Luận án Cosmic Ray Muon Radiography của Larry Joe Schultz - Đại học Portland State

COSMIC RAY MUON RADIOGRAPHY by LARRY JOE SCHULTZ A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in ELECTRICAL AND COMPUTER ENGINEERING Portland State University 2003 ACKNOWLEDGMENTS This dissertation could not have been completed without the kind support of many people throughout my midlife return to graduate school. My first note of thanks goes to my brother Roger Schultz who beat me to the punch in returning for a PhD and in so doing gave me the confidence that I could do it too. Doug Hall saw me wandering in the PCAT hallways at Portland State University and showed me what I needed to do to get started in graduate school. Doug provided lots of early guidance, a job, and some of the best teaching I ever experienced at a university level and I’m grateful for all of that.

George Lendaris inspired my interest in computational intelligence and provided me with the opportunity to get my feet wet in research. Although our research interests later diverged, George has remained a good friend and mentor and has strongly influenced my approach to problem solving. I encountered a few big bumps in the road along my path, and there were moments when I doubted my ability to stay the course. Tad Shannon took the time to listen and always seemed to find the right words to restore my confidence.

Tad also taught me a lot of mathematics and reviewed some of the mathematical developments in this dissertation. I’m thankful to Tad on several levels. i Kevin Vixie was instrumental in bringing me to Los Alamos National Laboratory and so enabled me to pursue this dissertation work. I am very appreciative of Kevin’s selfless assistance.

Thanks of course go to my colleagues on Muon Radiography team at Los Alamos, both for their contributions to the work and for allowing me to pursue significant portions individually for my dissertation. Thanks to Andy Saunders, John Gomez, Margaret Teasdale, Jason Medina, Bill Priedhorsky, Konstantin Borozdin, Gary Hogan, and Richard Schirato. Special thanks to Gary Hogan for his assistance with data acquisition for the experiment. Tom Asaki provided an invaluable service in helping with coding for tracing of ray paths through pixels and voxels.

Thanks to my entire dissertation committee, and very special thanks go to my two major advisors on this project, Andy Fraser of PSU and Chris Morris of LANL. Both provided intellectual guidance without which the project would never have been finished. Thanks to Andy for his diligence in reviewing the details and guiding the development of the reconstruction work and for helping me navigate the bureaucratic maze. I am eternally grateful to Chris Morris for providing me with the opportunity to do this work, and for his unwavering advocacy throughout the effort.

Thanks to Los Alamos National Laboratory and the Department of Energy for providing me with monetary support during this work. and Emma Schultz, have spent most of their working lives in support of public education at all levels. They passed their belief in the value of education on to me, and, more importantly, gave me their personal love and support ii throughout my educational process and life in general. My father and mother in law, Bill and JoAnn McCool, have also been particularly interested in and supportive of my doctoral work and never once called me a deadbeat husband when their daughter was putting me through school! And finally, my most significant thanks to wife, Robyn, and sons Connor and Caleb for their loving support and patience throughout the hours, days, weeks, and months of work required to get this done.

They’ll be happy to have Dad back, and Dad will be even happier to be back. iii TABLE OF CONTENTS Page ACKNOWLEDGMENTS. i LIST OF TABLES. viii LIST OF FIGURES.

ix CHAPTERS 1 INTRODUCTION.1 Information from the Heavens .2 A New Form of Radiography.3 The Author’s Role and this Dissertation .4 A Potential Application – Nuclear Contraband Detection .1 Cosmic Rays & Muons .1 Primary Cosmic Rays and the Atmospheric Cascade .2 The Muon Spectrum at the Earth’s Surface .2 How Muons Interact with Matter .3 Multiple Coulomb Scattering (MCS).3 Previous Work on Cosmic Ray Muon Radiography.4 Previous Work on Charged Particle Radiography .5 Overview of Computed Tomography .1 Transform-based CT .2 Algebraic-based CT. 31 3 CONCEPT AND PRELIMINARY CALCULATIONS .1 The Cosmic Ray Muon Radiography Concept .2 Using MCS to Segregate High, Medium and Low Z Materials.3 Preliminary Calculations on Material Segregation .1 Material Discrimination with Monoenergetic Muons.2 Material Discrimination with Realistic Muon Momentum Spread.3 Material Discrimination with Muon Momentum Spread and Momentum Measurement. 49 4 RECONSTRUCTON FRAMEWORK AND POCA ALGORITHM .1 The Tomographic Reconstruction Framework .1 Framework for the Traditional Case with a Deterministic Ray Signal.2 Framework for the Stochastic MCS Ray Signal .2 The Point of Closest Approach (PoCA) Reconstruction Algorithm .1 Description of the 2D PoCA Algorithm .2 Simulation Platform for Testing of the 2D PoCA Algorithm .3 Numerical Tests of the 2D PoCA Algorithm.4 Extending the PoCA algorithm to 3D .5 Summary of PoCA Results. 71 5 EXPERIMENTAL PROOF OF PRINCIPLE .1 Design of the Experimental Prototype .2 Front end electronics .1 Wire Chamber Signal Processing .3 Data Acquisition / Analysis .2 Setup and Calibration .1 Wire Chamber HV Plateau and Efficiency Tests.3 Chamber Resolution Estimation .3 Experimental Radiography Results .1 Tungsten Cylinder Test Object .1 Scattering Analysis and Simulation Cross-Validation.2 PoCA Reconstruction Optimized for Visual Appearance .2 Additional Test Objects.

102 v 6 MAXIMUM LiKELIHOOD RECONSTRUCTION .1 Maximum Likelihood Tomographic Reconstruction using Scattering Angle Information .1 The MLS Reconstruction Framework.2 The 2D MLS Reconstruction Algorithm .3 Numerical Tests of the 2D MLS Reconstruction Algorithm .2 Maximum Likelihood Tomographic Reconstruction using Scattering Angle and Ray Displacement Information.1 The 2D MLSD Reconstruction Framework.2 The 2D MLSD Reconstruction Algorithm.3 Numerical Tests of the 2D MLSD Reconstruction Algorithm .4 Performance Indices and Algorithm Performance.5 Extensions to the 2D MLSD Algorithm.2 Cosmic Ray Muon Momentum Spread.3 Convexity of the MLSD Cost Function .6 Summary of Extended 2D MLSD Algorithm Performance.3 The 3D MLSD Algorithm .1 The 3D MLSD Framework and Algorithm.2 Numerical Tests of the 3D MLSD Algorithm.4 Application of MLSD to Experimental Data .2 Items for Future Research .2 Application of MLSD to Nuclear Contraband Detection .3 MLSD with Adaptive Reconstruction Elements. 145 LIST OF REFERENCES. 147 APPENDICES vi A BLANPIED MUON GENERATOR. 152 B MUON MOMENTUM MEASUREMENT BY MULTIPLE SCATTERING.1 Inferring Material via Scattering of Particles with Estimated Momentum.2 Using Scattering to Estimate Momentum.3 Inferring Material via Scattering of Particles with Momentum also Estimated via Scattering.

164 C DERIVATION OF JACOBIAN AND HESSIAN OF COST FUNCTIONS FOR MLS AND MLSD ALGORITHMS.1 Jacobian and Hessian for the MLS Cost Function .2 Jacobian and Hessian for the MLSD Algorithm. 169 vii LIST OF TABLES Table page Table 2.1 Approximate energy loss experienced by muons traversing 10 cm of various materials. Approximate range of muons in various materials.3 Approximate multiple scattering for muons passing through 10 cm of various materials .1 Confidence intervals on scattering density after one minute of tracking 3 Gev muons through 10 cm of various materials.1 Performance Measurements for 2D Test Case Reconstructions .2 Performance Measurements for Extended 2D Test Case Reconstructions (10 runs for each case). 136 viii LIST OF FIGURES Figure page Figure 1.1 Illustration of cosmic ray muons passing through an object.1 Illustration of the particle cascade produced in the atmosphere.2 Experimental muon spectrum data for two arrival angles.3 Muon interactions when passing through matter.4 Multiple Coulomb scattering of a charged particle through material.5 Schematic of proton radiography beam line.6 Sample images created via multiple scattering proton radiography.7 Illustration of projections in CT.8 Illustration of how projections may be interpreted in the frequency domain.9 In Algebraic Reconstruction Techniques (ART), the object is broken into a discrete grid, and ray projections are modeled as weighted sums of cell values.1 The cosmic ray muon radiography concept.2 Multiple scattering in two dimensions .3 Radiation length as a function of material Z.4 Scattering density [per Eq.3)] of various materials.5 Discrimination of materials using scattering of 3 GeV momentum muons.6 Discrimination of materials using scattering of muons with momenta drawn from a model of the cosmic ray spectrum.7 Improved discrimination of materials using 2 minutes of exposure.8 Illustration of muon momentum measurement via multiple scattering through layers of material of known thickness and composition.9 Discrimination of materials using scattering of muons with momentum measured via 2 plates in the setup of Figure 3.1 A 2D object possessing a continuous characteristic function.2 Sampling the object by passing interrogating rays through it.3 Multiple scattering produces a stochastic ray signal.4 A small grid containing scattering density estimates with a single ray passing through.5 Illustration of the PoCA algorithm.6 Illustration of how the PoCA algorithm is used to reconstruct object scattering density.7 Setup for muon scattering simulation and PoCA reconstruction testing.8 Object setup for test case #1.9 PoCA reconstruction of scattering density for test case #1 (a), and reconstructed object classification (b).10 Ray crossing locations computed for the reconstruction of test case #1 (a), and illustration of how “erroneous” ray crossing location can occur.11 Test case #2 object setup (a), PoCA reconstruction (b), and PoCA classification (c).12 Ray crossing locations computed for the reconstruction of test case #2 (a), and illustration of mechanism for erroneous scattering localization.13 Test case #3 object setup (a), PoCA reconstruction (b), PoCA classification (c), and ray crossing locations (d).14 3D Test case #4 object classification.15 3D Test case #5 object classification.1 Cross-section of a generic multi-wire proportional chamber.2 Schematic of a delay-line readout drift chamber wire plane.3 Photographs of a time delay line wire plane (a), and a chamber enclosing for such planes (b).4 Schematic representation (a) and photograph (b) of detector positions and object area in the experimental prototype.5 Signal flow diagram for muon detector signal processing.6 Schematic of trigger logic .7 Photograph of front end electronics with major system components labeled.8 Sample Chamber Efficiency Curve .9 Typical histogram of muon frequency vs.

time delay line signal time difference.10 Typical histogram of muon frequency versus time delay line signal time sum.11 First image of experimental radiography of tungsten block test object (see text).12 Regions defining T) tungsten, S) steel beam, and B) background scattering for analysis .13 Ray scattering distributions for rays passing through region T (a), region S (b), and region B (c).14 PoCA reconstruction of the tungsten cylinder.15 PoCA reconstruction of the tungsten cylinder (simulation).16 PoCA Reconstructions of tungsten cylinder; experiment (a) and simulation (b), with heuristic modification to improve appearance.17 Aesthetically enhanced PoCA reconstruction of a c-clamp, made from 100,000 experimentally gathered muons.18 Aesthetically enhanced PoCA reconstruction of the letters “LANL” constructed of 1” lead stock, made from 100,000 experimentally gathered muons.1 Results for test case #1.2 Results for test case #2.3 Results for test case #6.4 Calculation of ray scattering and displacement for multiple layers of material .5 MLSD reconstructions of test case #1 (a), and test case #2 (b).6 Results for test case #6.7 MLS (a) and MLSD (b) reconstructions of test case #1 with all interrogating rays oriented vertically.8 Results for test case #3, one minute simulated exposure.9 PoCA and MLSD results for test case #3 for 1, 3, and 5 minute simulated exposures.10 Test case #7 objects, the letters “PSU” made of iron (a), the one minute MLSD reconstruction (b) and classification (c).11 Effect of position measurement error.13 PoCA (a) and MLSD (b) reconstructions for test case #1 with varying muon momenta and nominal position error levels.14 Results for 3D test case #4.15 Results for 3D test case #5. 141 xii CHAPTER 1 INTRODUCTION 1.1 Information from the Heavens When cosmic rays strike the Earth’s atmosphere, a cascade of many types of subatomic particles is created. By the time this shower of particles reaches the Earth’s surface, it is comprised primarily of muons.