binder that is coated on a polymer film [16]. The operational principle of the IPs can be divided into the following two parts: Neutron exposure of the IPs, and The optical readout of the IPs. By adding gadolinium or lithium to the phosphor, an imaging plate can be adapted for use in neutron beam [17]. The neutrons are absorbed by the neutron converter and converted into ionizing secondary radiation during exposure. This process is dependent on the neutron absorption cross section of the neutron converters. Many materials can be used in image plate s neutron converter such as 6 Li, Gd, 10 B, 235 U etc. 6 Li is generally

39 15 used in the form of 6 LiF powder. Gd compounds are transparent and are available in fine powders such as Gd 2 O 3 or just pure Gd is used. The average diameter of these powders of Gd 2 O 3 and 6 LiF are approximately 3.3 μm and 3.5 μm, respectively [18]. Due to the high absorption cross section of these materials, a layer of 8.3 μm is sufficient to absorb 63% of the neutrons for Gd. The secondary radiation that is emitted by Gd is conversion electrons with an average energy of approximately 70 kev and γ ray radiation of 0.3, 0.4, 1.2 MeV and other energies from different cascades resulting from the de-excitation of the excited Gd nuclei [18]. The ( 6 Li, n) reaction produces alpha particle of 2.05 MeV and a tritium nucleus of 2.74 MeV [18]. This secondary radiation is absorbed in the storage phosphor and generates electron/hole pairs which are subsequently stored in electron and hole storage centers. The storage is made up of photo-stimulated phosphor crystals (BaFBr: Eu 2+ ) or some other similar complex. It has an average diameter of approximately 5μm. Eu 2+ atoms are ionized to Eu 3+ when exposed to X-rays, ultraviolet light, electrons or protons. The liberated electrons are trapped in bromine vacancies which allow them to be released later by exposure to visible light. This will result in the emission of photo stimulatedluminescence (PSL), which can be collected by a photomultiplier tube. Since the late 1990s, most neutron radiography researchers and applications began to utilize imaging plates [20-24], especially after the bio-imaging analyzer system (BAS [19]) Image Plate reader made by Fuji Photo Film in Japan was made commercially available. Lasers could read out a pixel size of 25 μm or 50 μm squares. H. Kolbe [25] measured the spatial resolution to be 93 μm by using the imaging plate. An advantage of using the imaging plate is its high dynamic range, which is not typically limited by the imaging plate itself,

40 16 but by the readout device. However, there are disadvantages, including the fact that it is not a direct method, and the interference problems due to the inherent high sensitivity to the gamma background in neutron beams [26]. M.Tamaki [27] reported that a spatial resolution of approximately 200 μm utilizing an imaging plate containing dysprosium to eliminate gamma-ray fogging, but with the drawback of losing detection efficiency. Scintillation Screen/CCD camera Scintillation screens are commonly used for the conversion of neutrons into a visible light photon signal and then later recorded by a charged coupled device (CCD) system. This method is based on neutron capture reaction and phosphorescence phenomena. Phosphorescence is the luminescence produced by certain substances after absorbing radiant energy or other types of energy. In the scintillation screen the neutron is absorbed by a high cross section neutron absorbing material, the charged particles from the reaction interact with the phosphor to produce light photons and then are detected by the CCD camera. The CCD chip is an array of Metal-Oxide-Semiconductor capacitors (MOS capacitors), each capacitor represents a pixel. When applying an external voltage on the top plates of the MOS structure, charge (electrons and holes) are stored in the potential well. These charges can be shifted from one pixel to another pixel by digital pulses applied to the top plates. The charges can be transferred row by row to a serial output register. The image is a display of the electron distribution. These electrons are optically generated by the light signal emitted by the scintillation screen, i.e. the electrons are transferred from the valence band to conduction band by these photons. Some electrons can also get transferred due to thermal excitation. This contributes to the noise and is

41 17 called dark current in the CCD. Images that include the dark current can be corrected by subtracting the dark current image, which is the image taken with the neutron beam shutter closed. Early scintillation screen/camera combinations used a low-level light television camera [28] or intensified camera [29], which gave poor spatial resolution. In 1990, after the CCD camera became available, Kobayashi [30] applied it to neutron radiography work at Rikkyo Research Reactor. This digitized imaging technique can be updated to neutron computed tomography [31]. The scintillation screen/ccd camera combination has become a mainstay detector in neutron imaging family, providing good neutron sensitivity and excellent spatial resolution for many inspection applications [32-34]. Further resolution improvement is limited by the resolution of the scintillation screen [35]. Other detectors, such as the micro channel plate (MCP) [36], have been used in neutron imaging to convert initial radiation to electrons by a neutron converter, after which the electron image is amplified by a micro-channel plate in a process that involves creating an electron avalanche to generate luminescence at the phosphor screen. The image from the phosphor screen is then registered by a CCD camera [13]. High neutron absorbing materials such as 10 B, can be doped into the MCP structural material to do the conversion work, which produce amplified position sensitive electron signals [37]. The research results at the National Institute of Standards and Technology (NIST) using a high purity thermal neutron beam have indicated the promising capability of using MCP as a high spatial resolution neutron detector.

42 Neutron Computed Tomography In neutron computed tomography, the 3-D dimensional object is reconstructed by taking a series of 2-D neutron radioscopy projections at different angles by rotating the object relative to the neutron source. The data collected from the different radioscopic images are called sample projection data. The projection data can be mainly divided into two types, depending upon the geometry of the neutron beam: Parallel beam projection data, and Fan beam projection data. Figure 1.4 shows the beam geometry for the parallel beam and fan beam. In this dissertation, the neutron beam geometry for the reconstruction is assumed to be parallel [7] and the mathematics of parallel beam reconstruction algorithms will be discussed briefly below and the following section is a summary from Herman [47]. (a) (b) Figure 1.4. Projection data geometry in neutron computed tomography (a) parallel beam geometry [38]; (b) fan beam geometry [39].

43 19 In the parallel beam geometry, the projection data p(r, θ) can be shown to be the Radon transform of the two-dimensional neutron attenuation coefficient f(x, y) of the sample. p r, θ = (f x, y ) where, x = r cosθ s sinθ y = r sinθ + s cosθ 1. 6 (1. 7) and r-s is the rotated co-ordinate system in the counterclockwise direction by angle θ. The family of projection data p r, θ for an object function is called the sonogram. The reconstruction of the sonogram necessitates the calculation of the inverse Radon transform of the projection data p r, θ. There are many different algorithms for the reconstruction of the projection data, with each having its advantage and drawbacks. The algorithms for reconstruction are: Transformation based techniques like Fourier Techniques, Convolution Back Projection (CBP), Filtered Back Projection (FBP), Wavelet based reconstruction techniques, etc., Iterative Techniques like algebraic reconstruction technique (ART) and Modified ART (MART), Statistical reconstruction technique like Maximum Likelihood and Expectation Maximization Techniques, and Unconventional and mixed techniques like genetic algorithms, CBP and ART combined reconstruction, etc.

44 20 The Filtered Back Projection (FBP) technique is one of the most commonly used reconstruction technique that has been implemented in this dissertation and is discussed here. In FBP technique, the measurement obtained along each projection is projected back along the same angle. In this case, each back projection is identical to the other. Mathematically, the back projection along an unknown density line is given by: b θ x, y = p θ r δ xcosθ + ysinθ r dr (1. 8) where b θ x, y is the back-projected density due to the projection p θ r. The δ() function is Dirac delta function having a value of one at r=0. The back projection distributes density on the line. By integrating all the back projections over all the angles a laminogram function is obtained: π π + f x, y = b θ x, y dθ = p θ r δ xcosθ + ysinθ r drd (1. 9) 0 0 The laminogram function represents the distorted picture of the sample that needs to be corrected. Each projection of the δ function is also a δ function at the origin. If these functions are back projected, the resulting response (known as the impulse response) is given by: π π b r = δ r δ rcos θ φ r drdθ = 1 r 0 (1. 10) knowing the response to the impulse and assuming that linear systems theory applies, the following relationship holds:

45 21 f b x, y = f x, y 1 r (1. 11) Where denotes the convolution operation, which means the actual image is blurred by the 1 term. The 2-D Fourier transform of this equation is given by: r F b k, θ = F k, θ 1 k where k is the Fourier frequency. The 1 r (1. 12) blurring can be removed by the filtered back projection. For this case, Central Slice Theorem (CST), which is fundamental to computed tomography, is used. Let F k x, k y be the 2-D Fourier transform of the function f(x, y), i.e. F k x, k y = f x, y exp 2πj k x x + k y y dxdy (1. 13) where k x and k y are the orthogonal Fourier frequencies with units of radians per distance. Also, let P θ (k) be the 1-D Fourier transformation of projectionp θ (r), i.e. P θ k = P θ r exp 2πjkr dr. (1. 14) Allowing θ to vary from 0 to π radians and stacking them to get P θ (k), from CST, which gives: P k, θ = F k x, k y k x = kcosθ k y = ksinθ (1. 15) (1. 16) (1. 17)

46 22 2 k = k 2 x + k2 y. (1. 18) Using CST, Equation (1-9) can be written as π + + f b x, y = [ F k, θ exp 2πjkr dk]δ xcosθ + ysinθ r drdθ (1. 19) 0 Equation (1-19) can be reduced to: π + f b x, y = F k, θ exp 2πjk xcosθ + ysinθ dkdθ (1. 20) 0 Comparing Equation (1.20) with exact inverse 2-D Fourier transform of the 1-D Fourier transformation of the projection, which is: 2π + f x, y = F k, θ exp 2πjk xcosθ + ysinθ kdkdθ 0 0 π + = F k, θ exp 2πjk xcosθ + ysinθ kdkdθ 0 (1. 21) a factor of k (k>0) is observed as was expected. Substituting the F k, θ with 1-D Fourier transform {P θ (r)} and weighting it with k along each radial line to remove the blurring in the back projection as well as multiplying and dividing by k: f x, y = π + {P θ r } k exp 2 jk xcos + ysin k dkd k 0 (1. 22) In Computed Tomography Using Equation (1.22) is called the FBP reconstruction technique. The equation involves only 1-D Fourier transform which is calculated using the Fast Fourier Transform (FFT) techniques. The FBP algorithm can be written as: Each projection is individually transformed,

47 23 The transformed projection is weighed with k, The result is inverse transformed, and The result is back projected. The k term acts as a ramp filter that is not stable when implementing the FBP algorithm on a computer. Therefore, it is modified in order to remove the instabilities using various different kinds of filters that have different advantages and disadvantages. There are standard commercial computer routines available for image reconstruction using FBP. The equations for Filtered Back Projection (FBP) presented in this section are the standard formulas for reconstructing images from the projection data sets assuming that the projection data sets are continuous functions. Implementation of these formulas as a computer algorithm requires that each of the projection data functions, the convolution functions and the smoothing filters have some discrete sampling size [47]. The convolution method can be implemented as direct convolutions in the spatial domain to approximate the equations necessary to implement reconstruction [47]. Less computation time will be required if the Fourier Transform of the data and filters are taken and applied in the frequency domain and subsequently the final reconstructed image data is obtained by using the IFFT [47]. The application of the algorithms in the frequency domain can create interperiod interference artifacts in the reconstructed image and these artifacts can be eliminated by padding the projection data sets with sufficient zeros, which forces the interperiod artifacts out of the unimportant zeroed space and the interference over the whole component image space will be avoided [47].

48 Motivation and Statement of Research Objectives The first stage of this work was to design and develop a State-of-the-Art, high spatial resolution neutron imaging/tomography facility using a 6 Li doped scintillation screen, two mirrors and a cooled CCD camera [7]. The second stage of this work was to design a quantitative thermal neutron computed tomography model to evaluate water/ice mass using this imaging facility and develop a relevant method to reduce the errors that were associated with the water/ice quantification technique. This dissertation was intended to achieve the following goals: Introduce and develop a new concept design of research-reactor based, high spatial resolution thermal neutron imaging system which is used for quantitative measurement, Develop a relevant quantitative 3-D thermal neutron computed tomography (NCT) model to evaluate water/ice mass in order to meet the needs for the latest industry application of NCT technique, Identify and determine the dominating error sources for the research reactor-based thermal neutron imaging system quantitative measurement capability and, to develop a comparative analysis of different error reduction methods for water/ice quantification techniques using this thermal neutron imaging system, and Give suggestions and recommendations of error reduction methods to nondestructive evaluation engineers who work with thermal neutron imaging facilities. Chapter 2 provides the neutron imaging system design specifications using a cooled CCD camera and 6 Li doped scintillation screen. Chapter 3 introduces the

49 25 quantitative 3-D thermal neutron computed tomography model design which is used for water/ice quantification. Chapter 4 gives description of the simulation of the model and followed by experiment validation as well as initial water/ice quantification result. Chapter 5 presents a comprehensive analysis and error reduction methods for thermal neutron imaging system quantitative measurement capabilities and errors associated with water/ice quantification technique. This chapter also gives recommendations and suggestions of error reduction methods to non-destructive evaluation engineers who work with thermal neutron imaging/computed tomography facilities. Chapter 6 summarizes the dissertation and gives recommendations for future studies.

50 Chapter 2 26 NEUTRON IMAGING SYSTEM DESIGN 2.1 Overall Design Strategy The first stage of this work was to design and develop a state-of-the-art, high spatial resolution thermal neutron imaging/tomography facility with a large field of view to achieve the requirement for quantitative neutron computed tomography (NCT) [7]. A cooled CCD camera was to increase the sensitivity of the imaging system as much as possible since a light amplifier was not used. A dark working environment provided by a light-tight aluminum box with inside surfaces painted black was also required to avoid entrance of light from the ambient environment and light scattering inside the box, which was a source of noise in the images. Two high light reflectivity (94%), front surfaced mirrors were installed in an optimized location along the light path between the scintillation screen and the CCD camera based on the focusing and working distance of the CCD camera. Each mirror is mounted at 45 º relative to the horizontal line of the ground in order to obtain the maximum light reflectivity. A turn table was used to adjust the vertical alignment of the CCD camera, the mirror and the object were also incorporated into this imaging system to achieve the best quality of 2-D neutron radioscopy image projection data, which further improves the quality of 3-D neutron computed tomography images [7]. For the neutron computed tomography experiment, the cooling CCD camera chip was also exposed to thermal neutrons and other types of radiation (high energy neutrons

51 27 and gamma photons) coming out of the collimator of the reactor core for long periods of time. The gamma photons can directly interact with the CCD chip, which not only causes damage to the CCD chip, but also create spots in the collected 2-D radioscopic projection images. Subsequently, artifacts in the 3-D volume reconstructed tomography images are observed. This is another type of noise that needs to be corrected if quantitative information of the object is desired (however, the noise correction in the neutron radioscopy image was outside the scope of this thesis). Therefore, effective shielding of the neutron imaging facility becomes critical. Different shielding strategies and other design constraints for the system are discussed in detail in this chapter. It is important to understand the imaging system design to understand how the design affects the quality of the neutron radioscopy image and the subsequent affects the quantification of the water mass. Figure 2.1 shows the schematic diagram of the neutron imaging system design. Figure 2.1. The schematic diagram of the neutron imaging system [7]

52 Upper Portion of the Imaging System One of the most important design criterions for NCT experimental facility is to maximize the light photons from the scintillation screen that reach the CCD camera sensors while keeping the radiation levels at the CCD camera to a minimum. A conventional one mirror reflection thermal neutron imaging facility has the advantage of reflecting the maximum light photons but makes it difficult to extend the light path such that the CCD camera can be completely out of the radiation field. Therefore, a new neutron imaging system with two major components was designed and constructed for this research work. The system has two components with each one having one mirror to direct light photons. Hence, the system is called two mirror reflection imaging system. The upper portion of the imaging system, incorporates a 6 Li doped scintillation screen and a front surface mirror. Figure 2.2 shows the front view of this portion.

53 29 Figure 2.2. Front view of the upper thermal neutron imaging component, with a 28 cm 28 cm field of view. The first mirror has a dimension of 28 cm 39 cm and was approximately 5.7 cm behind the scintillation screen surface. The mirror was secured at 45 º relative to the horizontal plane, and the back plane of the mirror frame was 1.3 cm away from the back surface of the upper imaging component. The height of this part was 51.4 cm tall. Figure 2.3 shows the front view of the first mirror frame of the upper imaging part without the scintillation screen on.

54 30 Figure 2.3. Front view of the first surface mirror frame without scintillation screen. The upper portion of this thermal neutron imaging system was primarily used to convert thermal neutrons to light photons using the scintillation screen and to direct the light photons by the first mirror frame. The directed light photons are reflected by the second mirror, which was mounted in the lower portion of the imaging system. The detailed design of the lower portion is discussed in Section 2.3. Based on the dimensions given above, the total length of the light path for the upper portion imaging component was calculated as 57.2 cm.

55 Lower Portion of the Imaging System Adjunct Component Being a part of the lower portion of the imaging system, the adjunct component was designed to connect the upper and lower portion of the imaging system and hold the second mirror frame. The distance from the bottom of the upper portion of the imaging system to the center of the second mirror frame was approximately 40.6 cm. The second mirror was 28 cm 28 cm and was 45 º relative to the horizontal line of the ground. Figure 2.4 shows the inner structure of this part and the second mirror frame that was on the bottom. Figure 2.4. Inner structure of the adjunct portion of the imaging system. Directly in front of the second mirror frame, a square shape aperture with each side of length 19.8 cm was used to pass the light photons that were reflected from the

56 32 second mirror frame. After the light photons passed through the aperture, they were detected by the CCD camera which was installed in the lower portion of the imaging system. The light path length from the centerline of the mirror to the inner edge of the adjunct portion was approximately 15.2 cm. Therefore, the total light path in the adjunct portion of the imaging system was 55.3 cm Lower Portion The lower portion of the imaging system was connected to the adjunct portion and primarily used to house the cooled CCD camera and to support the materials to shield the CCD camera as discussed in Section 2.4. In order to reduce the radiation effects on the CCD camera chip, a separate radiation shield structure was designed and placed in front of the CCD camera. This structure has the same diameter as the lens of CCD camera to allow the light photons along with some undesired radiation to pass through. Figure 2.5 shows a detailed illustration of this portion s design.

57 33 Figure 2.5. A separate structure was used for stacking different shielding materials. The distance between the inner edge of the adjunct portion to the lens of the CCD camera was 40.6 cm, therefore, the total working distance of the CCD camera for this imaging system was cm. The dimensions for the rest portion of the lower system were 65.4 cm long 30.5 cm wide 30.5 cm tall. Figure 2.6 shows the inner structure for the rest of the lower imaging system.

58 34 Figure 2.6. Inner structure of lower portion of the thermal neutron imaging system. A QImaging Retiga 4000RV cooled CCD camera was used in this imaging system design. The Retiga 4000RV has a sensor array format of pixels, 12 bit gray scale depth, and sensitivity to low-light levels and allows integration time of 10 μs to 18 min [7]. Three onboard Peltier cooling stages provide cooling to -30 º C reducing dark current and random noise, which can occur during the long integration times needed in low neutron flux environments. A lens was fitted to the camera that allowed adjustment of the focal length between 70 mm and 200 mm. A remote controlled turntable was added on the back of the camera to adjust the vertical alignment of the CCD

59 35 camera, mirror and the object in order to minimize the artifact blurs caused by object unsharpness during the image capturing process [7] Radiation Shielding Design Shielding Strategy As described in the beginning of this chapter, radiation shielding of the CCD camera is critical to thermal neutron computed tomography experiment due to the long exposure of the CCD chips to the radiation flux. For a reactor-based neutron imaging system shielding design, one not only has to consider thermal neutron radiation damage to the CCD chips, but also the secondary radiation products such as gamma rays, which is the primary damage to the CCD sensors and can also cause spots in the images [7]. After the imaging facility was installed and tested, the gamma ray dose rate was measured by a calibrated probe at the location of the cooled-ccd camera chip to measure the effective radiation shielding. Gamma photons were the main radiation present that induced the spots in the collected radioscopic images by interacting with the CCD camera sensor array. Initially, lead bricks were put around the lower portion of the imaging system to effectively shield the gamma photons that come from (n, γ) reaction with hydrogen in the reactor pool. The other major concern was the radiative capture reaction of the thermal neutrons. The (n, γ) cross section for thermal neutrons can be very large and may reach to thousands of barns for certain nuclides [40]. The neutrons used for neutron imaging work at Breazeale Research Rector at The Pennsylvania State University are very well thermalized [41] and these neutrons interact with the atoms of materials in the upper and lower camera housing materials to produce additional gamma photons, which were not desired in the system. Therefore, the shielding problem for the

60 36 imaging system became straightforward. It became necessary to choose materials with large effective thermal neutron cross sections to absorb thermal neutrons before they entered into the imaging system and interacted with the housing and shielding materials, to effectively reduce the gamma photons dose rate to the CCD chips Shielding Materials Different layers of radiation shielding materials were used for the thermal neutron imaging facility shielding purpose. Flex Boron Sheet and boron aluminum plates (BORAL ), a flexible and a hard material respectively, each containing a high concentration of boron which has a very high thermal neutron macroscopic absorption cross section of approximately cm -1 [8], were used to shield neutrons. Flex Boron Sheet and BORAL were wrapped around outside of lead bricks and prevented thermal neutrons from interacting with the lead bricks and aluminum. The same shielding design architecture was also applied within the separate structure of the lower portion. (see Figure 2.5.) As indicated in Figure 2.7, the top portion of the imaging system was covered by an aluminum plate. Lead bricks formed the first layers around the imaging system. This layer was mainly used for shielding the gamma photons after thermal neutrons were absorbed by BORAL and Flex Boron Sheet, which covered the lead bricks as the second and third layer, as illustrated in Figure 2.8 and Figure 2.9. The gamma radiation dose to the CCD camera chips was reduced by 83% with this shielding design.

61 37 Figure 2.7. Lead bricks were placed around the lower portion of the imaging system as the first layer of shielding materials to absorb gamma photons. Figure 2.8. BORAL were placed around outside the lead bricks as the second layer of the shielding material to absorb thermal neutrons.

62 38 Figure 2.9. Flex Boron Sheet were placed around outside the BORAL plates as the third layer of shielding material to absorb thermal neutrons Spatial Resolution Modulation Transfer Function Theory for Neutron Imaging System Modulation Transfer Function (MTF) analysis was used to quantify the true spatial resolution of the imaging system [42]. A sharp knife-edge gadolinium foil was placed against the neutron converter [7], and an image was collected when the reactor power was 800 KW. Harms and Wynam indicated a function for the normalized edge data can be best described as the following [43]: g x = π tan 1 β x x 0 (2. 1) where in this equation,

63 39 β = system resolution parameter, and x 0 = x coordinate of knife edge center. Based on Harms and Wyman s theoretical calculation and Wrobel and Greim s experimental investigations [44], Equation (2.1) correctly described the density variation across the knife edge when the inherent un-sharpness was dominant. When geometrical un-sharpness dominates, the Gaussian Equation: g x = erf α x x 0 (2. 2) will best fit the density variation across the knife edge [42], the relationship between and α is: = α (2. 3) The first derivative of Equation (2.1) yields the following Equation: dg x dx = β π 1 + β 2 x x A sharp-cut gadolinium edge was placed against on the scintillation screen surface and imaged with the neutron imaging system. The location of the edge was estimated to be at location x 0 by assuming: x 0 = x if i f i (2. 5) where, x i = i th spatial coordinate, and f i = luminance value corresponding to the i th location.

64 40 The parameter x 0 and β were calculated using the method of non-linear least square fit [42]. This method optimizes a goodness fit of parameters by interacting between β and x 0. If the resulting curve g x fits the experiment data well, then the value β and x 0 were assumed to be correct for that particular edge position. After the edge parameter of β and x 0 was determined, the impulse response function was determined by taking the first derivative of Equation (2.1). Taking the Fourier transformation of Equation (2.4) gives the following transfer function for the scintillation screen/ccd camera system: H I u, β = β exp j2πx 2π u π 0u exp β (2. 6) Then the normalized MTF for the neutron imaging system, which combines the beam effects and the scintillation screen/ccd camera components, is written as: 2π u MTF u, l, θ, β = sinc 2 l tan θ u exp β (2. 7) The first zero value associated with the sinc function in Equation (2.7) is related to the effective beam divergence as compared to the parallel beam θ. According to the sinc function, the function MTF (u, l, θ, ) will be equal to zero when 2 l tan θ u = 1, from this analysis point, the beam divergence angle was calculated by setting: θ = tan l u (2. 8) The parameter β I for the scintillation screen/ccd camera system varies as a function of spatial positioning of the edge within the field of view. A periodic shifting pattern of the edge gray level was observed. This phenomenon occurs due to the fact that the edge

65 41 position was shifting relative to the pixel sampling locations. The parameter β i can be determined mathematically by removing β I from β I,i in the same measurement location, where β I,i denotes the system resolution parameter when component I and i are serially connected [42]: = 1 β i β I β I,i (2. 9) The parameter β I was determined by imaging a sharp edge material that was directly placed against scintillation screen surface, thus making MTF B u, l, θ, β = 1, where MTF B is the MTF component of the neutron beam [42]. The edge data was recorded and then processed, and the value of MTF i (u) was calculated as the following: MTF i u, β = MTF I,i(u, β) MTF I (u, β) = exp 2πu β i, for u, β i > 0 (2. 10) In order to define the physical meaning of β i, a parameter of f N has been introduced in order to quantify the amount of image degradation that can be attributed by component i. For a radioscopic neutron imaging system that is based on a discrete sampling procedure, the system s resolution is primarily dependent on the sampling distance or the Nyquist sampling frequency. The quantity of f N is defined as the fraction of information passed through the system between zero frequency and the Nyquist frequency, which is given: u N = 1 2 x where x is the sample spacing of the system, or pixel width. The value is proportional to the integral of the MTF over the frequency interval of (0, u N ) and is given by: f N = u N 0 MTF u, β i du u N 0 du = x β i π 1 exp xβ i 2. 12

66 42 This parameter f N shows the amount of image degradation that can be contributed by component i. Once the individual component parameters were known, the fundamental component value was determined. The local constant β I was measured as mentioned above so the component parameter β i can be calculated. The value of β I was varied spatially within the field of view due to the local shift-variant nature. Sampling the edge data to estimate the 1-D impulse response, it was easy to see the edge within the field of view of the CCD camera had an important effect on the MTF result Experimental Measurement and Results The spatial resolution of the designed neutron imaging system at the Breazeale Research Reactor was measured by directly imaging a 2.54 cm 2.54 cm size gadolinium foil edge on the scintillation screen. Using the procedure as described above, the MTF for the neutron imaging system was calculated. Figure 2.10 shows the normalized gadolinium knife edge intensity data and the corresponding curve-fit for the data at a reactor power of 800 KW [7]. The curve-fit parameters of β and x 0 was determined to be β = 9.545/ mm, x o = 2.658mm. Using the parameter β and x 0, the impulse response function was calculated. Figure 2.11 and Figure 2.12 show the normalized impulse response function and the corresponding MTF result for the designed neutron imaging system at Penn State. From the MTF analysis, at a 5% cutoff limit point, the calculated MTF was approximately 4.3 cycles/mm, which is equivalent to a minimum spatial resolving distance of 116 microns.

67 NORMALIZED INTENSITY NORMALIZED INTENSITY MEASUREMENT CURVEFITTED DISTANCE (mm) Figure Normalized knife-edge intensity data for the neutron imaging system. The dash line represents the curve fit result to the experimental measured data LSF DISTANCE (mm) Figure The neutron imaging system impulse response function derived from the gadolinium knife edge.

68 MODULATION TRANSFER FUNCTION Family 1 Family 2 Family FREQUENCY(1/mm) Figure Modulation transfer functions for the neutron imaging system Summary The neutron computed tomography system had the following features: 1) better radiation shielding, 2) better object alignment, 3) incorporated a larger neutron converter, and 4) used an advanced 12 bit cooled CCD camera. The NCT data from the designed imaging system showed that the noise and artifacts in the projection data have been greatly reduced as compared to the data acquired by the initial neutron imaging system, which was a Thomson tube scintillation screen and image intensifier, a CCD camera, a mirror, and an image acquisition computer system. As compared to the initial neutron imaging system, the signal-to-noise ratio for the designed imaging system was improved over 286%. Subsequently, the quality of the volume reconstructed images has been greatly

69 45 improved [7]. The MTF technique was implemented to quantify the true spatial resolution of the neutron imaging system, and measurements showed that a high spatial resolution of 116 microns was achieved. The newly designed imaging system has been successfully installed and tested at Radiation Science and Engineering Center (RSEC) at Pennsylvania State University for enhanced image quality, reduced error, and higher location precision. The related software and hardware were in place to achieve the goal of developing 3-D water/ice mass evaluation technique.

70 Chapter 3 46 QUANTITATIVE NEUTRON COMPUTED TOMOGRAPHY MODEL DESIGN As mentioned in Chapter 1, the second goal of this research was to design a quantitative thermal neutron computed tomography (NCT) model to evaluate water/ice mass in order to meet the needs of industrial applications of NCT technique. One possible method to quantify water/ice mass is to group together the voxels that represent water/ice in the 3-D reconstruction result of a water/ice column, which should have the same gray level value. The total volume of water/ice can then be determined. Therefore, the approximate amount of water/ice mass can be calculated. However, this method does not take into account the gray level value of voxels that are partially filled with water. Because of digitized nature of the 3-D reconstruction calculation, each voxel occupies the same amount of volume within the reconstruction result, but a voxel may represent a space only partially filled with material [45]. The changing of voxel gray level values represents those voxels that are partially filled with materials. This always occurs when two or more materials are present at the same interfacial boundaries. The resultant voxel gray level value represents a combination of two or more materials, each of which occupies a portion of the voxel volume and a background normalization correction method can remove the un-desired portion, leaving only the portion that needs to be quantified. Quantifying water/ice mass would result in an overestimated value compared to the theoretical value if partially filled voxels were treated as full voxels. This value will be underestimated if partially filled voxels are not taken into account [45].

71 47 Therefore, a more precise and straightforward evaluation method is needed in order to solve the problem of either overestimating or underestimating the true water/ice mass value from grouping method as mentioned above. Several things were understood through a literature review on general computed tomography theory and basic nuclear science: In a 3-D volumetric reconstruction calculation, voxel gray level value represents the total neutron macroscopic cross section of the material under investigation [47, 48]. The total macroscopic cross section is linearly proportional to the density of the material, therefore, the voxel gray level value is also linearly proportional to the density of the material. Theoretically, the materials, in this case, aluminum, that surround the water/ice would not affect the macroscopic cross section and voxel gray level value of water/ice. Both theoretical and experimental NCT models were investigated to confirm the relationship between density, macroscopic cross section and voxel gray level values of a material as described above. It is well-known that the NCT method is a non-destructive testing method that provides 3-D information of a sample object by recording a series of 2-D neutron radioscopic images at different angles and subsequently reconstructing the volume data. Therefore, to provide the theoretical volume data, one needs to calculate a series of 2-D neutron radioscopy images of the test object. Figure 3.1 shows the flow

72 48 chart of the 3-D experimental and theoretical neutron computed tomography methods model. Figure 3.1. Flow chart of the experimental and theoretical thermal neutron computed tomography model: (a). direct experimental NCT data acquisition, and (b). indirect simulated NCT data acquisition, which needs geometry and material attenuation property of the object. From the above flow chart, one can see that the direct experimental thermal NCT data acquisition is easy and straightforward, but the experimental method has the disadvantage of introducing undesired errors in the recorded 2-D neutron radioscopy images. Such errors are due to neutron beam scattering from the object to the scintillation screen, the divergent nature of the neutron beam coming out of reactor collimator, etc. These errors affect the voxel gray level values of the examined materials and therefore, a new method that is able to avoid or minimize the associated errors had to be devised.

73 49 In order to reduce all the associated errors in the 2-D neutron radioscopy image projections, one can implement method (b) in Figure 3.1. First, one can determine the effective total thermal neutron macroscopic cross section data of the materials which compose the object in the direct NCT experiment for the imaging system (attenuation property). By incorporating geometric information of the test object, the 2-D thermal neutron image projections can be developed by simulation. In the model, all of the undesired errors present in the experimental NCT method can be avoided. Therefore, the first task was to choose appropriate materials and determine their effective total thermal neutron macroscopic cross section data for the imaging system Determination of Effective Thermal Neutron Macroscopic Cross Sections of Selected Materials The first purpose of this experiment was to determine the effective total thermal neutron macroscopic cross sections for the materials that comprised the object used for the direct NCT experiment. These cross sections were experimentally determined and then used as input parameters to simulate a series of 2-D thermal neutron radioscopy image projections without errors associated with the neutron beam present. These 2-D projections were input into the 3-D CT volume reconstruction program, Octopus. The true voxel gray level values of the selected materials in the simulated NCT reconstructed volume images were then determined. The second purpose of this experiment was to determine if the facility responded to different materials as anticipated, based on the effective total macroscopic cross section data that were determined from the designed thermal imaging facility.

74 50 Four different metals, aluminum, iron, lead and copper, were first tested to determine their individual effective total thermal neutron macroscopic cross sections (attenuation properties) using the imaging system. Due to the non-perfect nature of the imaging facility (scintillation screen, neutron beam), the entire scintillation screen was divided into six different sections for this part of experimental analysis, and each sample material was imaged at each location on the scintillation screen. Figure 3.2 shows the blank beam shot image of the entire scintillation screen and positions where each material was measured. Figure 3.2. Blank beam shot image of the entire scintillation screen. The red arrows mark individual Position is where the metal samples were tested. One can see that the entire scintillation screen was circled with ring artifact noise. Positions 2 and 4d were the right and left boundaries of this ring artifact noise, Positions 1, 3, 4a and 5 were outside this circle. The ring artifact was thought to be

75 51 caused by higher thermal neutron flux or gamma photons. The lead, copper, stainless steel and aluminum samples were machined into step wedges and were measured at each marked location to test the imaging facility response. This procedure was important and the test results gave a general idea of: which area on the scintillation screen is imaging properly, which part of the scintillation screen can be used to conduct future experiments, a possible method for shielding the abnormal working region on the screen Experiment Set up and Measurement Method The iron, copper, lead and aluminum were machined into step wedge shapes and measured at each marked location on the scintillation screen. The thickness of each step was uniformly increased from 1.57mm to 12.56mm. The neutron exponential attenuation law was applicable for thin thickness and low neutron scattering material. Therefore, the total thermal neutron macroscopic cross section of the material can be determined through the following relationship: ln I sample I darkcur rent I t = 0 I darkcurrent t (3. 1) where in this equation: t : Total neutron macroscopic cross section of the material in the imaging system, I sample : Intensity gray level value of the sample material, I darkcurrent : Intensity of the dark-current image, I 0 : Intensity of blank beam image, and t: Each step thickness of the material.

76 52 Before the experiment, a dark current image was taken when the cooled CCD camera was in a steady state (normally 5 minutes after starting the CCD camera). The dark-current image was considered the inherent noise of the CCD camera, which can be minimized by subtracting it from sample and blank beam images, as shown in Equation (3.1). This yields the effective total thermal neutron macroscopic cross section of the sample material for the imaging facility. After subtracting the dark-current image from the raw blank and sample radioscopy images, power normalization has to be performed to correct the error due to small fluctuation in reactor power during the experiment Measurement Results and Discussion Figures 3.3 to 3.14 present the plots of the linear attenuation property of the aluminum sample step wedge and the corresponding calculated effective total thermal neutron macroscopic cross section at each step thickness for specific locations on the scintillation screen. The plots for other materials can be found in Appendix A (Figure A.1 through Figure A.36). The slope of the linear attenuation property of each sample material represents the total thermal neutron macroscopic cross section of the material. Table 3.1 lists the comparison of the reported [8] and experimentally determined total thermal neutron macroscopic cross sections of the materials using the imaging facility. Table 3.1. Comparison of the reported and experimental determined total macroscopic cross sections of the materials using the imaging facility. Materials Reported (1/mm) Experimental (1/mm) % difference Aluminum Copper Iron Lead

77 Macroscopic Cross Section of Al (1/mm) -ln(i/io) y = *x ln(i/io) linear Thickness(mm) Figure 3.3. Linear attenuation property of aluminum sample step wedge at Position 1 of the scintillation screen x Thickness (mm) Figure 3.4. Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 1 of the scintillation screen.

78 Macroscopic Cross Section of Al (1/mm) -ln(i/io) y = *x ln(i/io) linear Thickness(mm) Figure 3.5. Linear attenuation property of aluminum sample step wedge at Position 2 of the scintillation screen. 7.7 x Thickness(mm) Figure 3.6. Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 2 of the scintillation screen.

79 Macroscopic Cross Section of Al (1/mm) -ln(i/io) y = *x - 4e ln(i/io) linear Thickness(mm) Figure 3.7. Linear attenuation property of aluminum sample step wedge at Position 3 of the scintillation screen. 8.6 x Thickness(mm) Figure 3.8. Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 3 of the scintillation screen.

80 Macroscopic Cross Section of Al(1/mm) -ln(i/io) y = *x ln(i/io) linear Thickness(mm) Figure 3.9. Linear attenuation property of aluminum sample step wedge at Position 4a of the scintillation screen. 7 x Thickness(mm) Figure Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 4a of the scintillation screen.

81 Macroscopic Cross Section of Al(1/mm) -ln(i/io) y = *x ln(i/io) linear Thickness(mm) Figure Linear attenuation property of aluminum sample step wedge at Position 4d of the scintillation screen. 8 x Thickness(mm) Figure Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 4d of the scintillation screen.

82 Macroscopic Cross Section of Al (1/mm) -ln(i/io) y = *x ln(i/io) linear Thickness(mm) Figure Linear attenuation property of aluminum sample step wedge at Position 5 of the scintillation screen. 7.6 x Thickness(mm) Figure Corresponding calculated effective total thermal neutron macroscopic cross section of aluminum versus step wedge thickness at Position 5 of the scintillation screen.

83 59 The results show a reasonable agreement between the reported and experimentally determined total cross section values for selected materials. In other words, the imaging system responds correctly to different materials that have been measured and can be used to determine the total macroscopic cross sections of the different density polyethylene foams that were used as input parameters in the image projection simulations. All the materials were measured with the same experimental conditions (reactor power, image acquisition time, etc). One can see that aluminum responds differently at Positions 4a and 4d than at other positions on the scintillation screen. At Positions 4a and 4d, a variety of slopes between any two measured points in the linear-attenuation property plot of aluminum were found and the overall slope of the linear attenuation property plot was different from slopes in other positions. For copper, iron and lead (see Appendix A), overall slope trend for each material seems consistent throughout the imaging scintillation screen, and the calculated effective total thermal neutron macroscopic cross sections behave differently at Position 4d than at other Positions. For copper and iron, the measured macroscopic cross sections at Position 4d were shifting up and down about an average value of 0.063/mm and 0.072/mm, respectively, while at other Positions, the trend of the calculated thermal neutron macroscopic cross sections was gradually decreasing as thickness increases. For lead, at Position 4d, the trend of the calculated total macroscopic cross section was increasing as compared to shifting up and down in other positions. Therefore, Position 4d was a common unusual region for different materials. It was also observed that Position 4d was on the left arch of the ring artifact. One can see that Position 3 and the

84 neighbor surrounding area was a good position for future measurement as the measured results for all the materials were consistent. From the experimental step wedge results, the calculated macroscopic cross section versus step wedge thickness is not a constant for all measurement positions across the scintillation screen. Mathematically, this is due to the fact that at each measurement Position, the linear attenuation property can be described as having the form: ln I I 0 = Σ t x + b, the calculated macroscopic cross section versus the different step wedge thicknesses is dependent on step wedge thickness x and the curve fitting parameter, b. Physically, the curve fitting parameter, b, represents the errors associated with the measurement from the neutron imaging experiment such as neutron scattering effects for different step wedge thickness of the materials, gamma rays in the neutron beam, etc. The detailed analysis of these effects is presented in Chapter 5 of this dissertation Determination of total Thermal Neutron Macroscopic Cross Sections of different Densities P.E. foams Using the measurement method described above, the total thermal neutron macroscopic cross sections of different density P.E. foams were determined. Figures 3.15, 3.16 and 3.17 show the normalized measured thermal neutron radioscopy images of different density P.E foams at Position 3 and the nearby region on the scintillation screen. The data were taken at a reactor power of 800 KW and a CCD camera integration time of 49s.

85 61 Figure First recorded 2-D neutron radioscopy image for different density P.E foams after beam and power normalization. Figure Second recorded 2-D neutron radioscopy image for different density P.E foams after beam and power normalization.

86 62 Figure Third recorded 2-D neutron radioscopy image for the g/cm 3 P.E foam steps after beam and power normalization. Total thermal neutron macroscopic cross sections of six different densities P.E foam step wedges ( g/cm 3, 0.04 g/cm 3, 0.05 g/cm 3, g/cm 3, 0.2 g/cm 3, g/cm 3 ) were measured using the same procedure as for the metals. Figure 3.18 to Figure 3.29 present plots of the linear attenuation properties and the calculated total macroscopic cross sections as a function of thickness for each density P.E foam.

87 Macroscopic Cross Section (1/cm) -ln(i/io) y = 0.078*x ln(i/io) linear Thickness(cm) Figure Linear attenuation property of the P.E foam with a density of g/cm Thickness(cm) Figure Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of g/cm 3 versus thickness.

88 Macroscopic Cross Section (1/cm) -ln(i/io) y = 0.1*x ln(i/io) linear Thickness(cm) Figure Linear attenuation property of the P.E foam with a density of g/cm Thickness(cm) Figure Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of 0.04 g/cm 3 versus thickness.

89 Macroscopic Cross Section (1/cm) -ln(i/io) y = 0.12*x ln(i/io) linear Thickness(cm) Figure Linear attenuation property of the P.E foam with a density of g/cm Thickness(cm) Figure Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of 0.05 g/cm 3 versus thickness.

90 Macroscopic Cross Section (1/cm) -ln(i/io) y = 0.26*x ln(i/io) linear Thickness(cm) Figure Linear attenuation property of the P.E foam with a density of g/cm Thickness(cm) Figure Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of g/cm 3 versus thickness.

91 Macroscopic Cross Section (1/cm) -ln(i/io) y = 0.39*x ln(i/io) linear Thickness(cm) Figure Linear attenuation property of the P.E foam with a density of g/cm Thickness(cm) Figure Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of g/cm 3 versus thickness.

92 Macroscopic Cross Section (1/cm) -ln(i/io) y = 0.54*x ln(i/io) linear Thickness(cm) Figure Linear attenuation property of the P.E foam with a density of g/cm Thickness(cm) Figure Corresponding calculated total thermal neutron macroscopic cross section for the P.E foam of g/cm 3 versus thickness.

93 Total Macroscopic Cross Section (1/cm) Table 3.2 lists the calculated total thermal neutron macroscopic cross sections of selected different density P.E foams from the above measurement analysis. From basic nuclear science knowledge, there is a linear relationship between the total thermal neutron macroscopic cross section and density for a given material. Figure 3.30 shows the linear relationship between the total macroscopic cross sections of the selected P.E foams versus their densities. Table 3.2.Calculated total thermal neutron macroscopic cross sections of the selected P.E foams Densities(g/cm 3 ) Cross Sections (1/cm) y = 1.6*x Macroscopic Cross Section linear Density of P.E foam (g/cm 3 ) Figure Linear relationship between total thermal neutron macroscopic cross sections and the density for selected P.E foams.

94 70 From the described measurement analysis of different metals and different density P.E foams, one can see that the designed thermal neutron imaging system at the Breazeale Research Nuclear Reactor responded to different materials as expected. The imaging system was successfully implemented to test advanced fuel cells from a variety of automobile manufacturers and shows promising results both for qualitative and quantitative analysis. Chapter 4 continues to discuss design and experimental validation of the quantitative thermal neutron computed tomography model that was used for water/ice quantification.

95 Chapter 4 71 SIMULATION AND EXPERIMENTAL VALIDATION OF THE QUANTITATIVE NEUTRON COMPUTED TOMOGRAPHY MODEL D Thermal Neutron Radioscopy Projection Model As indicated in Figure 3.1, the 2-D thermal neutron radioscopy projection model was based on the materials and their measured total macroscopic cross sections and as well as the geometry used for the test object. The next step was to choose appropriate materials with largest mean free path of the candidate materials to compose the object. The reason for choosing material with the largest mean free path was to reduce the neutron scattering effect from object to the scintillation screen, which would otherwise cause errors in the resulting voxel gray level values of the investigated object. Tables 4.1 and 4.2 list the mean free path of the metals and different density P.E foams based on the measured total macroscopic cross sections in Chapter 3. Table 4.1. The mean free path of the metals calculated from the determined total thermal neutron macroscopic cross sections for the imaging system. Material Cross Section (1/mm) Mean free path (mm) Aluminum Copper Iron Lead Table 4.2. The mean free path of different densities P.E foams calculated from the determined total thermal neutron macroscopic cross sections for the imaging system. Density(g/cm 3 ) Cross Section (1/mm) Mean free path (mm)

96 72 From data in Table 4.1, aluminum was a good candidate material among the metals for the 2-D thermal neutron radioscopy projection model since it has the largest mean free path value for thermal neutrons among the four metals, such that the neutron scattering events from object to the scintillation screen can be minimized. The modeled object had the following detailed dimensions and features: The object was made of solid aluminum and has a cylindrical shape with a diameter length of 93.6 mm, The height of the aluminum cylinder was 28.1 mm, In the center of the cylinder, was a hole with a diameter of 23.4 mm and height of 28.1 mm, air fills in this hole, and At a radial distance of 35.1 mm from the center, there were six different sections from the top to the bottom. Each section was 4.68 mm in diameter and 4.68 mm in height and each section corresponds to one of the six different density P.E foams that was measured in Chapter 3. In Chapter 3, it was shown that the calculated total macroscopic cross sections of different density P.E foams were dependent on the thickness. Therefore, to evaluate the approximate total macroscopic cross sections at 40 pixels (4.68 mm), a linear interpolation or polynomial curve fit method was used to calculate the values of the total macroscopic cross sections at this value.

97 Interpolated Macroscopic Cross Section (1/cm) 73 Table 4.3. Calculated total thermal neutron macroscopic cross sections of different density P.E foams at thickness of 4.68mm. Densities (g/cm 3 ) Linear Interpolation (1/mm) Polynomial fit (1/mm) Figure 4.1 shows linear relationship between total thermal neutron macroscopic cross sections of the P.E foams at thickness of 4.68 mm for the different densities y = 2.6*x Macroscopic Cross Section linear Density of the P.E foam (g/cm 3 ) Figure 4.1. Linear relationship between the calculated total thermal neutron macroscopic cross sections of the P.E foams at 4.68 mm and the density.

98 74 Based on the theoretical relationship between the total macroscopic cross section and the density, the measured total macroscopic cross sections have a linear relationship with the material density. This analysis further demonstrates the performance of the imaging system was within expectation and could be implemented to perform the NCT experiments Analytical Simulation of the 2-D Thermal Neutron Radioscopy Projections The following assumed conditions must be satisfied in order to make the simulation reasonable: The detector for the simulation had exactly the same size as the object, which was sensors. Each sensor had the same area as one pixel area of the imaging system and thus, the detector was composed of sensors, Each sensor was responsible for detecting the un-collided thermal neutron flux that passes through a pixel size area of the object. In other words, it was assumed that both a target (a pixel size area of the object) and a sensor were so small that the sensor subtends a small solid angle at the target, The intensity for the blank beam was based on a reactor power of 800KW and with a cooled CCD camera integration time of 49s at an open beam condition, which was equivalent to a gray scale value of These same conditions applied to other 2-D thermal neutron projection simulation, The thermal neutron beam intensity was kept as a constant over the entire object plane, The object was rotated from 0 º to 180 º at a rate of 0.5 º /projection, and a total of 361 projections were simulated, and

99 75 All the total macroscopic cross sections for aluminum and different density P.E foams used in the simulation were based on the data that are listed in Tables 4.1 and Simulation Results and Discussion Figures 4.2 through 4.13 present the simulation results of the 2-D thermal neutron radioscopy projection data and the corresponding cross sectional reconstruction calculation results for different density sections of P.E foam in the model object.

100 76 Figure 4.2. Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the g/cm 3 P.E foam.) Figure 4.3.The corresponding cross-sectional reconstruction result for the first density section ( g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.2.

101 77 Figure 4.4. Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the g/cm 3 P.E foam) Figure 4.5. The corresponding cross-sectional reconstruction result for the second density section ( g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.4.

102 78 Figure 4.6. Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the g/cm 3 P.E foam.) Figure 4.7. The corresponding cross-sectional reconstruction result for the third density section ( g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.6.

103 79 Figure 4.8. Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the g/cm 3 P.E foam.) Figure 4.9. The corresponding cross-sectional reconstruction result for the fourth density section (0.125 g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.8.

104 80 Figure Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the g/cm 3 P.E foam.) Figure The corresponding cross-sectional reconstruction result for the fifth density section (0.200 g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.10.

105 81 Figure Simulated 2-D neutron radioscopy projection (red-line corresponds to the horizontal plane of the g/cm 3 P.E foam.) Figure The corresponding cross-sectional reconstruction result for the sixth density section (0.333 g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.12.

106 Voxel Gray Values 82 Table 4.4 lists the average voxel gray value for each density P.E foam in the simulated cross-sectional slice compared to the corresponding total macroscopic cross section value for each density P.E foam with thickness 4.68 mm that was stacked from top to bottom in the object. Table 4.4. The average voxel gray value of each density P.E foam in the simulated cross sectional slice and the corresponding thermal neutron macroscopic cross section of thickness 4.68 mm which is stacked from top to bottom in the object. Densities (g/cm 3 ) Cross Section (1/mm) Voxel Gray Value Figure 4.14.shows a linear relationship between voxel gray values and the cross section values listed in Table y = 1*x Voxel Gray Values linear Interpolated Macroscopic Cross Section (1/cm) Figure Linear relationship between voxel gray values and the corresponding total macroscopic cross sections for each density P.E foams.

107 83 From the above simulation, the following conclusions can be made, which confirm the theory presented in the beginning of Chapter 3: The voxel gray value of a material represents the attenuation property of that material. It is a dimensionless quantity and its value is linearly related to the total macroscopic cross section of the material, For the same material, the total thermal neutron macroscopic cross section has a proportional linear relationship with the density of the material. The voxel gray value also has a linear relationship with the macroscopic cross section of the material. Therefore, the voxel value has a linear relationship with the density for the same material, Theoretically, the surrounding materials do not affect the quantitative voxel value information of the materials that were being investigated, and As shown in Figure 4.14, the voxel gray value versus macroscopic cross section curve nearly pass through the origin, which means the voxel gray value goes to zero when the corresponding macroscopic cross section value goes to zero.

108 Experiment Validation of the Model An experiment was conducted to verify the simulation result in section The neutron source was a 800 MW TRIGAIII research reactor and the thermal neutron flux at the imaging plane for 800 KW was approximately n/cm 2 -s [7]. Figures 4.15 and 4.16 show the designed object for NCT experiment according to the simulation model and the experiment setup. Figure Top view of the designed object which was used for the NCT model.

109 85 Figure Thermal neutron computed tomography experiment setup to validate the simulation model. The designed object was sitting on a turntable which was mounted on an aluminum stand, such that the whole object can be in Position 3 and nearby regions of the scintillation screen. From the analysis in Chapter 3, Position 3 and neighboring areas on the scintillation screen was considered the best position to conduct NCT experiment. The bulk of the object was made of aluminum. The cooled CCD camera was controlled by the image data collection computer and was synchronized with the motion control system of the turntable using a software plug-in developed by Heller for Image-Pro Plus [7].

110 86 Four large pieces of boron aluminum plates (BORAL ) were placed in front of scintillation screen to reduce the amount of gamma radiation dose to the CCD sensor associated with the long time runs of NCT experiment. The BORAL shielding plates placed in front of the scintillation screen were used to absorb those thermal neutrons that did not interact with the test object, but still were incident upon the scintillation screen, thereby reducing the amount of remaining neutrons inside the imaging system that can cause undesired prompt gamma rays. The viewing path between the CCD camera and the mirrors directly exposed the CCD sensor to neutrons remaining inside the imaging system, which could interact with the mirrors [49] and imaging system housing materials to produce gamma rays that could have damaged the CCD sensor [7]. Table 4.5 lists the measured gamma radiation dose to the CCD sensor before and after the BORAL shielding plates were placed in front of the scintillation screen. Table 4.5. The measured gamma radiation dose at the position of CCD sensor before and after BORAL shielding plates were placed in front of scintillation screen. Shielding Condition Beam Shutter Closed (mr/hr) Beam Shutter Open (mr/hr) Without BORAL plates With BORAL plates The BORAL shielding plates placed in front of the scintillation screen were effective in reducing the amount of gamma dose to the CCD sensor by almost 50% Measurement Results and Discussion Figure 4.17 to Figure 4.28 show the measurement results of the projections from the NCT experiment and the corresponding reconstructed cross-sectional slice data for different density P.E foam sections.

111 87 Figure Experimental measurement result of NCT projection data. The red-line indicates the location of the first density section ( g/cm 3 ) of P.E foam. Figure The corresponding cross-sectional reconstruction result for the first density section ( g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.17.

112 88 Figure Experimental measurement result of NCT projection data. The red-line indicates the location of the second density section (0.04 g/cm 3 ) of P.E foam. Figure The corresponding cross-sectional reconstruction result for the second density section (0.04 g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.19.

113 89 Figure Experimental measurement result of NCT projection data. The red-line indicates the location of the third density section (0.05 g/cm 3 ) of P.E foam. Figure The corresponding cross-sectional reconstruction result for the third density section (0.05 g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.21.

114 90 Figure Experimental measurement of NCT projection data. The red-line indicates the location of the fourth density section (0.125 g/cm 3 ) of P.E foam. Figure The corresponding cross-sectional reconstruction result for the fourth density section (0.125 g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.23.

115 91 Figure Experimental measurement result of NCT projection data. The red-line indicates the location of the fifth density section (0.2 g/cm 3 ) of P.E foam. Figure The corresponding cross-sectional reconstruction result for the fifth density section (0.2 g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.25.

116 92 Figure Experimental measurement result of NCT projection data. The red-line indicates the location of the sixth density section (0.333 g/cm 3 ) of P.E foam. Figure The corresponding cross-sectional reconstruction result for the sixth density section (0.333 g/cm 3 ) of the object. The location of this cross-sectional slice is indicated by the horizontal red-line in Figure 4.27.

117 Voxel Gray Level Value Table 4.6 lists the comparison of the average voxel gray value for aluminum and the different density P.E foams of the designed test object from the experimental measurement and simulation results. Table 4.6. Experimental and simulation results of voxel gray values for aluminum and different density P.E. foams of the designed test object. Materials Experiment Simulation % difference g/cm 3 P.E foam g/cm 3 P.E foam g/cm 3 P.E foam g/cm 3 P.E foam g/cm 3 P.E foam g/cm 3 P.E foam Aluminum Figure 4.29 shows the plot of the average voxel gray value versus densities for the different density P.E foams from experimental measurement and simulated result Simulation Experimental Density of the P.E foams (g/cm 3 ) Figure Comparison plot of average voxel gray values versus densities of different density P.E. foams from experimental measurement and simulation results.

118 Voxel Gray Values 94 Figure 4.30 shows the comparison plot of the average voxel gray value of different density P.E foams versus the corresponding thermal neutron macroscopic cross section Simulation Experimental Macroscopic cross sections of the different density P.E foams (1/mm) Figure Comparison plot of average voxel gray values versus corresponding thermal neutron macroscopic cross sections for different density P.E foams from experimental and simulation results. The experimental voxel gray values results for different density P.E foams is approximately linear with the corresponding densities and total macroscopic cross section as was expected (91% linear curve-fit). As indicated in Table 4.6, there is a significant difference between simulation and experimental measurement results for voxel gray values. Part of this discrepancy was due to the fact that the experimental setup changed between the computed tomography test object projection data acquisition and the experiments which measured the macroscopic cross sections of the aluminum and different density P.E foams. In the first case, BORAL shielding plates were placed in front of the scintillation screen while in the second case they were absent. An experiment

119 was conducted to demonstrate this, a detailed experimental procedure and measurement result can be found in Appendix B Initial Water/Ice Mass Evaluation Result Using Neutron Computed Tomography Technique D NCT Water/Ice Mass Evaluation Theory After the NCT facility and quantitative neutron computed tomography model were successfully designed and developed, the next important research goal was to evaluate water/ice mass in a simple geometry using the NCT technique. This was important for the following two reasons: 95 To test the performance of the designed NCT facility quantitative measurement capability and to demonstrate an accurate and feasible method for Water/Ice mass evaluation using NCT technique, To meet the latest industry needs for quantitative non-destructive evaluation inspection. Neutron computed tomography generates a 3-D volumetric reconstruction, which is comprised of individual elements, or voxels. A voxel may represent a volume of space only partially filled by a material and each voxel in the reconstruction occupies the same volume. Excluding the water/ice mass value represented by partially filled voxels can cause a lower evaluation result; However, considering these partially voxels as fully filled voxels can cause a higher evaluation result [45]. Therefore, a method that can precisely evaluate Water/Ice mass value represented by these partially fulfilled voxels had to be devised in order to accurately quantify the total water/ice mass in a simple geometry.

120 96 In 2-D neutron radioscopy projection data, removing attenuation effects of material other than water can be done by background normalization. Consider a 2-D neutron radioscopic image of thin slab aluminum, where the secondary neutron scattering effect is neglected. The pixel gray value of aluminum in the image represents the attenuated neutron intensity of neutrons that passed through aluminum slab that were recorded by the detector system of the neutron imaging system. The pixel gray value of aluminum in the image is described as [45]: G dry = C o e Σ Al t Al + G offset (4. 1) If there is a cavity inside the aluminum slab and the cavity is filled with water, then the pixel gray value of the overall image can be described as [45]: G wet = C o e Σ Al t Al e Σ water t water + G offset (4. 2) where in the above equations, o, Σ, and t denote the incident neutron flux, the total macroscopic cross section and the thickness of aluminum or water respectively. G dry and G wet represent pixel gray value of aluminum without and with water filling the aluminum slab cavity. C and G offset represent the gain of the imaging system and resulting gray value offset. The offset value in the image is caused by CCD camera charge build-up. It can be easily removed by subtracting a dark current image, an image recorded by the CCD in the absence of light [46]. Dividing Eq. (4.2) by Eq. (4.1) removes the attenuation effects of aluminum and isolates water attenuation term. This process is called background normalization [45]: G wet G dry = e Σ water t water (4. 3)

121 97 In 3-D NCT, the voxel gray value represents the combination of the total macroscopic cross section, Σ t, of various materials present at the voxel s spatial location [47, 48]. In 2-D neutron projection data, the influence of aluminum on the water can be removed by using Eq. (4.3), and the reconstruction of a series of background normalized 2-D neutron projection data will yield 3-D water column alone. In this process, two sets of projection data are needed, one set with presence of water and one set without the presence of water. For the 3-D water/ice evaluation method using NCT, it was important to quantify the relationship between the water/ice mass and the corresponding voxel gray value for fully and partially filled voxels. Consider two voxels, one is fully filled with water and the other one is partially filled with water. The water density in the two voxels is different since the two voxels volume are the same while water mass inside the two voxels is different. From Figure 4.14 and conclusions that were made from the quantitative NCT model simulation analysis, there is a linear relationship between the voxel gray value and the corresponding total macroscopic cross section for a material with different densities, which can be described as: G 1 Σ t1 = G 2 Σ t2 = G 3 Σ t3 = = G n Σ tn = k (4. 4) Therefore, the relationship between voxel gray value and the macroscopic cross section of water in the fully and partially filled voxels can be written as [45]: G F Σ F = G P Σ P (4. 5)

122 98 G F and G P represent voxel gray value of water in the fully and partially filled voxels, Σ F and Σ P represent the macroscopic cross section of water in the fully and partially filled voxels. Eq. (4.5) can be written as: G F G P = Σ F Σ P (4. 6) where Σ P = ρ P A g M ς t and Σ F = ρ F A g M ς t, ρ P and ρ F represent the densities of water in the partially and fully fulfilled voxels. A g is Avagadro s number, M is the molecular weight of water and ς t is the total neutron macroscopic cross section of water. Equation (4.6) can be written as [45]: G F G P = Σ F Σ P = ρ F ρ P = m F V F V P m P (4. 7) where m F and m P represent the amount of water mass in fully and partially filled voxels. V P and V F represent the volume of fully and partially filled voxels by water. Since partially and fully filled voxels occupy the same volume in space, V P = V F, Eq.(4.7) can be re-written as: G F G P = m F m P (4. 8) Re-arranging the above equation, water mass in partially filled voxels can be calculated as [45]: m P = m F G P G F (4. 9) In practice, the gray level value used for G F is the gray level value of a voxel with a volume fullly filled with water. The total water mass is calculated on a voxel-by-voxel

123 50.8mm 57.15mm 99 basis; multiplying each voxel by the fully-filled voxel s water mass as determined from the imaging system s pixel mapping and assuming a water density of 1mg/mm 3. Water mass inside a fully filled voxel is estimated as: m F = ρ water R s 3 (4. 10) where ρ water is the density of the water and R s is the pixel mapping of the imaging system, which is mm/pixel. Summing the individual voxel water mass will yield the total water mass in a 3-D reconstruction NCT water column. This method was successfully designed, implemented and tested Arthur Kevin Heller, he named this method reference gray level G F method. Given the water density and the existing pixel mapping of the imaging system, the water mass inside a fully-filled voxel is calculated to be mg Experimental Setup for 3-D NCT Water/Ice Mass Evaluation A cylindrical aluminum test sample with a cavity in the center was used for the 3-D NCT water/ice mass evaluation experiment. The dimension of the test sample and the cavity is shown in Figure mm 25.4mm Figure 4.31.The aluminum cylinder test sample for 3-D NCT water/ice evaluation experiment and its dimensions.

124 100 The 3-D NCT water/ice mass evaluation experiment was conducted using the designed NCT facility at Beam Port #4 at the Penn State Radiation Science and Engineering Center (RSEC). The neutron source is a 1MW TRIGA Reactor, housed at Penn State s RSEC, which produces a thermal neutron beam having an L/D of 150 and thermal neutron flux of n/cm 2 -s at 800KW. Two sets of projection data were collected, one of the dry sample without water/ice filling in the cavity and one of the wet sample with water/ice filling in the cavity. Each projection set contained 601 images acquired at 0.3 º /projection intervals. All the projections were taken with an integration time of 49s and a reactor power of 800 KW. Image processing analyses were performed on a dedicated data processing computer using the neutron and X-ray tomography reconstruction software, Octopus V8.2, the 3-D visualization program, VG Studio Max 1.2 and a 2-D neutron radioscopic image water quantification code, PSUMagic [50] D NCT Water/Ice Mass Evaluation Results and Discussion A dark-current image was subtracted from all projections to remove the G offset term in Equations (4.1) and (4.2) before reconstruction. Each wet sample image in the projection data set was background normalized using its corresponding dry sample image. Octopus V8.2 was used to generate cross-sectional slices that were used to create a 3-D volume image in VG Studio Max 1.2. The resulting reconstruction produced the sample s water column alone. An example of the 3-dimensional NCT reconstruction result of the sample s water column alone with a diameter of mm is shown in Figure 4.32.

125 101 Figure A 3-dimensional NCT reconstruction result of water column with diameter of mm [45]. Voxels of fractional water/ice mass were likely to occur along the outer edge of the water column. The reference gray level value, G F, was taken to be the average gray value of water column s interior voxels in the x, y and z directions. For a comparison, the amount of water presented inside the cavity of the aluminum cylinder test sample was also calculated using PSUMagic. A theoretical water mass was determined using the dimension of the cavity inside test object sample in Figure 4.31 and an assumed water density is 1 mg/mm 3 [45]. The evaluation method was also applied to quantify ice mass. The cavity within test sample was filled with 300mg of water measured using a syringe, a water mass less than the test sample s theoretical maximum value to allow for ice expansion, and then the water was frozen using dry ice. Dry nitrogen gas was blown over the aluminum test

126 sample to minimize condensation on its surface. After the temperature was stabilized, series of 2-D projection image data were collected, and the reconstruction analysis was performed. Results of both water/ice phase analysis are listed in Table 4.7 [45]. Table 4.7. Results of Liquid and Ice phase water mass analysis. Method (Phase) Water Mass(mg) Error (%) Theoretical (Liquid) NA PSUMagic (Liquid) Reference Gray Value (Liquid) Theoretical (Ice) 300 NA Reference Gray Value (Ice) From this analysis, one can see that the 3-D NCT water/ice mass evaluation method yields a very accurate value of water column mass within 2% of the theoretical value. PSUMagic also confirmed this result by calculating a water mass value of 346.0mg, which is within 0.1% of the theoretical value. The results in Table 4.7 demonstrate that the 3-D NCT imaging technique is not only capable of obtaining important 3-D information about a sample s interior structure and material properties that other traditional methods cannot provide, but also reveals that the reference gray value method is a reliable and accurate approach to evaluate water/ice mass using the 3-D NCT imaging technique. For a fuel cell under cold-start conditions, i.e. fuel cell battery car in winter time, ice becomes a critical concern. The freeze/thaw experienced during startup can lead to degradation of fuel cell performance. Therefore, providing an accurate and viable method to evaluate ice mass could be valuable in determining damage caused by ice formation and how it would be mitigated. However, the 3-D NCT reference gray value quantification approach is a time-consuming method, which requires acquisition of

127 103 two separate projection data sets. Future NCT work at the Penn State Breazeale Research Nuclear Reactor will include exploration water/ice mass evaluation methods only requiring a single set of projections [45].

128 Chapter ERROR CORRECTION AND ANALYSIS METHODS FOR QUANTITATIVE NEUTRON COMPUTED TOMOGRAPHY Neutron radioscopy images can be degraded by many factors. In general, there are three types of errors associated with neutron imaging technique: neutron scattering and associated cupping artifacts, beam hardening effects and geometric un-sharpness effects, All of which can cause blurring on the neutron radioscopy images and can be potential error sources for the quantitative 3-Dimensional NCT water/ice mass evaluation method Neutron Scattering Effects Neutron scattering in the object, has long been recognized as one of the many factors that degraded the neutron radioscopy projection image quality and corresponding 3- dimensional computed tomography reconstruction results [51]. Prior research in this area in the international community has concentrated on trying to use the rigorous Point Spread Function (PSF) approach that utilizes the Monte Carlo simulation method to determine the shape of the PSF as a function of object to detector distance, object thickness, and various scattering and absorption cross sections [51]. Some researchers have also tried to use the PSF de-convolution method, but the computational requirements and the necessary prior knowledge have made this option unattractive as a formal method for removing the object scattered neutron contribution from radiographic and computed tomography images [52, 53]. Though computationally expensive, recent advances in computer technology, particularly in the area of parallel computing processing, have made the Monte Carlo technique an effective and powerful tool for

129 105 image formation simulations [54, 53, 55]. With such methods, it is possible to isolate individual parameters and perform sensitivity studies with the assurance that only the parameter of interest is being changed. Two representative works were done by Mora and Raine in this area [56, 57]. In particular, Mora utilized the Monte Carlo technique to determine the scattering-blur effect from the neutron radiographic/radioscopic imageformation process, and provided a methodology to quantify and qualify the blurring effect. A novel technique was developed by Mora for correcting blurring effects in neutron tomography reconstructions. In Mora s work, the scattering blur effect was shown to be a convolution of the radioscopic/radiographic projection with a blurring function. A de-convolution correction method utilizing the Maximum-Entropy Formalism was developed and tested. The formalism was shown to be an unbiased procedure to correct for the scattering blur. Enhancement of tomograms was achieved by the scattering-blur de-convolution of the individual projections [56]. Raine utilized MCNP to simulate the neutron flux profile data along the object plane and to estimate the shape of the scattering function for different object geometries and sizes. Based on the results from these simulations, a correction algorithm was developed that estimated the Object Scattering Function (OSF) using the wings of the pixel data [57]. The scattering correction algorithm was successfully tested on the MCNP simulated projection data as compared to ideal radiographic and tomographic projection lined data that were also generated by MCNP [57]. As discussed above, the main deviations from the ideal radioscopy image are caused by neutron scattering, which can be caused by the neutrons passing through the sample being scattered and hitting the scintillation screen. This is also called the Sample

130 106 Scattering Component [11]. The sample scattering component appears as extra intensity in the radioscopy images, which was being interpreted as an increase in transmitted neutron intensity or a reduced effective macroscopic cross section of the material. In additional to this, neutrons missing the sample can be scattered in the surrounding environment of the sample and hit the scintillation screen. This scattering component from the surrounding environment is called the background scattering component. This background scattering component also causes an extra intensity on the scintillation screen. The background scattering is often divided into two components [11]: The first component refers to those neutrons that do not reaching the scintillation screen directly, but are scattered at the beam catcher or at the borders of the imaging facility and scattered back to hit the scintillation screen. These neutrons can be blocked by limiting the beam size to the size of the scintillation screen. The second component refers to those neutrons that pass through the scintillation screen and are scattered back from the mirror to the scintillation screen. Hassanein compared absorption rates for different chemical elements doped scintillation screen and he found out that most neutrons are not absorbed but can penetrate a Li 6 doped scintillation screen and hence can be backscattered [11]. A 28cm 28cm Li 6 doped scintillation screen was used in NCT facility at RSEC of Penn State. Therefore, both sample and backscattered neutrons need to be corrected for the accuracy of the 3-D NCT water/ice mass evaluation work at Penn State. A set of experiments was conducted to test the backscattered neutron effect on the scintillation screen of the NCT facility at RSEC. Figure 5.1 shows the experimental setup for the test.

131 107 Figure 5.1. Experimental setup for testing the impact of backscattered neutrons effects on the scintillation screen of NCT facility at RSEC. The moving BORAL plate was moving uniformly at step size of 20mm from left to the right side of the scintillation screen. A sample material was mounted against the left edge of scintillation screen, and two pieces of BORAL plates were put on the top and bottom of the scintillation screen while the other piece was moved from the left side of the scintillation screen to the right side using automatic control equipment. The purpose of this experiment was to demonstrate, while uniformly increasing the open beam size, the impact of backscattered neutrons from the beam catcher and mirror on the scintillation screen. The incident neutrons entering the portion of the scintillation screen that was covered by BORAL plates were completely absorbed. Only neutrons entering the uncovered portion of the

132 108 scintillation screen were backscattered to the scintillation screen by the mirror and the beam catcher and produced light photons. Therefore, the measured gray value behind the shielding plates represents the backscattering component. Figure 5.2 and 5.3 represent the gray level value in the open beam area and the backscattered component. Figure 5.2. The recorded neutron beam intensity in the shielded open beam area when the BORAL shielding plate moved from left to right side of the scintillation screen.

133 109 Figure 5.3. The recorded neutron beam intensity in the selected area behind the shielding area (Backscattered component) when the BORAL shielding plate moved from left to right side of the scintillation screen. The background scattering increases with the opening of the beam size. The background scattering neutrons were not only present behind the shielded area, but also in the open beam area. Table 5.1 lists the backscattered component and open beam gray value ratio from the experimental setup. The backscattering component is up to 8% -13% of the open beam gray values. This value is in agreement with a similar experiment conducted by Hassanein at the neutron imaging facility at NEUTRA, which was up to 10% [11]. It is not difficult to see that backscattered neutrons from beam catcher and the mirror on the scintillation screen is a significant error contribution to 3-D NCT water/ice mass evaluation work using the neutron imaging facility at Penn State.

134 110 Table 5.1. The ratio of backscattered component and open beam gray value measured from the experiment setup. Distance (mm) Back Scattered Component and Open Beam Gray Value Ratio Copper, lead and iron wedge samples were put against the scintillation screen individually while the BORAL plates were moving from the left to right side of the scintillation screen. The effective macroscopic cross sections of these samples were measured against the moving distance of BORAL plates across the scintillation screen. Figures 5.4, 5.5 and 5.6 show the measured results. The effective macroscopic cross section of these samples decreased as the BORAL plate was moving from the left side of the scintillation screen to the right. This is due to the fact that the backscattered neutrons increased in intensity as the open beam size increased and raised the apparent neutron transmission for the sample material. This experiment further demonstrated that Background Neutron Scattering was a significant source of error which can affect quantitative evaluation.

135 Effective Macroscopic Cross Section of Iron (1/mm) Effective Macroscopic Cross Section of Copper (1/mm) Distance (mm) Figure 5.4. The measured effective macroscopic cross section of copper as BORAL plate moving from left to right side of the scintillation screen Distance (mm) Figure 5.5. The measured effective macroscopic cross section of iron as the BORAL plate moving from left to right side of the scintillation screen.

136 Effective Macroscopic Cross Section of Lead (1/mm) Distance (mm) Figure 5.6. The measured effective macroscopic cross section of lead as the BORAL plate moving from left to right side of the scintillation screen. Hassanein proposed a method of correcting error due to Background Neutron Scattering. The inspected sample is replaced by a black body, i.e. a sample that is assumed to be opaque for neutrons [11]. This can be any object made of polyethylene. Ideally, the black body has the same size and shape as the sample. Since the black body blocks more neutrons than the sample in the radioscopy image, the measured background scattering behind the black body is scaled by the factor f bgscat [11]. f bgscat = Σ x,yф x, y Σ x,y Ф x, y bb (5. 1) where Ф x, y is the measured intensity of the sample radioscopy image at the pixel location (x, y), Ф x, y bb is the measured intensity of the black body radioscopy image at the pixel location (x, y). The scaling factor should be taken into account for beam

137 113 fluctuations between the measurement of the sample and the black body radioscopy image. The correction for the background scattering is then obtained by subtracting the scaled background scattering from the originally measured flux [11]. Ф bgscat cor = Ф x, y f bgscat Ф x, y bb (5. 2) However, this correction method for the background scattering is an approximate method. Similar to the sample neutron scattering correction, a more accurate method would be to find a Point Backscattered Function for the background scattering, which depends on the position and a subsequent de-convolution technique [11]. Since it is difficult to find a defined model to measure or simulate the backscattered neutrons from the environment that hit the scintillation screen, the effort to measure the Point Backscattered Functions becomes unattractive. The best correction method for background neutron scattering would be to find a practical approach to limit the background neutrons Background Neutron Scattering Correction Method As discussed and analyzed in the previous sections, backscattered neutrons were an error source for the 3-D water/ice mass evaluation work using NCT facility at Penn State. It was more reasonable to find an approach to limit the background neutrons scattering such that the quantitative measurement results could be improved. Figure 5.7 shows a method that was implemented in RSEC at Penn State to reduce the background neutron scattering effect. The surrounding area of sample materials was completely covered by the BORAL plates and was put directly against the scintillation screen. In this way, BORAL plates not only absorbed those neutrons which bypassed the sample and were incident on the scintillation screen that could be scattered back by the mirror and the

138 Incident neutrons Incident neutrons Sample scattered neutrons Incident neutrons 114 beam catcher to produce additional light photons on the scintillation screen, but also limited those neutrons which were scattered by the sample material and were incident on the its surrounding area in the scintillation screen. BORAL Shielding Plate BORAL Shielding Plate Li-6 scintillation screen Figure 5.7. The surrounding area of sample materials are completely covered by the BORAL plates and were put directly against the scintillation screen. Please note that the transmission neutrons through the sample and gamma rays produced from the absorption of the neutrons in the sample are not shown in this picture. Iron, aluminum, lead and copper sample step wedges were tested using this shielding experiment setup to measure the effective macroscopic cross sections. Table 5.2 lists the measurement results as compared to the reported value. The detailed linear attenuation plots can be found in Appendix C. The measurement results listed in Table 5.2 show a great improvement of the measured macroscopic cross sections for the materials with the BORAL shielding plates in front of the scintillation screen as compared to the case with no shielding, which are listed in Table 3.1.

139 Table 5.2. Comparison of the reported and experimental determined total macroscopic cross sections of the materials with BORAL shielding plates in front of the scintillation screen using the imaging facility. 115 Cross Sections Material Report (1/mm) Shielded (1/mm) % difference Aluminum Copper Iron Lead Another experiment was conducted to ensure that this was a neutronic effect instead of ambient light photon reduction inside the imaging housing. Figure 5.8 shows the experimental setup, where the inside of the scintillation screen was shielded by opaque paper. The opaque paper was transparent to neutrons while the light photons were shielded by the opaque paper. As indicated in Figure 5.8, there was a center cut in the opaque paper which had exactly the same spatial location as the materials measured in front of the scintillation screen. A comparison of the measured macroscopic cross sections between this experimental setup and the open beam condition is listed in Table 5.3. The detailed linear attenuation properties of the measurements for the materials can be found in Appendix C. From the measured result, it is not difficult to see that the amount of ambient light photons inside the imaging facility did not influence the quantitative measurement results.

140 Table 5.3. The measured total macroscopic cross sections of the materials for the open beam condition and the opaque paper behind the scintillation screen. Measured Cross Sections Material Open Beam (1/mm) Opaque Paper (1/mm) Copper Iron Lead Figure 5.8. Experimental setup with opaque paper behind the scintillation screen which was used to shielding light photons. The center cut in the opaque paper has the exactly same spatial location as where the sample was measured in front of the scintillations screen. Putting BORAL plates in front of the scintillation screen was an effective method to reduce the errors introduced by background neutron scattering in quantitative

141 117 measurements using the imaging facility. This method also was implemented to reduce the errors associated with the 3-D NCT water/ice mass evaluation work in RSEC at Penn State. However, this method reduces the field of view, which may limit its use for large objects. The shielding experiment showed the background neutron scattering attributes 8%-13% of the open beam gray value, which means the background scattering neutron intensity was 8%-13% of the incoming neutron intensity. Therefore, it is possible to subtract the background neutron scattering component from the collected open beam and sample projections. Assuming R refers to the ratio of background scattering neutron intensity to the incoming neutron intensity I 0, due to the uniform additive effect of the background neutron scattering on the neutron radioscopy image, the sample image and the blank beam image with background neutron scattering effect can be written as: I sample = I 0 e t t + R I 0 + I darkcurrent I 0 = I 0 + R I 0 + I darkcurrent 5. 3 Therefore, t = ln I sample I darkcurrent R I 0 I 0 I darkcurrent R I 0 t 5. 4 The image processing for the above correction procedure can be summarized as: Subtract dark current image from both sample and blank beam neutron radioscopy images.

142 118 Determine the incoming neutron intensity I 0 (true blank beam radioscopy image gray value without background neutron scattering effect). I 0 can be determined by re-arranging Equation (5.3) I 0 = (I 0 I darkcurrent )/(1 + R). Depending upon specific conditions, R can be chosen different values from 8% to 13%. For the macroscopic cross sections measurements, R was chosen as 13% due to the fact the all the materials were imaged in the open beam condition. The ratio of background neutron scattering component to incoming neutron intensity was determined to be 13% when the shielding plate was moving from left to the right side of the scintillation screen and leaving the scintillation screen area open. Once the parameter R and true blank beam radioscopy image gray value I 0 were determined, subtract the backscattering component R I 0 from both sample and blank beam radioscopy images, Perform power normalization (PN) to both sample and blank beam radioscopy images without the backscattering effect. Perform beam normalization using Equation (5.4) to find out the effective total macroscopic cross section of the material without the backscattering effect. Figures 5.9 through 5.12 show the measurement results of the total macroscopic cross sections for the selected materials after background neutron scattering correction. In each figure, the measurement result of each material was compared to the theoretical value, scattering correction (shielding) and direct measurement results. The measurement results after background neutron scattering correction for the materials are summarized in Table 5.4.

143 Table 5.4. Comparison of the reported and the determined total macroscopic cross sections of the materials with the background neutron scattering correction method using Eq. (5.4). Cross Sections Materials Reported (1/mm) Corrected (1/mm) % difference Aluminum Copper Iron Lead As compared to the measurement results in Table 3.1, the corrected results using Eq. (5.4) have improved. This was as expected since Eq. (5.4) corrects the background neutron scattering effect in the measurement results while the background neutron scattering effect was present in the measurement results in Table 3.1. It was also easy to determine that the results obtained using Eq. (5.4) were not as improved as the measurement results using the BORAL shielding plates, which is listed in Table 5.2. This was due to the fact that Eq. (5.4) only corrects the background neutron scattering effect and the sample neutron scattering effect was still present in the measurement results. As has already been discussed, the BORAL shielding plates not only corrected the background scattering effect, but also limited the sample scattering effect.

144 -ln(i/io) -ln(i/io) y = x - 7E y = x + 7E-17 B.G Scattering Correction Scattering Correction (Shield) 0.06 Theoretical y = x y = x Direct Measurement Thickness of Aluminum Step Wedge (mm) Figure 5.9. The linear attenuation property of aluminum step wedge after background neutron scattering correction. The scattering correction (shield), direct measurement results and the theoretical value are also plotted in the same figure y = x + 4E-15 1 B.G Scattering Correction 0.8 y = 0.081x + 2E-15 Scattering Correction (Shield) 0.6 Theoretical y = 0.062x + 2E-15 y = x Direct Measurement Thickness of Copper Step Wedge (mm) Figure The linear attenuation property of copper step wedge after background neutron scattering correction. The scattering correction (shield), direct measurement results and the theoretical value are also plotted in the same figure.

145 -ln(i/io) -ln(i/io) y = x + 6E-15 B.G Scattering Correction y = x + 2E-15 Scattering Correction (Shield) 0.6 y = x Theoretical y = 0.07x + 5E-16 Direct Measurement Thickness of Iron Step Wedge (mm) Figure The linear attenuation property of iron step wedge after background neutron scattering correction. The scattering correction (shield), direct measurement results and the theoretical value are also plotted in the same figure y = 0.038x + 3E y = 0.031x + 4E-16 B.G Scattering Correction Scattering Correction (Shield) Theoretical y = 0.025x - 4E-16 y = x Direct Measurement Thickness of Lead Step Wedge (mm) Figure The linear attenuation property of lead step wedge after background neutron scattering correction. The scattering correction (shield), direct measurement results and the theoretical value are also plotted in the same figure.

146 122 In Chapter 4, the trend for the simulation and experimental results of the voxel gray values for the different density P.E foams was determined to be linear, while the absolute values of the voxel gray values for the different density P.E foams between the simulation and experimental results were different. Recall that the simulated voxel gray values for the different density P.E foams were equal to the measured macroscopic cross sections of the P.E foams for the imaging system, which were determined in the open beam condition with the background neutron scattering effect present in the projection data. The experimental results of the voxel gray values for the different density P.E foams, however, were determined with the BORAL shielding plates in front of the scintillation screen as indicated in Figure (i.e. with limited background neutron scattering effect present in the projection data) Therefore, it would be interesting to use Eq. (5.4) to analyze these different density P.E foams projection data and determine the macroscopic cross sections of the different density P.E foams with limited background neutron scattering effect. The parameter R was chosen to be 10% for the background neutron scattering correction for the different density P.E foams. This was due to the fact that the experimental for the NCT model was conducted under the condition which the scintillation screen was partially covered by the BORAL shielding plate. The open beam area which was not covered by the BORAL shielding plates (See Figure 4.17) was found to be 140cm 2, the total area of the scintillation screen was 784cm 2. The ratio of uncovered area to the total area of the scintillation screen was found to be 18%. Recall from Table 5.1, the measured ratio of the backscattered component to the blank beam R was linearly increasing with the distance of the shielding plate moving across the scintillation screen plane. Considering the height of the scintillation screen was a

147 123 constant, which means R was also linearly increasing with the open beam area on the scintillation screen as the shielding plate was moving. Based on the data in Table 5.1, a linear interpolation was made to calculate R with the uncovered area to the total area of the scintillation screen ratio of 18%. R was determined to be For calculation convenience, R was chosen as 10% for the background neutron scattering calculation correction for different density P.E foam. The results are listed in Table 5.5 and the detailed linear attenuation plots can be found in Appendix C. Table 5.5. Experimental and simulation results of voxel gray values for aluminum and different density P.E. foams after the background neutron scattering correction for the designed test object. Material Experimental Simulation (Correction) % difference g/cm 3 foam g/cm 3 foam g/cm 3 foam g/cm 3 foam g/cm 3 foam g/cm 3 foam Aluminum Compared to the results in Table 4.6, after the background neutron scattering correction, one can see that the difference between the simulated and experimental results of the different density P.E foams and aluminum voxel gray values is improved over 100%. Still, there is a large discrepancy between the simulated and experimental data. The experimental data were taken when the test object was at a certain distance away from the scintillation screen and the geometric unsharpness plays a role in the quantitative measurement. The simulation results were based on the measurement data

148 124 when the materials were in contact with the scintillation screen and, in this case the geometric unsharpness does not play a significant role in the quantitative measurement Cupping Artifacts and Beam Hardening In X-ray imaging, beam hardening is the process of increasing the average energy level of an X-ray beam by filtering out the low-energy photons as they pass through the object. When penetrating an object, the X rays of lower energies are more readily attenuated than those of higher energies. As the thickness of an object increase so too does the preferential attenuation of the lower energy X rays [58]. Beam hardening induced Cupping Artifacts are well known in X ray imaging field. Cupping artifacts from beam hardening occur when X ray beam transmitted through the center of a large object become harder than those passing through the edges of the object due to the greater amount of material the beam has to penetrate. Because the beam becomes harder in the center of the object, the resultant profile of the linear attenuation coefficient appears as a cup. Depending on the individual reactor facility used for neutron imaging work, beam hardening effect can also be expected due to the fact that the neutron beam used for neutron radioscopy work is usually poly-energetic. However, a fellow graduate student, Arthur Kevin Heller, analyzed the measurement result of neutron beam energy distribution of Beam Port #4 in RSEC and the cross sections of aluminum and water in the energy range of Beam Port #4 [58]. He provided evidence that beam hardening is not a concern for the 3-D water/ice mass evaluation work due to the following reasons: The measured neutron beam energy distribution of Beam Port #4 which is used for neutron radioscopy work in the RSEC indicates a very well thermalized beam. The majority of the neutrons in the beam have energies of ev. The beam

149 125 shape closely matched a Maxwell-Boltzman distribution. Epithermal neutrons and fast neutrons are virtually non-existent. In other words, there is no higher energy which the beam can shift towards. The plots of the cross sections of aluminum and water within the energy range of Beam Port #4, the value of the cross sections for the materials are relatively constant across the measured energy range of the neutron beam. This means that the materials comprising the cylindrical samples are attenuating neutrons equally at all energies within that range. The beam hardening artifacts cannot occur with a flat energy dependent total cross section Cupping Artifacts and Neutron Scattering The ideal neutron radioscopy projection data used for 3-D NCT reconstruction would be those transmission images that exactly obey the exponential law of attenuation (Eq.3.1) with a mono-energetic neutron beam. There were various reasons why this assumption does not hold for real neutron imaging experiments. The main deviations from the ideal image come from the neutron scattering effect. Neutrons passing through the sample material could have been scattered and hit the scintillation screen. This sample scattering component appeared as an extra intensity in the neutron radioscopy images, which can be interpreted as a reduction in neutron attenuation or as lower mass density of the material [11]. The neutrons that missed the sample material could have been scattered by the materials surrounding and behind the sample (e.g. mirror and beam catcher). This background scattering component also caused an extra intensity on the scintillation screen. Like those induced by beam hardening, cupping artifacts could also

150 126 be caused by neutron scattering effect [59]. The scattering contribution had an influence on the measured neutron transmission similar to X- ray beam hardening in X- rays radiography; i.e. the measured transmission values were higher than expected and this deviation was increasing with the straight path traveling distance of the radiation through the object. This usually lead to a loss of contrast and blurred object boundaries in the neutron radioscopy images and violated the assumption of a purely exponential law of neutron transmission used in the tomography reconstruction calculation. In the reconstructed slices through the object, an inhomogeneous attenuation coefficient distribution was indicated in a region that consisted of the same material. Kasperl and Vontobel successfully implemented an iterative method for cupping artifacts reduction used in X-ray computed tomography to neutron tomography data of a massive copper cylinder with a central conical bore [59]. In this paper, the acquired neutron radiography projections are heavily influenced by a scattering contribution originating from the sample, which violated the exponential law of narrow beam attenuation. Kasperl and Vontobel observed that the neutron scattering effect lead to similar effects similar to beam hardening in X-ray computed tomography. They tested the performance of an iterative method and demonstrate that the method mitigated the cupping artifacts in neutron tomography caused by the neutron scattering. Cupping artifacts due to neutron scattering effects appear in the normalized 3-D NCT water/ice column cross sectional reconstruction slices. They were one of the errors that influence the accuracy of the 3-D NCT water/ice mass evaluation results presented in Chapter 4 of this work. The 3-D NCT water/ice mass quantification method was based on normalizing voxel gray values in the reconstruction slices to the gray value of a

151 127 reference voxel. The reference voxel was usually a voxel known to represent a full volume of water. If the cupping artifact is presented on each reconstruction slice, there will be an overshooting water/ice mass region beyond the normalized voxel gray value region and the overall water/ice mass value is overestimated. Therefore, the cupping artifact is one of the errors that influence the accuracy of 3-D NCT water/ice mass evaluation results and needs to be corrected. Recall that a practical method that limited the sample neutron scattering and the background neutron scattering was implemented to improve the perceived neutron macroscopic cross sections of the materials. The same method should also reduce the cupping artifacts which are due to neutron scattering in the reconstruction slices Proposed Experiment Setup for Neutron Scattering Induced Cupping Artifacts Reduction As discussed in Section 5.1.3, neutron scattering induced cupping artifacts was one of the errors present in 3-D NCT water/ice column reconstruction slices and influenced the accuracy of the mass evaluation result. A fast and practical method was needed to reduce the cupping artifacts in order to improve the 3-D NCT water/ice quantification results. Similar to the shielding technique that was implemented in measuring the effective macroscopic cross sections of different materials, an aluminum cylinder test object was used for this case. The aluminum cylinder test object was 25.4 mm in diameter and mm in height, a cavity with a diameter of mm and 50.8 mm in height was in the center of the aluminum cylinder and the cavity was filled with water. Four large pieces of BORAL shielding plates were put around the test object and completely covered the scintillation screen. As discussed in Section 5.1.1, this shielding

152 128 configuration could limit both sample and background neutron scattering effects. A total of five different distances: 0 mm, 35 mm, 70 mm, 105 mm and 140 mm away from the scintillation screen were examined. At each location, both dry and wet sample neutron radioscopy images of the sample object were collected with an integration time of 120 seconds. (Note that dry and wet sample object radioscopy images were collected in two different processes, all the dry sample object radioscopy images at different distances were collected at one time and all the wet sample object radioscopy images at different distances were collected at another time. Dry sample image refers to the radioscopy image of the aluminum cylinder test object without water inside the cavity. Wet sample image refers to the radioscopy image of the aluminum cylinder test object with water inside the cavity.) Another set of dry and wet sample radioscopy images at each distance without the shielding plates in front of the scintillation screen was also collected Measurement Results and Discussion The suggested number of projections count for an NCT run was approximately 1.5 times the number of detector row pixels. The CCD camera used in the neutron computed tomography facility has 2048 pixel row, this recommended a total of 3072 projections had to be collected [58]. Considering the total reactor beam time it took to acquire all the projections at each location, it was almost impossible to finish collecting all the projections at each location based on the reactor daily schedule. However, Arthur Kevin Heller, provided an alternative approach to overcome this time constraint. With the symmetric cylindrical geometry of the sample object, a dry and wet sample object neutron radioscopy projection images was collected at each distance. Due to the fact that any images acquired will be the same for all viewing angles, it was

153 129 possible to record a single projection image that could be duplicated to produce a semiartificial, complete projection data set. The sequence of the fully duplicated radioscopy images must be reflected at equiangular intervals between 0 º and 180 º. Octopus V8.2 was given the semi-artificial projection data set as an input and it was essentially tricked into believing the samples were fully rotated through 180 º and produced a reconstruction image. This CT projection data acquisition and subsequent CT reconstruction and analysis method was called Pseudo-CT. Heller provided a detailed comparison between Pseudo-CT and True-CT analysis for the 3-D NCT water/ice mass evaluation results, and the measured mass values were all within 0.6% between Pseudo-CT and True-CT analysis [58]. Therefore, Pseudo-CT analysis method was an alternative approach to substitute True-CT analysis method for symmetrical geometry objects. It overcomes the lengthy time needed to acquire all the projections for the True-CT but provides the same accurate result as True-CT. The pseudo-ct analysis method was applied to the single radioscopy images at each distance for both shielding and without shielding configurations in front of the scintillation screen. After performing reconstruction of the test object at different objectdetector distances with and without shielding configurations, Figure 5.13 to Figure 5.22 show the comparisons for the cross-sectional reconstruction slice images of the water column and the corresponding cupping artifacts plots.

154 Voxel Gray Values 130 (a) (b) Figure Cross-sectional reconstruction results of the mm diameter water column when the object-detector distance is 0 mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen mm 0mm Distance (Pixels). Figure The corresponding voxel gray values across the mm diameter water column.

155 Voxel Gray Values 131 (a) (b) Figure Cross-sectional reconstruction results of the mm diameter water column when the object-detector distance is 35 mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen mm 35mm Distance (Pixels) Figure The corresponding voxel gray values across the mm diameter water column.

156 Voxel Gray Values 132 (a) (b) Figure Cross-sectional reconstruction results of the mm diameter water column when the object-detector distance is 70 mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen mm 70mm Distance (Pixels) Figure The corresponding voxel gray values across the mm diameter water column.

157 Voxel Gray Values 133 (a) (b) Figure Cross-sectional reconstruction results of the mm diameter water column when the object-detector distance is 105 mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen mm 105mm Distance (Pixels) Figure The corresponding voxel gray values across the mm diameter water column.

158 Voxel Gray Values 134 (a) (b) Figure Cross-sectional reconstruction results of the mm diameter water column when the object-detector distance is 140 mm using Pseudo-CT analysis method: (a) without shielding plates and (b) with shielding plates in front of the scintillation screen mm 140mm Distance (Pixels) Figure The corresponding voxel gray values across the mm diameter water column.

159 Heller[58] used a quantity χ c to describe the degree of cupping artifacts across the water column reconstruction slice in this dissertation, which was defined as: 135 χ c = G amax G amin G amax 5. 3 where in this equation, G amax represents the average maximum voxel gray values across the water column reconstruction slice and G amin represents the average minimum voxel gray values across the water column reconstruction slice. Normally, G amax was the average voxel gray value chosen from the maximum values in the cupping artifacts, and G amin was the average voxel gray values chosen from the minimum values in the cupping artifacts. Table 5.6 summarizes the calculated χ c values from the shielding experiment for the 4mm diameter water column at different object-detector distances. Table 5.6. A list of the calculated χ c from the experiment at different object-detector distances. Distance (mm) Before Shielding (χ c ) After Shielding(χ c ) % Improvement % % % As expected, it was easy to see that putting BORAL shielding plates in front of the scintillation screen was an effective way to reduce the cupping artifacts which were caused by neutron scattering effects. The perceived macroscopic cross section of water was also increased due to the fact that the BORAL plates limit the sample material and background neutron scattering effects. At an object-detector distance of 70 mm and 105 mm, there were no cupping artifacts present for both the shielded and unshielded

160 136 configurations. Heller provided a possible explanation for the disappearing of cupping artifacts at certain object to detector distances. According to Heller, the object-todetector distance played a role in producing cupping artifacts when the sample was smaller than the apparent width of the beam source aperture. He suggested that reducing cupping artifacts requires moving the sample object closer to the scintillation screen. However, it was important to note that moving the object closer to the scintillation screen can increase the neutron scattering effect from the sample to the scintillation screen, which as already discussed, was another error source for introducing the cupping artifacts. Figure 5.23 shows the research result from Heller [58], and from this plot, there was a certain range of object-to-detector distance from 70 mm to 105 mm, the cupping was disappeared. Figure Magnitude of the cupping versus object-to-detector distance for the mm cavity diameter sample. (From Heller [58])

161 137 Due to the current design of the imaging system and experimental setup for the True-CT experiment, the Newport Model 496 rotary table and the location of the scintillation screen limit the minimum object-to-detector distance to 140 mm. This location was where the projection data of the test object for 3-D NCT water/ice mass evaluation was collected. The cupping artifacts were present in the reconstruction slice of the water column at object-to-detector distance 140 mm. Hibiki [60] suggested that the neutron scattering effect can be ignored if the object-to-detector distance is on the order of the width of the object being imaged. This was helpful in explaining why at an object-to-detector distance of 70 mm and 105 mm, the cupping artifacts have been eliminated. However, this did not explain the fact that at an object-to-detector distance of 140 mm, the cupping artifacts were present in the mm water column reconstruction slices. In order to precisely determine if the neutron scattering from the test sample to the detector existed in the recorded neutron radioscopy image at object-to-detector distance of 140 mm, MCNP (Monte Carlo N-Particle Transport Code) was utilized to simulate the neutron scattering events from the sample for the experiment setup. With the support from a fellow graduate student Cihangir Celik, an MCNP simulation input deck was constructed to simulate the neutron transmission including scattering events by the aluminum sample object at an object-to-detector distance of 140 mm. The model included an aluminum sample with a mm diameter cavity filled with water, a parallel neutron beam with a thermal neutron spectrum and a neutron tally detector grid. The number of attenuated neutrons through the object at discreet spatial locations was recorded in the detector grids. For comparison purposes, the ideal image of the same test

162 Normalized Intensity 138 object was also simulated using an exponential attenuation law model [58]. Figure 5.24 shows the comparison of the normalized intensity line profile for the test object with a mm diameter cavity in the center using the MCNP and the neutron attenuation law Ideal MCNP Distance (pixels) Figure The normalized line profiles of the test object with mm diameter cavity in the center for the object-to-detector distance of 140 mm using MCNP and neutron attenuation law. Both sample dry and sample wet images were generated by an MCNP and with an ideal neutron attenuation method. The neutrons passed through the object and were recorded by the detector grid, and the results were written to a text file. The text file was then imported into Image J software as a text image and saved as a TIFF file to create the corresponding MCNP and ideal simulated radioscopy images [58]. Blank beam, sample dry and sample wet images were created such that the full Pseudo-CT analysis method could be applied. Figure 5.25 shows the corresponding mm diameter water column

163 Voxel Gray Values 139 voxel gray values in the reconstruction slices from the radioscopy images of the test object generated by MCNP and ideally simulation method Ideal MCNP Distance (pixels) Figure The corresponding mm diameter water column voxel gray value in the reconstruction slices from the radioscopy images of the test object generated by MCNP and ideally method. The object-to-detector distance is 140 mm. From Figure 5.24, the normalized line profiles of the test object using MCNP and ideally simulation methods perfectly match up with each other when the object-todetector distance is 140 mm. The MCNP model simulates the neutron transmission through the object including scattering from the sample object while the ideal simulation method does not take into account the neutron scattering events from sample to detector. However, the normalized intensity of the MCNP and the ideal simulation models were in good agreement. In other words, at an object-to-detector distance of 140 mm, the neutron

164 140 scattering from the object to the detector was not significant. This can also be confirmed in Figure The voxel gray values through the mm diameter water column reconstruction slices matched up with each other using the corresponding radioscopy images generated by MCNP and ideal models. There was no cupping artifact present in the reconstruction results. However, there was a discernable cupping artifact in the reconstruction slices from the experimentally collected radioscopy projection data when the object-to-detector distance was 140 mm. Recall that in Section and Section 5.1.4, a sample and background neutron scattering events correction method was proposed to reduce the cupping artifacts. The background neutron scattering events can increase the intensity on the scintillation screen and would create similar effects on the scintillation screen as the sample neutron scattering. The background neutron scattering events from the beam catcher and mirror to the scintillation screen were not considered in the MCNP simulation, and the background neutron scattering for the imaging system contributes a significant source of error as previously discussed. Therefore, the cupping artifact present in the mm diameter water column reconstruction slices could have resulted from the background neutron scattering if the background neutron scattering component was not subtracted from both dry and wet sample image projection data set. From the above analysis, the following conclusions can be made: For the test object with a cavity diameter of mm at an object-to-detector distance of 140 mm, sample neutron scattering from the sample to the detector was not significant, The background neutron scattering is an additive effect on the neutron radioscopy image and can cause similar effects on the scintillation screen as the sample

165 141 neutron scattering. Both types of scattering can increase the intensity on the scintillation screen and produce cupping artifacts in the reconstructed slices images, and Putting BORAL shielding plates in front of the scintillation screen and covering the surrounding area of the sample object was a fast and practical method to eliminate sample and background neutron scattering events as well as reducing the scattering induced cupping artifacts Geometric Unsharpness Evaluation and Correction Method for the Neutron Computed Tomography System in RSEC In X-rays radiography imaging, the geometric unsharpness, U g, of the inspection setup needs to be taken into consideration, especially when using geometric magnification. Geometric Unsharpness refers to the loss of object definition that is the result of geometric factors of the radiographic equipment and setup. It occurs because the radiation does not originate from a single point but rather over an area. Consider Figure 5.26, where the source size was a finite area rather than a point source. Different radiation paths can be taken from the point of origin in the source such that the edges of the object become less defined. Three factors in combination affect the unsharpness: the distance between the source aperture to the object a, the object-to-detector distance b and the diameter of the finite source aperture f. The finite size of the X-ray tube focal-spot, the source-to-object and object-to-detector distances are used to calculate the geometric unsharpness of the X-ray radiography imaging inspection setup. As illustrated in Figure 5.26, the geometric unsharpness, caused by the finite size of the X-ray radiation source, was determined by the a/f ratio and the distance of the object to the image plane b.

166 a b 142 Beam Source Focal Point f Object Ug Penumbra Umbra Image Plane Figure Illustration of geometric unsharpness in X ray imaging inspection setup. The geometric unsharpness is calculated as: U g = a f 1 b (5. 4) For X ray radiographic imaging, the source size was obtained by referencing manufactures specifications for a given X ray source. As the source size decreases, the

167 143 geometric unsharpness also decreases. For a given size source, the unsharpness can also be decreased by increasing the source to object distance, a, but this comes with a reduction in radiation intensity. The object-to-detector distance b was usually kept as small as possible to minimize the geometric unsharpness Geometric Unsharpness for Neutron Radioscopy Imaging: Similar to the geometric unsharpness definition used in X-ray radiographic imaging, in neutron radioscopy, the collimation ratio, L/D, is defined as the ratio of the distance from the inlet aperture to the object divided by the diameter of the inlet aperture of the neutron collimator. This L/D ratio plays a crucial role in the geometric unsharpness of neutron radioscopy. Like X-ray imaging shown in Figure 5.26, the geometric unsharpness in neutron radioscopy, caused by the finite size of neutron source, is determined by L/D ratio and the object-to-detector plane distance, L : U g = L D 1 L (5. 5) The L/D ratio for a neutron radioscopy system is usually measured by ASTM standard test method E [61] and the L/D ratio was determined to be approximately 150 for the Thomson tube based neutron radioscopy imaging system in RSEC at Penn State [9]. However, the L/D ratio for the newly designed neutron computed tomography facility in RSEC at Penn State is 113, based on the value of L=4800 mm and D=42.4 mm. The experimental setup for the 3-D NCT water/ice mass evaluation has an object-todetector distance of 140 mm, and the geometric unsharpness at this position was calculated as 1.23 mm Considering that the pixel mapping of the imaging system was 0.117mm/pixel, the geometric unsharpness is 10.5 pixels. Figure 5.27 shows a magnified

168 144 2-D neutron radioscopy image of the normalized mm diameter water column and the blurring edge caused by the geometric unsharpness at an object-to-detector distance of 140 mm. U g Ug Figure The magnified in normalized 2-D neutron radioscopy image of the mm diameter water column with object-to-detector distance of 140 mm. The blurred edge of water column due to the geometric unsharpness is indicated in the image. The blurring edge due to geometric unsharpness was presented in the left, right, top and bottom portions of the normalized 2-D neutron radioscopy image of water column. A pseudo CT reconstruction of the 2-D image from Figure 5.27 was made and

169 Voxel Gray Values 145 Figure 5.28 shows a line profile of the voxel gray values in the center of the water column region from the cavity sample Distance (Pixels) Figure The line profile of the voxel gray values through the center of the mm diameter water column with object-to-detector distance of 140 mm. Note the edges of the profile bended outward, which is caused by the geometric unsharpness True Magnification M and Geometric Magnification m for the Neutron Radioscopy System. Heller and the author of this dissertation made joint efforts to investigate the true magnification and geometric magnification of the neutron radioscopy imaging system and the impacts on the water/ice mass quantification results [58]. If neutrons were emitted from a point source, the magnification could be determined by the ratio of source-to-detector distance divided by the source-to-object distance. This ratio is called

170 146 geometric magnification. In reality, the neutrons used in thermal neutron radioscopy work in RSEC at Penn State were emitted from a finite area of neutron inlet aperture with diameter of 42.4 mm from the reactor collimator. The magnification resulted with neutrons from the finite area source is called true magnification, M. Figure 5.29 illustrates magnification from a point source and a finite area source. Point Source D Finite Area Source L d d Object Object L Ug u Ug I I (a) (b) Figure Illustration of a magnified image produced from a point source (a) and from a finite area source (b). For point source neutron beam as indicated in Figure 5.29 (a), the geometric magnification m is defined by: L + L m = ( ) 5. 6 L The true magnification, M, for the point neutron source is the same as the geometric magnification m, which is:

171 147 L + L M = m = ( ) 5. 7 L However, for a finite area neutron beam source as indicated in Figure 5.29 (b), as the object-to-detector distance L increases, the apparent size of the object being imaged on the image plane would also increase. This magnification effect was a result of divergent nature of the neutron beam coming out of from the reactor collimator. Curry [62] indicated the magnification of an object as: M = m + (m 1) D d 5. 8 where: M = The true magnification of the object m = The geometric magnification of the object, which is described by Eq (5.6). d = Diameter of the object and D = Diameter of the neutron inlet aperture. In Equation (5.8), M is referred to the true magnification of the object and it takes into account the neutron beam source size, D. The magnified size of the sample object I on the image plane in terms of sample s true dimension d is then given by: I = M d (5. 9) From Equations (5.5) and (5.8), when the neutron beam source size, D, goes to zero (i.e. point source), then the geometric unsharpness U g goes to zero and the true magnification, M, is equal to m. Considering the dimensions L=4800 mm, L =140 mm, D=42.4 mm and d= 3.988mm for the neutron beam of the neutron radioscopy imaging system and the 3-D NCT water/ice mass evaluation experiment setup, the true magnification, M, and the

172 Normalized Voxel Gray Value 148 magnified size of the sample object, I, on the image plane were calculated to be M =1.34 and I= 5.33mm, respectively. Figure 5.30 shows the line profile of normalized voxel gray values through the center of a mm diameter water column cross sectional slice that was reconstructed from the experimental projection data. The un-sharp outline due to geometric magnification and unsharpness is indicated by the black line and the red line represents the ideal voxel gray values through the mm diameter water column under that magnified condition. The object-to-detector distance was 140 mm Un-sharp Ideal Measured 140mm Distance (Pixels) U g U I U g Figure The line profile of the normalized voxel gray values through the center of a mm diameter water column cross sectional slice that was reconstructed from experimental projection data. The un-sharp outline due to geometric unsharpness and geometric magnification, is indicated by the black line. The ideal voxel gray values under the magnified condition are indicated by the red line.

173 149 The length of the water column under the magnified condition was calculated to be I=5.33 mm and the corresponding pixels on the image plane was 45 pixels based on the current system resolution of 0.117mm/pixel with object-to-detector distance of 0 mm. If the object was close to the scintillation screen, i.e. object-to-detector distance was 0 mm, the corresponding pixels on the image plane was calculated to be 34 pixels. When the object-to-detector distance was 140 mm, the object was magnified on the image plane and the number of pixels represent the object was increased. At the same time, because the real dimension of the object was kept as a constant, the system s spatial resolution under magnified condition was decreased. Forty five pixels represented the water column including the geometric unsharpness. This was confirmed by observing the length of the water column, I, represented by the measured data with the object-to-detector distance of 140 mm in Figure The spatial location for the left edge of the magnified object was at (128, 0) and the right edge of the magnified object was at (173, 0). The area under rectangular red line represents the amount of voxels representing water needed to be quantified in order to get an accurate water mass value under magnification at an object-to-detector distance of 140 mm. However, due to the geometric unsharpness effects, the water mass was represented by the area under blue trapezoid line. Therefore, the number of voxels representing water mass under the two symmetry triangular area was excluded for the 3- D NCT water mass evaluation technique because of the geometric unsharpness. From this perspective, the geometric unsharpness was the predominate error for the 3-D NCT water/ice mass evaluation work for the current imaging system setup and this error needed to be corrected or reduced.

174 Proposed Geometric Unsharpness U g Correction Method for 3-D NCT Water/Ice Mass Evaluation Work The geometric unsharpness in the neutron radioscopy images was one the dominate error for the quantitative NCT evaluation work when the object was away from the scintillation screen. The most effective method to reduce the geometric unsharpness was to increase the collimation ratio, L/D assuming the neutron beam s angular divergence was not large, e.g. less than 1. However, the object-to-detector distance L was dependent on the NCT experiment setup and the radioscopy imaging system, i.e. for 3-D NCT water/ice mass evaluation in this work, L was equal to 140mm due to the fact that the current design of the imaging system and experimental setup for the NCT experiment, the Newport Model 496 rotary table and the location of the scintillation screen limit the minimum object-todetector distance to 140 mm. The L/D of the neutron radioscopy imaging system in the reactor facility was determined based on the object-to-detector distance L. Therefore, reducing the geometric unsharpness for the current neutron radioscopy imaging system was not an easy task. One correction method was designed, implemented and tested by the author to increase the effective L/D ratio for the current neutron radioscopy imaging system in RSEC at Penn State. Figures 5.31 and 5.32 show the before and after designs to increase L/D to reduce geometric unsharpness.

175 155.6mm Standing Table 190.5mm 151 Reactor Beam Door Divergence Beam Groups II Divergence Beam Groups I Parallel Beam Groups Sample 140mm Scintillation Screen 254mm Figure Top view of the 3-D NCT water/ice mass evaluation experiment setup before increasing effective L/D ratio to reduce geometric unsharpness.

176 155.6mm 2063mm Wooden Spacer BORAL plate BORAL plate Standing Table mm Reactor Beam Door Divergence Beam Groups I &II Parallel Beam Groups Sample 140mm Scintillation Screen 254mm Figure Top view of the 3-D NCT water/ice mass evaluation experiment setup after increasing effective L/D ratio to reduce geometric unsharpness.

177 153 In Figure 5.32, please note that the wooden spacer was above the beam flight path. The experimental setup to increase the effective L/D and to reduce the geometric unsharpness was straight forward. As illustrated in Figure 5.31, the geometric unsharpness was caused by the divergent neutron beam Groups I & II coming out of the reactor collimator. Divergence neutron beam Group I refers to those neutrons coming out from the left and right boundary regions of the reactor collimator. Divergent neutron beam Group II refers to those neutrons coming out from central region of reactor collimator. Figure 5.32 shows an experimental setup for limiting those divergent neutron beams coming out of the reactor collimator. Two parallel BORAL plates were used to limit the divergent neutron beam Groups I & II. The length of the parallel BORAL plates was 2063 mm and was extended from the scintillation screen surface to the reactor collimator outlet aperture. The divergence neutron beams Groups I & II coming out from the collimator were absorbed by the BORAL plates as indicated by Figure The two parallel BORAL plates were evenly spaced by a long wooden spacer. The length of the wooden spacer was approximately 1920 mm and it extended from the reactor collimator outlet aperture to the spatial position directly before test object. A space with a length of 140 mm was left open for the purpose of pulling the sample out after collecting the wet sample projection data without shutting down the reactor to collect the blank beam projection data. Based on the geometry of this experimental setup, the width of the wooden spacer was calculated. The calculation of the width needed for the wooden spacer was based on the boundary condition, i.e. by considering a neutron of divergence neutron beam Group II, could have possibly been transmitted

178 2063mm BORAL plate BORAL plate 140mm 154 through the edge of the test object and then recorded by the scintillation screen. Figure 5.33 shows the basic geometry for the calculation. Collimator Outlet Aperture Sample d 0 1 d 0 Scintillation Screen Figure The geometry needed for the width of wooden spacer calculation. The diameter of the sample object was 25.4 mm, it was not possible to make the width of wooden spacer 25.4 mm due to the fact that there was space, d 0, needed on both sides of the sample such that the sample could be removed after collecting the wet sample projection data. As illustrated in Figure 5.33, consider a neutron of divergence beam Group II coming out from the reactor collimator outlet aperture without being absorbed by the BORAL plates, penetrates through the edge of the sample and recorded by the

179 155 scintillation screen. The space d 0 was calculated based on the geometry of the experimental setup and the known dimensions: d 0 2d = and d 0 was found to be 1.99 mm or inches, which means if the space d 0 was more than 1.99 mm or inches, the neutrons would have been transmitted through the edge of the sample and recorded by the scintillation screen. If the space, d 0, was less than 1.99 mm or inches, the neutrons would be absorbed by the BORAL plates before recorded by the scintillation screen. For convenience, the space d 0 was set to be 1.58 mm or inches. Therefore, the total width of wooden spacer was estimated as 25.4 mm+1.58 mm 2=28.57 mm or inches. The new neutron inlet aperture diameter for the neutron radioscopy imaging system was mm or inches and the effective L/D was calculated to be 168. Figure 5.34 shows the front view image of the BORAL shielding including wooden spacer and its dimensions.

180 Figure Front view of the BORAL shielding (Aluminum Boron Carbide Plates) structure including wooden spacer and its dimensions. 156

181 Measurement Results and Discussion Two experiments were conducted to test the effect of the long BORAL shielding structure for the measurement of the geometric unsharpness on the reconstruction slices of the diameter water column images. The first experiment was performed without the shielding structure. As shown in Figure 5.31, the rotary table for the sample was removed and the sample was put on an aluminum standing table at an object-to-detector distance of 140 mm. Single dry, wet and blank beam images were taken during this experiment, and the integration time for each image was 120 seconds at a reactor power of 800 KW. The second experiment was performed identically to the first one but with new the shielding structure. The geometric unsharpness U g with the shielding structure was estimated as: U new g = L ( L = 140mm D ) ( 4800mm = 0.833mm 28.57mm ) new In terms of pixels, the geometric unsharpness U g was calculated as: U g new = 0.833mm 0.117mm /pixel = 7pixels Recall that the geometric unsharpness was calculated to be 10 pixels without the shielding structure in place. Therefore, approximately 3 pixel reduction in geometric unsharpness was observed in the 3-Dimensional reconstruction slices of the water column region with the shielding structure. Figure 5.35 shows the experimental setup for the geometric unsharpness reduction.

182 158 Figure Experiment setup for the geometric unsharpness reduction. The Pseudo CT analysis method was performed on both image sets of the mm diameter water column with and without the parallel BORAL shielding plates. After performing reconstruction analysis for both image sets, the voxel gray level values of the reconstruction stack averaged from slices 200 to 450 were chosen for comparison purposes. Figure 5.36 shows the mm diameter water column reconstruction stack averaged from slices 200 to 450 for both image sets. Figure 5.37 shows the average voxel gray value comparison for the mm diameter water column with and without the parallel BORAL shielding plates.

183 Normalized Voxel Gray Values 159 (a) (b) Figure The mm diameter water column reconstruction stack averaged from slices 200 to 450. (a) without BORAL shielding plates and (b) with BORAL shielding plates. 1.2 Without Shielding With Shielding 1 (With Shielding: 188, ) (Without Shielding: 190, ) 0.8 (Without Shielding: 213, 0.957) (With Shielding: 214, ) (Without Shielding: 174, 0.024) (With Shielding: 223, ) (With Shielding:177, 0.023) (Without Shielding: 225, ) Distance (Pixels) Figure The comparison of the normalized voxel gray values for the mm diameter water column reconstruction stack averaged from slices 200 to 450 with and without BORAL shielding plates in place.