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Design and Evaluation of Gamma Imaging Systems of Compton and Hybrid Cameras

Permanent Link: http://ufdc.ufl.edu/UFE0024347/00001

Material Information

Title: Design and Evaluation of Gamma Imaging Systems of Compton and Hybrid Cameras
Physical Description: 1 online resource (168 p.)
Language: english
Creator: Feng, Yuxin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: coded, compton, gamma, hybrid, image, iterative, os, proton
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Systems for imaging and spectroscopy of gamma-ray emission have been widely applied in environment and medicine applications. The superior performance of LaBr3:Ce detectors established them as excellent candidates for imaging and spectroscopy of gamma-rays. In this work, Compton cameras and hybrid cameras with a two-plane array of LaBr3:Ce detectors, one for the scattering and one for the absorbing detector arrays were designed and investigated. The feasibility of using LaBr3 in Compton cameras was evaluated with a bench top experiment in which two LaBr3:Ce detectors were arranged to mimic a Compton camera with one scattering and eight absorbing detectors. In the hybrid system the combination of the imaging methods of Compton and coded aperture cameras enables the system to cover the energy range of approximately 100 keV to a few MeV with good efficiency and angular resolution. The imaging performance of the hybrid imaging system was evaluated via Monte Carlo simulations. The image reconstruction algorithms of direct back-projections were applied for instant or real time imaging applications; this imaging system is capable of achieving an angular resolution of approximately 0.3 radians (17?). With image reconstruction algorithms of Expectation Maximized Likelihood, the image quality was improved to approximately 0.1 radians (or 6?). For medical applications in proton therapy, a Compton camera system to image the gamma-ray emission during treatment was designed and investigated. Gamma rays and X-rays emitted during treatment illustrate the energy deposition along the path of the proton beams and provide an opportunity for online dose verification. This Compton camera is designed to be capable of imaging gamma rays in 3D and is one of the candidates for imaging gamma emission during the treatment of proton therapy beside of the approach of positron emission tomography. In order to meet the requirement for spatial resolution of approximately 5 mm or less to meaningfully verify the dose via imaging gamma rays of 511 keV to 2 MeV, position sensing techniques with pixilated LaBr3 (Ce) crystal were applied in each detector. The pixilated LaBr3 (Ce) crystal was used in both the scattering and absorbing detectors. Image reconstruction algorithms of OS-EML were applied to obtain 3D images.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yuxin Feng.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Baciak, James.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024347:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024347/00001

Material Information

Title: Design and Evaluation of Gamma Imaging Systems of Compton and Hybrid Cameras
Physical Description: 1 online resource (168 p.)
Language: english
Creator: Feng, Yuxin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: coded, compton, gamma, hybrid, image, iterative, os, proton
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Systems for imaging and spectroscopy of gamma-ray emission have been widely applied in environment and medicine applications. The superior performance of LaBr3:Ce detectors established them as excellent candidates for imaging and spectroscopy of gamma-rays. In this work, Compton cameras and hybrid cameras with a two-plane array of LaBr3:Ce detectors, one for the scattering and one for the absorbing detector arrays were designed and investigated. The feasibility of using LaBr3 in Compton cameras was evaluated with a bench top experiment in which two LaBr3:Ce detectors were arranged to mimic a Compton camera with one scattering and eight absorbing detectors. In the hybrid system the combination of the imaging methods of Compton and coded aperture cameras enables the system to cover the energy range of approximately 100 keV to a few MeV with good efficiency and angular resolution. The imaging performance of the hybrid imaging system was evaluated via Monte Carlo simulations. The image reconstruction algorithms of direct back-projections were applied for instant or real time imaging applications; this imaging system is capable of achieving an angular resolution of approximately 0.3 radians (17?). With image reconstruction algorithms of Expectation Maximized Likelihood, the image quality was improved to approximately 0.1 radians (or 6?). For medical applications in proton therapy, a Compton camera system to image the gamma-ray emission during treatment was designed and investigated. Gamma rays and X-rays emitted during treatment illustrate the energy deposition along the path of the proton beams and provide an opportunity for online dose verification. This Compton camera is designed to be capable of imaging gamma rays in 3D and is one of the candidates for imaging gamma emission during the treatment of proton therapy beside of the approach of positron emission tomography. In order to meet the requirement for spatial resolution of approximately 5 mm or less to meaningfully verify the dose via imaging gamma rays of 511 keV to 2 MeV, position sensing techniques with pixilated LaBr3 (Ce) crystal were applied in each detector. The pixilated LaBr3 (Ce) crystal was used in both the scattering and absorbing detectors. Image reconstruction algorithms of OS-EML were applied to obtain 3D images.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Yuxin Feng.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Baciak, James.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024347:00001


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1 DESIGN AND EVALUATION OF GAMMA IMAGING SYSTEMS OF COMPTON AND HYBRID CAMERAS By YUXIN FENG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 Yuxin Feng

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3 To my wife, my son, and my parents.

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4 ACKNOWLEDGMENTS I would like to express my grat itude to those who have contri buted to this work. First, I would like to deeply thank my academic advisors, Professor James Edward Baciak, Jr for his support, excellent guidance, and encouragem ent to complete my Ph.D. I also would like to express my thanks to my dissert ation committee members: Professor Alireza Haghighat, Professor David R. Gilland, and Professor Bernard A. Mair f or their careful review of my research proposal, dissertation, and thoughtful suggestions. I would like to thank Professor Rebecca Detwiler for her helpful discussion and suggestions. In addition, I would like to tha nk the faculty in the Universi ty of Florida Proton Therapy Institute (UFPTI) collaboration for the Compton camera project: Professor Zuofeng Li for helpful discussion on proton therapy. I enjoyed the wonderful time with my former and current lab-ma tes: Lintereur, Azaree and Victoria Spring Cornelison who have read my ma nuscripts and provided helpful suggestions and corrections. Most importantly, I would like to thank my parents and all of my family for their unconditioned love, infinite supports, and enco uragement. Without them, I would never have chance to fulfill my dream. I also thank my son, Gabriel, who fills my life with fun, bright, and happy. Finally, I would like to express my gra titude to my wife, Qiong, whose love and support made this possible.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4LIST OF TABLES................................................................................................................. ..........7LIST OF FIGURES.........................................................................................................................8ABSTRACT...................................................................................................................................12 CHAP TER 1 INTENTION AND OBJECTIVES.........................................................................................142 COMPTON CAMERA...........................................................................................................22Compton Scattering............................................................................................................. ...25Efficiency................................................................................................................................27Angular Uncertainty............................................................................................................ ...31Geometrical Uncertainty................................................................................................. 31Energy Resolution........................................................................................................... 34Doppler Broadening........................................................................................................37Optimization of Geometries................................................................................................... 383 CODED APERTURES........................................................................................................... 40Aperture Patterns....................................................................................................................41Optimum and Simple Configurations..................................................................................... 45Geometries Design.............................................................................................................. ....47Active Coded Aperture Cameras............................................................................................ 494 IMAGE RECONSTRUCTION ALGORITHMS................................................................... 51The Simple Back-Projection Algorithm................................................................................. 51Filtered Back-Projection Algorithm....................................................................................... 54Iterative Approach............................................................................................................. .....57Decoding Coded Aperture Images.......................................................................................... 59LABR3 :CE SCINTILLAT ION DETECTOR................................................................................61Scintillation Mechanisms........................................................................................................62Spectroscopy with LaBr3:Ce Detectors..................................................................................63Timing Properties of LaBr3:Ce...............................................................................................65

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6 5 EXPERIMENT AND HARDWARE..................................................................................... 68LaBr3 Detector........................................................................................................................68Data Acquisition Hardware....................................................................................................69Experiment..............................................................................................................................72Spectroscopy...........................................................................................................................73Image......................................................................................................................................74Conclusions.............................................................................................................................786 DESIGNS AND SIMULATION OF HYBRID CAMERA................................................... 79Optimization of Compton Camera.......................................................................................... 80Coded Aperture........................................................................................................................83Prototype Hybrid Gamma Camera and Simulation................................................................ 85Discussion...............................................................................................................................93Conclusions.............................................................................................................................947 DESIGN OF A COMPTON IMAGING CAME RA FOR MEDICAL APPLICATIONS ..... 95Introduction................................................................................................................... ..........95High Resolution Compton Cameras for High Energy Photons.............................................. 97Compton Camera Approach...................................................................................................99Image Reconstruction...........................................................................................................103Results and Discussion......................................................................................................... 105Conclusions...........................................................................................................................1098 CONCLUSIONS & FUTURE WORKS.............................................................................. 111APPENDIX A CODES FOR HYBRID CAMERA IN GEANT.................................................................. 115B CODES FOR COMPTON CAMER IN GEANT................................................................. 132C AN EXAMPLE OF IMAGE RECONSTRUCTION CODES............................................. 148D AN EXAMPLE OF RESPONSE MATRIXES GENERATION CODES ...........................152LIST OF REFERENCES.............................................................................................................160BIOGRAPHICAL SKETCH.......................................................................................................168

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7 LIST OF TABLES Table page 5-1 Comparison of scin tillation crystals...................................................................................61

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8 LIST OF FIGURES Figure page 1-1 Structure of IBIS is shown in (a) that com bine coded mask on the top shown in (b) and a Compton imager composed of ISGRI and PICsIT on the bottom shown in (c)...... 172-2 The cross sections of photon interaction with LaBr3 as function of the energy of incident photon...................................................................................................................252-3 The Feynman diagram for the Compton scattering process.............................................. 262-4 Slab geometry used for numerical calculation................................................................... 282-5 For a photon at 662 keV, the probability of observing a single Compton scatter event as a function of the thickness of scattering detectors.........................................................302-6 The configuration of one scattering detector and one absorbing detector.........................322-7 Angular uncertainties as function of distance between the scattering and absorbing detectors...................................................................................................................... .......332-8 The energy spectrum of Cs-137 observed with LaBr3.......................................................352-9 The fitting of energy resolu tion as a function of energy.................................................... 352-10 Angular uncertainty included from the uncertainty of energy measurement.................... 362-11 Comparison between Doppl er broadening of Si and LaBr3 ...............................................362-12 Doppler broadening effects in angular uncertainty as f unction of scattering angle.......... 372-13 (a) The efficiency as a function of angul ar uncertainty, (b) angular uncertainty as a function of thickness.......................................................................................................... 383-1 The illustration of coded aperture cameras........................................................................ 403-2 Fresnel zones coded aperture on the left and random pinhole on the right ...................... 413-3 Schematic drawings of the two types of optimum' configurations discussed The left configuration is called 'cyclic.'........................................................................................... 463-4 Schematic drawing of the 'simple' configuration The sizes of the mask and detector are equal...................................................................................................................... .......473-5 SPI Mask is the tungsten alloy elem ents on top of the support structure ........................ 474-1 The geometry of a Compton scattering event.................................................................... 51

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9 4-2 Examples of two-hit event mapped onto hemisphere........................................................ 524-3 The image of a beam of photons one with energy of 662 keV at a polar angle of 30o and an azimuthal angle of =40o. .....................................................................................534-4 The two coincident hits in Compton camera..................................................................... 585-1 LaBr3 Crystal and its Hexagonal structure of LaBr3 .........................................................625-2 a) Binary kV and electron diffusion, and b) STE migration in the scintillation process................................................................................................................................635-3 The energy resolution at 662 keV as func tion of temperature on left and BrilanCe 380 detector on right.......................................................................................................... 645-4 The energy spectrum of 22Na............................................................................................ 645-5 The fitting of energy resolu tion as a function of energy.................................................... 655-6 Background spectrum measured with Br ilanCe 380 LaBr3 detector in 10 hours............. 665-7 Temperature dependence of LaBr3:5% Ce3+ scintillation decay curves. The solid curves are drawn to guide the eye and are not fitted curves [61]...................................... 666-1 The sketch of experimental setup...................................................................................... 686-2 232Th Spectra from LaBr3:Ce (upper) and NaI(Tl) (lower)...............................................696-3 The picture of NI PCI-MIO16E-1 card and block diagram..............................................706-4 SCB-68 printed circuit diagram......................................................................................... 716-5 The configuration mimicked in the expe riment with two detectors. The center detector was the primary scattering detector..................................................................... 736-6 The energy spectra of coincident events in the two detectors........................................... 746-7 The image reconstructed with back-projection method on the top and the zoomed in image on the bottom........................................................................................................... 756-8 The calculated efficiency map of the syst em as function of the original position of incident photons.................................................................................................................776-9 The reconstructed image with EML iterative method....................................................... 787-1 The configuration of the hybrid gamma camera used for evaluation with Monte Carlo simulation............................................................................................................... ..82

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10 7-3 The shadows of the scattering detectors on the 10 x 10 array of absorbing detectors when the cam era was centered at (0, 0, 0) a nd irradiated by a point source at (250cm, 0 cm, 1500 cm)................................................................................................................. .857-4 The image reconstructed by decoded the shading pattern on the bottom layer resolved with the detector array approach. On the top it was obtained from 2x104 events at 662 keV; on the bottom layer reso lved with the detector array approach form 2x105 events at 662 keV............................................................................................867-5 The image reconstructed by dec oded the shading pattern from 2x104 events at 100 keV.....................................................................................................................................877-6 The reconstructed image of the same tw o sources at 662 keV with back-projection method implemented in Compton camera approach......................................................... 877-7 The image reconstructed with back-pro jection method is on the left. The image on the right is obtained with filtered back-projection method................................................ 907-8 The efficiency of the hybrid camera as f unction of the original location of incident photons with 100 keV on XY plan at z= 1500 cm............................................................. 927-9 The reconstructed image of 100 keV photons from two-hit events................................... 928-1 The comparison the dose delivery with proton and photon beams. Adapted from http://www2.massgeneral.org/cancer/about/pr oviders/radiation/proton/principles.asp....968-2 The energy spectrum of the prompt gamma emission induced by 200 MeV proton beam in water.................................................................................................................. ...968-3 The configuration of the Compton camera is on the left. The sizes of detectors and the pixel are on the right....................................................................................................988-4 The efficiency of single Compton scatteri ng as function of thickness of the detector......998-5 The relative efficiency as f unction of scattering angle for LaBr3 Compton imaging system..............................................................................................................................1008-6 The angular uncertainty induced from positioning as function of the distance between detectors............................................................................................................. 1018-7 The angular uncertainty induced from un certainty in measurement of energies as function of scattering angle.............................................................................................. 1028-8 The angular uncertainty indu ced from Doppler broadening............................................1028-9 The point source and the Camera setup for simulation on the left. The point source reconstructed with OSEML from two-hit events on the right.........................................105

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11 8-10 The map of the Compton camera as func tion of the original location of incident photons on XY plan at z= 15 cm ..................................................................................... 1068-11 3-D image reconstruction of a point source with OSEML algorithm. The different slices correspond to different depths................................................................................1078-12 The converge seed of OSEML algorithm in creased with decreasing of the size of subset................................................................................................................................1078-13 The images reconstructed with OSEML algorithm for 2x107 incident photons at 511 keV on the left and 2.2 MeV on the right........................................................................ 1088-14 Two orthogonal Compton cameras with th e same configuration of Figure 8-4..............109

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12 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DESIGN AND EVALUATION OF GAMMA IMAGING SYSTEMS OF COMPTON AND HYBRID CAMERAS By Yuxin Feng May, 2009 Chair: James E. Baciak Major: Nuclear Engineering Sciences Systems for imaging and spectroscopy of gamm a-ray emission have been widely applied in environment and medicine applications. The superior performance of LaBr3:Ce detectors established them as excellent candidates for im aging and spectroscopy of gamma-rays. In this work, Compton cameras and hybrid cameras with a two-plane array of LaBr3:Ce detectors, one for the scattering and one for the absorbing dete ctor arrays were designed and investigated. The feasibility of using LaBr3 in Compton cameras was ev aluated with a bench top experiment in which two LaBr3:Ce detectors were arranged to mimic a Compton camera with one scattering and eight absorbing detectors. In the hybrid system the combination of the imaging methods of Compton and coded aperture cameras enables the system to cover the energy range of approximately 100 keV to a few MeV with good efficiency and angular reso lution. The imaging performance of the hybrid imaging system was evaluated via Monte Ca rlo simulations. The image reconstruction algorithms of direct back -projections were applie d for instant or real time imaging applications; this imaging system is capable of achieving an angular resolution of approximately 0.3 radians (17 ). With image reconstruction algorithms of Expectation Maximized Likelihood, the image quality was improved to approximately 0.1 radians (or 6o).

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13 For medical applications in proton thera py, a Compton camera system to image the gamma-ray emission during treatment was designed and investigated. Gamma rays and X-rays emitted during treatment illustrate the energy deposition along the path of the proton beams and provide an opportunity for online dose verification. This Compton camera is designed to be capable of imaging gamma rays in 3D and is one of the candidates for imaging gamma emission during the treatment of proton th erapy beside of the approach of positron emission tomography. In order to meet the requirement for spatial resolution of approximately 5 mm or less to meaningfully verify the dose via imaging gamm a rays of 511 keV to 2 MeV, position sensing techniques with pixilated LaBr3 (Ce) crystal were applied in each detector. The pixilated LaBr3 (Ce) crystal was used in both the scattering and absorbing de tectors. Image reconstruction algorithms of OS-EML were a pplied to obtain 3D images.

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14 CHAPTER 1 INTENTION AND OBJECTIVES Radiation detection and measurement have ma ny applications in nondestructive diagnosis, radiology, radiation therapy, etc. The Gamma camera is one of the most important instruments that has the capability of spatially resolving gamma-ray sources. Usually, gamma camera performance is evaluated based on spatial re solution, energy resolution, time resolution, and efficiency. However, a camera capable of performan ce that is suitable for all applications is not practical due to limitations such as technique and budget. Therefore, it is critical to design gamma cameras according to a particular application. Historically, imaging techniques employ stra ight-line ray optics. One example of an imaging technique that uses stra ight-line ray optics is the grazing incidence reflection approach, which has been applied to image low energy x-rays in ASCA and Chandra [ 1, 2]. However, this approach is infeasible for photons above approxi mately 20 keV due to the penetration power of higher energy gamma-rays. There are two alterna tive collimation approaches for imaging high energy photons: mechanical collimation and elect ronic collimation. Mech anical collimation involves integrating collimators w ith detectors to generate a spa tially deferential response [3]. These alternative techniques are referred to as multiplexing techniques. One common signature of multiplexing techniques is that the direction of the incoming rays is modulated (or coded) spatially or temporally before detection. The image of the source is reconstructed by decoding the observation after detection. Multiplexing techniques can be further divided in two classes: those based on temporal and those on spatial multiplexing [3]. A simple example of temporal multiplexing is the scanning collimator that was used in The Large Area Count er (LAC) of the Japanese X-ray satellite Ginga

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15 [4]. Examples of spatial multiplexing techniqu es are pinholes or multi-pinhole collimation in small animal SPECT, and coded apertures in Gamma-ray telescopes. The spatial multiplexing techniques can be divided into two subclasses. In the first subclass, two or more collimator grids, widely se parated, are placed in front of a detector. In the second subclass, one or more arrays of opaque a nd transparent elements are placed in front of a detector. It is difficult to achieve both high reso lution and high efficiency with the first subclass of collimators because the thick collimators and septals required to attenuate the gamma-rays lead to low efficiency and heavy weight. Instru ments of the second subclass are referred to as 'coded-aperture systems these systems improve e fficiency while preserving spatial resolution in the middle energy range (around a few hundreds of ke V). However, coded-aperture systems still suffer from the high penetration power of gamma-rays of a few MeV. The second approach, the electr onic collimator, utilizes the relationship between the direction of incident photons and the properties of events with multi-coincident hits. Two typical examples of electronic collimation systems are positron emission tomography (PET) and the Compton camera. In PET, a pair of coincident hits is at tributed to two 511 keV photons from an annihilation event that are emitted in opposite dir ections. The line connecting the positions of the pair indicates the location of annihilation. Th e second example of electr onic collimation is the Compton camera, in which the direction of an in cident photon is derived from the measurements of Compton scattering events. With the measured positions of Compton scattering and absorption of the scattered photon as well as the energies of the recoil electron and scattered photon, the direction of the incide nt photon can be constrained on th e surface of a cone. This is based on the Compton relationship between the scat tering angle and the ener gies of the incident and scattered photons. Compton camera and coded ap erture systems have been successfully used

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16 in gamma/x -ray astrophysics to resolve celestial sources from a few hundr ed keV to a few MeV. However, systems for nuclear medicine, industry, and homeland security applications are still being developed. Historically, high energy astrophysics is one of the areas where Compton cameras have been well developed. One of the typical examples of Compton telescopes us ed in astrophysics is the imaging Compton telescope (COMPTEL) on board the Compton Gamma-Ray Observatory (CGRO) [5]. The Compton telescope utilizes Compton events w ithin two layers of gamma-ray detectors to reconstruct an image of a gamma -ray source in the energy range 1 to 30 MeV. The telescope has a wide field of view of 60o, angular resolution of 1 3, and energy resolution of 5% 10%. COMPTEL accomplished a major break through in gamma-ray astronomy. Following the successful mission of CGRO, new Co mpton telescopes have been developed with more advanced techniques and higher levels of performance than that of COMPTEL, such as the Imager on Board Integral Satellite (IBIS). IBIS is composed of two detector layers (ISGRI and PICsIT) on board the International Gamma Ray Astrophysics Laboratory ( INTEGRAL) [6], as seen in Figure 1-1. In addition, IBIS is a hybrid cam era, integrat ing coded aperture and Compton imaging. IBIS was optimized for high-angular resolution (12), a wide field of view (FOV = 29x29), and moderate energy resolution point sour ce imaging. ISGRI is a low-energy detector made of CdTe, and it operates in the energy range of 15 keV 1 MeV. PICsIT is a high-energy detector made of CsI which operates in the energy range of 175 keV 10 MeV [6]. The hybrid design allows IBIS to achieve the desired performance level ove r a broad range of energy: 15 keV to 10 MeV. The hybrid design takes advantag e of higher efficiency and superior angular resolution of Compton cameras compared to conventional gamma cameras with mechanical collimators [6]

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17 Figure 1-1. Structure of IBIS is shown in (a) th at combine coded mask on the top shown in (b) and a Compton imager composed of ISGRI and PICsIT on the bottom shown in (c). Without mechanic collimation, the Compton cam era offers a wide field of view and high efficiency in the collection of photons with the capability of re solving directions of incident photons. Compton cameras have potential uses in nuclear medicine applications, such as SPCT and PET. In order to take advantage of hi gh efficiency, high resolution, and high energy coverage in Compton cameras, Todd and Nightingale in 1974 proposed the first Compton imaging system for the possible applications in nuclear medicine [7]. Since 1974, the developments in position sensing techniques ha ve provided opportunities for inventive designs such as that in Singhs group, CIMA Collabor ation, and others. Singhs group evaluated and designed a Compton camera with pixelated germ anium as the scattering detector and a conventional Anger camera as the absorbing dete ctor [8]. The scattering detector was built by Pehls group [9]. CIMA Colla boration designed and constructe d C-SPRINT Compton Camera by using a silicon pad as a scattering detector and NaI as an absorbi ng detector [8]. Furthermore, a benchtop module for very high resolution small animal Compton-PET was constructed with silicon pads and BGO, by CIMA Collaboration [8]. Another novel design of high resolution Compton enhanced PET was proposed by Zaidi a nd his colleagues [10]. Two key components in ISGRI PICsITPICsIT ISGRI a b c

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18 Zaidis design are a matrix of long scintillati on crystals and an array of hybrid of photon detectors which enhances the efficiency by r econstructing a significan t fraction of Compton events within the crystals. However, it is still necessary to optimize Compton imaging systems to the level of performance suitable for clinic appl ications due to limited efficiency in observing single Compton events and uncertainty in the de termination of scattering angle. In order to increase the efficiency in observing single Comp ton events, the approach of stacked multiple layers has been investigated a nd applied [11]. Tracking recoiled electrons in Compton scattering has also been explored as a method to reduce the uncertainty in the determination of the scattering angle [12]. For applications in industry, environment, and homeland security, imaging of gamma-rays with moderate angular resolution, about 0.3 radians, and high sensitivity is desired for the energy range of several hundred keV to a few MeV. The Compton camera is a possible approach due to its high efficiency and wide fi eld of view. For example, the Raging Compton Camera (RCC) was proposed and investigated by Martin and his co lleagues [13]. In RCC, a segmented HPGe with 4x4 planar array detectors was used as the scatte ring detector while an array of NaI scintillation detectors served as the absorbing detectors. Howeve r, the efficiency of this design is low and its size is too large. The progress in the techni ques for locating interacti ons in 3-D has brought new opportunities to improve the performance of Comp ton imaging systems. Resolved interaction locations and energy deposition at each interaction location allo ws observation of the Compton events (including recoil electrons and scattered photons in Compton scattering) within one detector which significantly increases the relativ e efficiency. For example, the Compton camera has been designed with the room temperature semiconductor CdZnTe with 3-D position sensing

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19 [14]. High energy resoluti on of 1-2% was achieved with single and double hit events. The angular resolution of th is system was about 12o after the image was reconstructed with Maximum Likelihood Expectation Maximization (MLEM) [15]. In order to increase the efficiency, a system with a 3-D array of CdZnTe detectors has been investigated [16]. Currently, the cost of this system is too high for wide spread application in industry, environment, and homeland security. However, a high efficiency and affordable system of gamma imaging is still in high demand. With newly developed large scintillation crystals of high atomic number, such as LaBr3, and optimized designs, an affordable system with high efficiency and moderate angular resolution is possible over a broa d range of energies. This dissertation provides a design for a hybrid gamma-ray imaging system that integrates Compton imaging and coded aperture imaging approaches to achieve high efficiency and mode rate angular resolution in a broad energy range from several hundred keV to a few MeV by using LaBr3 detectors. Without using expensive and complicated position sensing techniques, LaBr3 scintillation dete ctors were selected as both scattering and absorbing detectors. LaBr3 scintillation detectors have been recently develpoed with better energy resolution and higher efficiency than NaI dete ctors with the same geometry. The fast decay of scintillation in LaBr3 crystals reduces dead time and random coincident events in Compton camera applications. The good energy resolution of the detectors is appreciated not only for the identification of isotopes, but also for improving the angular resolu tion of the system. The angular uncertainty in a Compton camera depends on the precision of the determination of the in teraction position and the energy deposition. LaBr3 (Ce) scintillation detectors have been fine-turned to achieve energy resolution of less than 3% at 662 keV [17] and fast decay ( 16 ns) [18]. These attributes have

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20 made it a good candidate for both the scattering and absorbing detectors in Compton imaging systems [19]. In the designed hybrid gamma camera presente d in this work, events with two coincident hits are used for Compton imaging while single hit events are utilized for coded aperture imaging. A two hit event is defined as any two of the LaBr3 detectors being triggered coincidently within the time resolution. Th e camera has a two-plane configuration and by changing the sizes of the LaBr3 detectors and the distance between the detectors, the camera can achieve the highest efficiency fo r a given angular uncertainty or the smallest angular uncertainty for a given efficiency. The probability of a si ngle Compton scattering, an d angular uncertainty, are functions of the thickness of the LaBr3 crystals, the distance between the scattering and absorption planes, and the spacing between the de tectors, which are calculated numerically. In this dissertation, the principles of the Co mpton imaging system are reviewed in Chapter 2. Optimization method for the Compton cameras is also presented also in Chapter 2. Coded aperture imaging theory is reviewed Chapter 3. The energy resolution and timing properties of LaBr3 detectors are reviewed in Ch apter 4, where the results of sp ectroscopy of several isotopes are also presented. The image reconstruction algorithms are reviewed in Chapter 5. The experimental setup and hardware used are summarized in Chap ter 6. A prototype and simple simulation of the hybrid Compton and coded apertu re imaging system is presented in Chapter 7 where the performance of the designed camera wa s evaluated based on Monte Carlo simulations in Geant4. In Chapter 8 a novel design of Comp ton cameras is presented which achieved a high spatial resolution suitable for medical appli cations, such as imaging gamma emission during photon therapy treatment. The lessons learned and the evaluations of this hybrid imaging system

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21 are summarized in Chapter 8. In Chapter 9 the future work and major challenges are briefly discussed.

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22 CHAPTER 2 COMPTON CAMERA Detection of gamma-rays is an important tool in identifying their emitters because they carry the finger prints from nuclei, characterist ic energy lines given off in nuclear decay or photo-nuclear reactions. Also, gamm a-rays generally have higher en ergies than characteristic xrays, and thus are more observable through shielding barriers. Emission imaging systems utilizing gamma-ray imaging have both high angular resolution and high efficiency, and are in great demand for medical, environmental, and ho meland security applications to locate and identify radiation sources. Imaging systems with mechanical collimators, such as pinholes in small animal SPECT, parallel holes in SPECT, and coded apertures in telescopes, have been well developed for imaging X/ -ray emissions. However, it is difficult to infer the directions of incident gamma-rays as compared to x-rays with these systems, due to the higher energy and lower modulation levels of gamma-rays as compared to lower energy X -rays in these systems.. For these mechanical collimation systems, the image quality and efficiency decrease with increasing gamma ray energy. In order to image high energy gamma rays with high efficiency and angular resolution, electronic collimation methods have been develope d, such as timing coincidence techniques used in pair emission tomography (PET) systems and Compton camera systems. In Compton cameras, the measurement of the position and deposite d energy of two or more coincident interactions constrain the sour ce onto a conic surface [20]. Since there is no attenuation material between source and detect ors, electronic collimation systems have been expected to achieve a higher effi ciency and superior angular reso lution compared to conventional gamma cameras with mechanical collimators in the energy range of a few hundred keV to a few MeV. The Compton imaging approach has been us ed extensively for applications of astrophysics

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23 [21] and nuclear medicine [22, 23, and 24]. In these the application, the detector system geometries are optimized to address the issues of limited efficiency in observing single Compton events and uncertainty in determinati on of the scattering angle, e.g. [25]. This angular uncertainty depends on the prec ision of the interac tion locations and the deposited energy measurements. Therefore, dete ctors with high resolution in energy and space are needed to build Compton imaging sy stems with high angular resolution. LaBr3(Ce) scintillator crystals provide a good energy re solution of less than 3% at 662 keV [26]. Additionally, with its higher atomic numb er and density as compared to Si, LaBr3 may allow us to build higher efficiency Compton cameras A narrow coincident time-window is also achievable because of its short deca y time (16 ns) [27]. Above all, LaBr3(Ce) is a good candidate for both the scattering and absorbing detectors for Compton cameras. Figure 2-1. Illustration of the pr inciple of a Compton Camera In this dissertation, we inves tigate the geometries of a Co mpton imaging system with a two-plane configuration; paramete rs include the sizes of detector the distance between scattering and absorbing planes, and the sp acing between detectors in the same plane. We generated a database of LaBr3 detector configurations to optimize th e efficiency and angular uncertainty for Homeland Security and medical phys ics applications, based on the numerical calculations of the 1 eE21 e E E

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24 probabilities of single Compton scattering and the angular uncertainty induced from uncertainties in interaction location, energy measurement, and Doppler broadening. In this Chapter, we investigate the impact of the geometry, confi guration, and detection material on the efficiency and angular uncertainty of Compton camera, based on the principles of a Compton camera, as illustrated in Figure 2-1 an d stated in equations 2.1 and 2.2. The principle of Compton imaging is base d on the Compton relationship 0 1 0 10 0112 0 2 0 (2.1) 1(1cos()) 11 cos()1 (2.2)eE E E mc mc EE EEE where E 0 is the energy of the incident photon; E 1 is the energy of the scattered photon; Ee1 is the energy of the recoil electron; is the scattering angle with re spect to the direction of the incident photon, m0 is the rest mass of the electron; c is the speed of light. Based on eq. (2.2) the direction of an incident photon can be constrained on the surface of a cone if 1 E and 1e E are measured. The axis of the cone is indicated by a line extended from the location of Compton scattering to the position of the first interacti on of the scattered photon. The half angle of the cone is the scattering angle The efficiency of the Compton camera is dete rmined by the efficiency of observing single Compton events; this is the probability of a Compton scattering event and the chance of resolving this event. The probability of the Compton scattering event depends upon the cross section of Compton scattering in materials and is a function of the ener gies of incident and scattered photons and the scatteri ng angle. In general, Compton im aging is an efficient approach

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25 for imaging photons above a few hundred keV to a few MeV, the energy region where Compton scattering is dominant for La Br, as shown in Figure 2-2. Figure 2-2. The cross sections of photon interaction with LaBr3 as function of the energy of incident photon. (This plot adapted from http://physics.nist.gov/PhysRe fData/Xcom/Text/XCOM.html) Compton Scattering An illustration of the interaction probabilities in units of mass attenuation of primary photons interactions in LaBr3 are shown in Figure 2-2. The figure, from the NIST XCOM website[106], shows that the primary photon in teractions, i.e. photoelectric absorption, incoherent scattering, and pair production, are dominant in the energy ranges E < 200 keV, 300

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26 keV < E < 7 MeV, and E > 8 MeV, respectivel y. The Compton scattering cross section and attenuation coefficients shown here are deri ved from the Klein-Nishina Equation [28]: 0 11 0102 2 2 0 2 0 2 0sin() (2.3) 2 E EE r d dEEE e r mc where e is the charge of an electron a nd m0 is the rest mass of the electron, is the photon scattering angle, and 0E 1E are energies of the incident and scattered photons as stated above. This formula and the Compton relationship in eq (2.1) use the free elec tron approximation (the photon scatters from a free electron) where th e scattering angle and photon energy uniquely determine the energy of the scatte red photon and recoil electron. Ho wever, the effects of atomic structure are needed for low phot on energies and large scattering angles, conditions where the electron binding energy is comparable to th e kinetic energy imparted to it by the photon. For scattering with an atomic electron, the cross section is a function of the initial momentum of the electron and momentum exchanged through binding effects, as seen in the Feynman diagram for the Compton s cattering process in Figure 2-3. Figure 2-3. The Feynman diagram for the Compton scattering process. The circle in the line of the incoming atom A indicates that the electron is initially bound to the atom and represents the probability that the electron with a four-momentum(,)ee p Ep

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27 interacts with the incoming photon with a four-momentum 00(,) KEp into a final state e given by (,)ee p Ep and 11(,)KEp If the binding energy is ne glected and the electron is considered to be initially at rest, the cross sec tion for the process is given by the Klein-Nishina formula. However, the more accurate expressi on for Compton scattering from a bound atomic electron, represented with the double di fferential cross se ction, is [29]: 1 102 2 2 1/2 2 01111 1 2 () (2.4) 2zzE r RR pJ p EEqRRRRRR In what follows we use na tural units, i.e., c=1 and =1. Where is the solid angle ( ); ()()zxyJpdpdpp is the Compton profile; () p is the wave function of bound electron; 01 01222cos() qEEEE is the modulus of momentum transfer vector 12qpp ; 11 01 1(1cos()zpq E EEE p qq is the projection of the initial momentum of the electron on the direction momentum transfer q ; and 01 0 012cos() 1, 1cos().zEE REq RREE q Extensive tables of atomic and shell-wise Compton profiles for al l elements have been calculated with the Hartree-Fock approximation by Biggs et al [ 30]. In Compton scattering with a bound electron, the energy of scattered photon and el ectron are no longer uniquely determ ined by the energy of initial photon and the scattering angle. The energy of scattering photons is a distribution around the energy given by Compton relationship in eq. (2.1). Efficiency The efficiency of a Compton camera is determined by the probability of observing single Compton scattering. For this work, this probability was calculate d based on simple slab geometry of a pencil beam irra diating the center of th e scattering slab, as shown in Figure 2-4.

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28 This simplified case was used to illustrate the effect of detector thickness and distance between scattering and absorbing planes on the efficiency of observing single Compton scattering events. For a given geometry, the efficiency of the Compton imaging system depends on the properties of the detector material used for the scatterer and absorber. With a low atomic number, silicon is a desirable material for the sc attering layer in a Compton imaging system with double sided strip detectors, due to its good energy resolution, sm all Doppler broadening effect, and capability for position sensing [23, 31]. It is true that the photoelect ric process is dominant over a broader energy-range for higher Z materials, such as LaBr3, compared with lower Z materials, such as Si. However, in th e energy range above a few hundred keV, LaBr3 detectors may have a higher probability for observing single Compton scatte ring events than Si detectors with the same thickness, due to th e higher Z and higher density of LaBr3 compared with that of Si [24]. Furthermore, at high energies, the angu lar uncertainty induced from Doppler broadening effects is less significant compared with those induced from the uncertainties in position and energy. Therefore, the high Z LaBr3:Ce crystal is still a good ca ndidate for the scattering detector. H T1 T2 E 0 Figure 2-4. Slab geometry us ed for numerical calculation. E 0 E L

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29 The formulas used to calculate the proba bilities for observing a single Compton scattering event in a scatter (eq.1) and ab sorption of a scattered photon in the absorber (eq.2) are below. 0 w() ()() cos() () or 12(,,,) (1) iEx inch SCiaescape ETx escape EDd PTxEeNP ddE e P eothers () cos() 000(,,)(1)sin() (2) (,) (,,,)(,,) (3)j i DET Absj T ijSCiAbsjPETe EffTTdEdxdPTxEPET where E0 is the energy of incident photon; inchd ddE is the double differential cross section for incoherent scattering; arctan() 1 R Tx i; arctan() 2 R x ; is the attenuation coefficient; PSC is the probability of single Compton scattering in the scattering plane; Pescape is the probability of escape from the scattering detector after a single Compton scattering event, and PAbs is the probability of absorption in the absorbing plane. Eff (Ti,Tj) is the efficiency of the detector system for a single Compton event that s cattered on detector i and absorbed in detector j; Ti and Tj are the thickness of scattering i and absorbi ng detectors j, respectively; R is the radius of the detector; D is solid angle of the absorbing detect or subtended by the scattering detector; Dw is the distance between the scat tering location to a point on the wall of a scattering detector where the scattered photon escaped; E is the en ergy of the scattered photon; and x is the depth where scattering occurred. As a result of the competition between probabili ties of Compton scattering and attenuation, a maximum probability of single Compton scattering occurred at a smaller thickness in LaBr3 than in Si, as seen in Figure 2-5a and 2-5b. Figure 2-5a shows that for a photon with energy of

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30 662 keV the probability of single Compton scattering is higher for LaBr3 than for Si detectors with the same thickness, below a turning point of approximately 2 cm. For the ratio of the probability (a) (b) Figure 2-5. For a photon at 662 keV, the probabil ity of observing a single Compton scatter event as a function of the thickness of scatteri ng detectors (a); rati o of single Compton scattering probability to total interaction probability as function of the thickness (b). The range of scattering angle 0< <180o corresponds to all possible directions; <40o and >130o are forward and backward directions, respectively. 0 1 2 3 4 5 10-3 10-2 10-1 100 Thickness (cm) Without Interaction 0 < < 18 <40o Silicon LaB r 3(Ce)>130o Single Compton Scattering Probability (PSC) 0 1 2 3 4 5 10-3 10-2 10-1 100 Thickness (cm) LaBr3(Ce) Silicon0< <180o <40o>130 Ratio of Single Compton Scattering

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31 or single Compton scattering a nd the total interaction probabi lity, the turning point is around 1.25 cm, as seen in Figure 2-5b. The figures also show that the forward single Compton scattering is dominant in a simp le slab geometry case. Also, the figures show that the turning point of detector thickness incr eases with the energy of the in cident photon. Since the energy range of interest for Homeland Security and me dical imaging applications extends from a few hundred keV to a few MeV, we evaluated our de sign at the Cs-137 source energy of 662 keV as this corresponded to approximately the middle of the energy range. In order to illustrate the depende nce of efficiency on the scatte ring angle, the efficiency for forward scattering within 40 and backward scat tering greater than 130 were calculated and plotted in Figure 2 as well. This shows that the efficiency is about one order of magnitude higher for forward scattering than for backward. Angular Uncertainty In addition to the efficiency, the angular resolution is another important parameter in evaluating the performance of Compton cameras and is closely related to the uncertainty in the determination of the scattering angle. The angul ar uncertainty of a Compton imaging system has three primary components. Geometrical Uncertainty One is the uncertainty in the locations of the initial Compton scattering event in the scatter detector, and the subsequent sca tter in the absorber detector [32], as seen in Figure 2-7.

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32 Figure 2-6. The configuration of one scatte ring detector and one absorbing detector. 222 2 2 12 2 1 2 2 2 2 2 (2.9) 1 (2.10) (sin()) 1 (2.11) (sin())SA SS AArBB R rB R 11 22; ; SoSo A SAS R rrRrr R rrRrr 1 2 121 212 222cos(), cos(), ()()(),xxyyzzR R Bnn Bnn PQPQPQPQ where is the uncertainty of the scattering angle determined by the simple back projection ; Sr and Arare the uncertainty vectors in scattering and absorbing de tectors, respectively; and S and A are the angular uncerta inties contributed from scatteri ng and absorbing detectors. o rSr Ar 1 R 2 R Z X Y

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33 In our calculations, we assumed that the source is infinitely far and that the position of each interaction is the center of a detector, which introduced a dependence of the angular uncertainty on the detector geometry, as shown below: 222221 ()2cos()sin()2 (2.12) rzr H where H and L are the vertical and lateral distance s between a scattere r and an absorber respectively; r and z are the radius and thickness of each cr ystal in a detector respectively; and is the scattering angle. For given geometries of r = 2.5 cm and z =1.5 cm, the angular uncertainty as function of H is shown in Figure 2-7. According to Figure 2-7, a design with a 20 cm separation be tween scattering and absorbing detectors can achieve 0.3 radians angular uncertainty, fo r the given detector dimensions stated below. 0 20 40 60 80 100 120 140 160 180 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Scattering angle (degree)Angular uncertainty (radian) H = 100 cm H = 10 cm LaBr3 Figure 2-7. Angular uncertainties as function of distance between the scattering and absorbing detectors.

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34 Energy Resolution The second contribution to the angular resolu tion is the uncertain ty in measuring the deposited energy in each detect or. If the uncertainties in the measured energy deposition were Ee1 and Ee2 in the scattering and absorbing detectors respectively, the induced uncertainty in determination of the scattering angle is described below: where E 0 and E 1 are the energies of incident and scattered photons respectively, and m0 is the rest mass of an electron. In our investigation we used the en ergy resolution as the function of energy that was obtained from ca libration of a BrilLanCe 380 LaBr3(Ce) detector produced by SAINT-GOBAIN company. The angul ar uncertainty induced is s hown in Figure 2-8. It shows that angular uncertainty due to energy measurement decreases with increasing photon energy. However, it should be noted that eq. (5) is valid only for the case where the scattered photon is absorbed in the second detector. For an inci dent photon with unknown ener gy, the escape of the scattered photon from the second de tector results in artifacts in the back projection image, but these could potentially be eliminated if the system response was correctly modeled using the iterative image reconstruction approach as show n in following Chapters where the iterative approach was applied. The absorbing efficiency of the scattered photon was evaluated based on the photon peak efficiency of the twohit events in th e section above. In our investigation we derived out an empirical formula to represent the energy resolution as a function of energy based on the spectroscopy of calibrated sources, as shown below: 8.82830.13270.0195 () (2.14) EEEkeV Where, E is the energy of an incident photon. An example of the observed energy spectrum of Cs-137 is shown in Figure 2-8, the fitting of this formula with the measurement is shown in 0 1 02 2 2 221/2 0 12 221, (5) sineeE mc EE EE

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35 Figure 2-9. Combining eq.(2.13) with eq.(2.14), we calculated the contribution of the energy uncertainty to the angular uncertainty, which is shown in Figure 210. According to this figure, the angular uncertainty of 0.3 is achievable with our current energy resolution, for photons with energies above 500 keV and at scatteri ng angles above ~10 and below 150 0 200 400 600 800 1000 1200 1400 1600 0 200 400 600 800 1000 1200 1400 1600 1800 Energy (keV)Counts/channel Cs-137 2.82% Figure 2-8. The energy spectrum of Cs-137 observed with LaBr3. 0 200 400 600 800 1000 1200 1400 5 10 15 20 25 30 35 Energy (keV)Energy resolution (keV) Fitting Measured Figure 2-9. The fitting of energy re solution as a function of energy.

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36 0 50 100 150 200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Scattering Angle (degree)Angular uncertainty (radian) 100 keV 2000 keV 662 keV 500 keV 300 keV Figure 2-10. Angular uncertainty included from the uncertain ty of energy measurement. 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Deposited Energy (MeV)Normalized Recurrency E0 = 662 keV Sita = 81o LaBr3 Si Figure 2-11. Comparison between Doppler broadening of Si and LaBr3 E0 = 662 keV = 81o

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37 Doppler Broadening The third contribution to the angular uncertainty is the Doppler broadening caused by the uncertainty in the energies and momentums of the bound electrons in at oms. As previously mentioned, due to these uncertainties, there is no longer a one-to-one relationship between the kinetic energy of the recoil electron and the scat tering angle, for the sc attered photon of a given energy, but rather a broa dening around the energy, as seen in Figure 2-11. Doppler broadening effects in Compton scatteri ng therefore lead to uncertainty in the scattering angle. Based on the Compton profile calculated with the Hartree-Fock method [30], the angular uncertainty attributed to D oppler broadening was obtained based on FWHM calculations of Doppl er profiles of LaBr3, NaI, and Si. This introduced an intrinsic limitation on the angular uncertainty of a Compton image syst em, as illustrated in Figure2-12, which also shows that the angular uncertainty of Doppler broadening is less significant for Si than for LaBr3 and NaI. 0 50 100 150 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 (degree)Angular uncertainty (radian) Figure 2-12. Doppler broadening effects in angular uncertain ty as function of scattering angle.

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38 The results show that an angular resolution of ~ 0.3 radians is achievable for scattering angles above 30 and below 160s. For applicat ions requiring high angular resolution, it is important to keep in mind that there is an angular uncertainty over the limit of ~ 0.05 radians due to the Doppler broadening effect. Scattering angles between 40o and 140o are a desired angular range for detection the scattered photons in Compton camer as for high angular resolution applications. According to Figure 2-6, Compton scattering efficiency is highest for scattering angles of 0o to 90o. 0 1 2 3 4 5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Thickness of the first detector (cm)Angular uncertainty of geometry (radian) H=100 cm dH= 4 cm E0 = 662 keV 0 0.2 0.4 0.6 0.8 0 0.02 0.04 0.06 0.08 0.1 0.12 Angular uncertainty of geometry (radian)Efficiency of Compton camera E0 = 662 keV H= 58 cm H=100 cm Figure 2-13. (a) The efficiency as a function of angular uncertainty, (b) a ngular uncertainty as a function of thickness. Optimization of Geometries To optimize the efficiency of a Compton imag ing system for a given angular resolution, we studied the relationships between the angular uncertainty, efficiency, th ickness of the crystal, and the distance separating the scattering and abso rbing detectors, using numerical calculations, as shown in Figure 2-13 (a), and (b) that were obtained by averag ing the scattering angles over 0o to 90o with the weighting of effici ency. The uncertainty of pos ition in our method as described depends on the geometry of the crystal in each detector and distances be tween the detectors in the array, which also leads to uncertainty in the derived scattering angle. As the crystal a b

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39 dimensions also affect the efficiency of the cam era, a geometrical optimization balancing the two effects was needed. In general, a larger distance between the sc attering and absorbing detectors reduces the angular uncertainty. However, in creasing the distances between dete ctors also decreases the solid angle of the absorber subtended by the scattere r, and decreases Compton efficiency. These effects must be balanced in optimization of a design. In my dissertation, I will present the deta iled design of a Compton camera and further investigate the optimization of the angular uncertainty and effi ciency under the constraints of coded aperture imaging implementation.

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40 CHAPTER 3 CODED APERTURES A coded aperture imaging camera is composed of a coded aperture and a position-sensitive detector. The coded aperture encodes the directio ns of incident photons. The image of incident photons is reconstructed via a decoding process. The coded aperture is composed of 'mask elements' that usually have an equal size and are distributed in a pre-determined pattern, which is placed on a regular grid. The position-sensitive dete ctor has a spatial resolu tion that is sufficient to resolve the mask-pattern grid. Figure 3-1. The illustration of coded aperture cameras. In the coded aperture camera, photons from a particular direction project the mask on the detector; this projection has the same coding as the mask pattern, but is shifted relative to the central position over a distance uniquely correspo nding to this direction of the photons, as seen in Figure 3-1. The detector accumulates the sum of a number of shifted mask patterns. Each shift of the mask patterns encodes th e position and its streng th of the pattern represents the source intensity at that specific position. The detector may detect photons in cident from any position within the field of view. The accumulated distri bution of hits may be decoded to an image by determining the shift and the strength of every possible mask pattern. Proper performance of a coded aperture camera requires that every view ed position is encoded uniquely on the detector

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41 (that is, each source pos ition creates a unique shadow pattern on the detectors). An important difference to direct-imaging systems is the fact that Poisson noise from an y source in the field of view is, in principle, induced at any other position in the reconstructed image. The imaging quality of the camera is closely related to the type of mask pattern, the optical design of the camera, the spatial resolution of the detector and the decoding (reconstruction) algorithms. Aperture Patterns In order to achieve a desired imaging performa nce, the mask pattern usually satisfies two conditions. First, the autocorre lation function (ACF) of the ma sk pattern should be a delta function. Second, the signal-to-noise ratio of a coded source in fiel d of view should be as high as possible. Historically, two types of mask patterns were proposed: a pattern of Fresnel zones [33] and the random pinhole pattern [ 34, 35], as seen in Figure 3-2. The random pinhole pattern was proposed as an extension of a pinhole camera. Th e pinhole camera has ideal imaging properties Figure 3-2. Fresnel zones coded aperture on the left and random pinhole on the right. with respect to its ACF, but delivers a poor signalto-noise ratio because of the small diameter of the pinhole necessary to achieve a good angular resolution. In the random pinhole camera, the open area of the plate is increased by randomly placing many duplicate pinholes in the plate. By

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42 keeping the diameter of holes sm all, the angular resolution is pr eserved. The random character is necessary to achieve a -like ACF. However, both Fresnel zone and random pi nhole mask patterns are not ideal and their ACFs do not have perfectly flat sidelobes that may introduce artifact structure in decoded images. Later, ideal families of patterns were f ound that are based on cyclic difference sets [36, 37]. A cyclic difference set D, defined by the parame ters n, k and z, is a collection of k integer numbers {I1, I2,...,Ik} with values of 0i I n such that for any 0 J (mod n) the congruence ij I IJ (mod n) has exactly z solution pairs (,)ij I I within D [38]. An example of a cyclic difference set D with n=7, k=4 and z=2 is the collection {0, 1, 2, 4}. Cyclic difference sets can be represented by a binary sequence ai (i=0, ..., n-1) with ai=1 if i is a member of D and ai=0 otherwise. In this example, ai is given by 1110100. ai in turn can stand for the discredited mask pattern, assigning a transparent element to ai=1 and an opaque one to ai=0. The cyclic autocorrelation cl of ai is: 1 mod(,) 0 if mod(,) 0 (3.1) (1) if mod(,) 0 1n liiln ikl n caa kk zl n n Ii between 0 and n such that for any J 0 (mod n) the congruence Ii Ij=J (mod n) has exactly z solution pairs (Ii, Ij) within D. A mask pattern based on ai consequently satisfies condition 1. ai has the characteristic that every difference i j between a pair of ai, aj = 1 is equally sampled and therefore th ese arrays are also called Unif ormly Redundant Arrays (URA) [36]. From the ACF, it can be anticip ated that it is advantageous with respect to condition 2 to have a difference between k and z that is as large as possible, for k determines the signal and z the background level (and its noise). Additionally, the optimum ope n fraction of the mask pattern

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43 is also dependent on specific conditions concer ning the field of view. The maximum difference is reached if n = 4t-1, k = 2t-1 and z = t-1 if t is integer. These cycl ic difference sets are called Hadamard difference sets [38,39] and can be classified into at least three types, according to the value of n: 1) Quadratic residue sets: n is prime (the members of this set are given by the squares, modulo n, of the first (n+1)/2 integers); 2) Twin prime sets: n = p(p+2) for integer p, p and p+2 being prime; 3) Pseudo-noise sets: n = 2m -1(m>1 is integer). Some Hadamard difference sets may belong to mo re than one class, th e existence of a set with a value for n given by a class is guaranteed. The above example is a quadratic residue set as well as a pseudo-noise set. A charac teristic for Hadamard sets is th at k = (n-1)/2, i.e. for large n the mask pattern is about half open. The cyclic autocorrelation then is: 1 mod(,) 01 if mod(,) 0 2 (3.2) 3 if mod(,) 0 4n liiln in ln caa n ln Another collection of cyclic difference sets are the Singer sets, and are characterized by n= (t m+1-1)/(t-1), k=(t m-1)/(t-1) and z=(t m-1-1)/(t-1) where t is a prime power. The equivalent mask pattern will have smaller open fractions than those based on Hadamard sets; for t>>1 the open fraction approximates 1/t One way to construct a pseudo-noise Hada mard set is the fo llowing [40]: if p(0),...,p(m-1) are the factors of an irreducib le polynomial of order m ( p(i) is 0 or 1) then ai is defined by a shift register algorithm: 1 0() (0,..., 2-2) mod(2) (3.3)m m imij japjai

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44 The first m values of this recursive relation, a0,..., am-1, can be chosen arbitrarily; a different choice merely results in a cyclic shift of ai. If n can be factorized in a product of two integers (n = p q ), it is possible to construct a two-dimensional array aij (i=0,...,p-1; j=0,...,q-1) from the URA ai (i=0,...n-1). The arranged mask pattern is thus called the 'basic pattern'. The ordering of ai in two dimensions should be such that the autocorrelation char acteristic is preserved. This mean s that in a suitable extension of the basic p q pattern, any p q section should be orthogonal to any other p q section. A characteristic of a URA ai is that any array s ia formed from ai by applying a cyclic shift to its elements (mod(,) s iisnaa) is again a URA which is orthogonal to ai. Therefore, the autocorrelation characteristic of the expanded aij is fulfilled if every p q section is a cyclic shift of the basic pattern. The pseudo-noise arrays have the convenient pr operty that they can easily be wrapped in almost a square of n>>1: if m is even, n can be written as 2221(21)(21)mm mn such that p and q only differ by 2. There are several practical prob lems in the manufacturing of two-dimensional mask plates. In the traditional x-ray range ( up to 120 keV), an opaque mask element may be completely surrounded by transparent elements. For photon energies above 100 keV, this issue of mechanical support is less constraining because tr ansparent materials can easily be found at these energies. A practical problem of masks occurs in applications beyond a few hundred keV: the opaque elements generally need to be very thic k. Mask element sizes cannot be small because the mask itself would act as a narrow-field collimator. This is not a serious problem in our design

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45 because thinner opaque may be used and partially opaque events can be eliminated based on the records of hits on the front ap erture (acting as an active mask) or scatterer. The autocorrelation characteris tic remains valid only if the coding is performed by the use of a complete cycle of a basic pattern. As soon as the coding is partial, systematic noise will emerge in the side-lobes of the autocorrelation functi on. In order to be able to record a full basic pattern for every position in the observed fiel d of view, we need to design an optical configuration of mask and detector. The optical design of a coded mask camera involves the sizes of the mask, the mask elements, and the det ector, as well as the number of basic patterns used in the mask, the distance between mask and detector and the size and placement of an optional collimator. The design should also provid e optimal angular resolution and a wide field of view. Optimum and Simple Configurations From the previous section, for ideal imaging properties, it is n ecessary to record a complete cycle of the basic pattern for every pos ition in the observed field-of-view (FOV). This can be accomplished by configuring the mask and detector in one of the following two ways, as illustrated in Figure 3-3 [41]. In one configuration, the mask consists of one p q basic pattern, while the detector has a size of 2121 p q mask elements. By the implementation of a collimator in front of the detector, the observed FOV is restricted to those positions in the FOV from where the mask is completely projected on th e detector, as seen in the right of Figure 3-3. In the second configuration, the mask consists of a mosaic of almost 22 cycles of the basic pattern 2121 p q mask elements, while the detector is as large as one basic pattern, as seen in the left of Figure 3-3. A collimator is a pplied to restrict the FOV of any position on the

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46 detector to the region from which one complete cycle of the basic patte rn is projected on the detector. This type of configura tion often is called 'cyclic' because of the nature of the mask. Figure 3-3. Schematic drawings of the two types of 'optimum' conf igurations discussed. The left configuration is called 'cyclic.' Both types of collimators deliver a pyramidical-to-zero response function to the collecting detector area over the observed FOV. In practice, for high sensitivity applic ations, the cyclic type is usually the choice based on the argument of preservation/maximization of the collecting area. There is also an alternative c onfiguration that is the so calle d simple or 'box-type' system in which full coding is relaxed, as seen in Figur e 3-4 [42]. The detector has the same size as the mask, which consists of one basic pattern. No co llimator is then needed on the detector. To prevent photons that do not pass th e mask from entering the detector, shielding is used. In this simple system only the on-axis position is coded w ith the full basic pattern (the fully-coded field of view (FCFV)), the remainder of the FOV is partially coded (partia lly-coded field of view PCFV). The off-axis sources will introduce false peaks.

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47 Geometries Design The mask of this design follows the configuratio n of the cyclic type in which the mask has a larger size than that of detect or. In order to increase the FCFV three duplicated patterns are arranged as seen an example in Figure 3-5. Figure 3-4. Schematic drawing of the 'simple' configuration. The sizes of the mask and detector are equal. Figure 3-5. SPI Mask is the tungsten alloy elements on top of the support structure [41].

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48 The field of view and geometri c resolution are related to the mask and detector parameters. The field of view is function of the size of detector (dd) and distances of source to the aperture (a) and the aperture to the detector (b), as seen below (3.4) 1 1dd FOV m b m a The angular field of view is defied as from its axis and: arctan (3.5) 2 FOV a In case of a cyclic system, this becomes: arctan (3.6) 2dd b The angular resolution is most commonly defined as the dist ance that must separate two sources in the object plane so that their images ar e still perceived as two separate points. Usually the two sources are resolvable if they are separa ted by at least one full wi dth at half maximum of the point spread function (PSF). In the case of no modulation of the aperture transparency, either complete transparency or opacity, the FWHM on the detector plane is the same as the size of magnified hole by the factor m. Therefore the FWHM on the object plane is: (3.7) 1m gmmmp mab app bmb where m p is the size of an aperture hole. That indi cates that the best resolution of a coded aperture is the size of an aperture. Th e angular resolution can be defined as arctanarctan (3.8)g mp m ab

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49 Active Coded Aperture Cameras Based on the knowledge reviewed above, we propos e a simple coded aperture camera that utilizes active scattering detector s in the front layer as the co ded aperture and the absorbing detectors in the rear layer as the position sensitive detector. An example of the mask design can be adapted from the design of coded aperture used in SPI coded aperture mask on board INTEGRAL[41], as seen in Figure 3-6. In comparison with conventional coded apertu re designs, our design uses an active coded aperture that has an advantage in utilizing the recorded photon interactions in the aperture to improve its opaqueness by eliminating the events with double hits; one in the coded aperture (scattering detectors) and the other in the absorbing detector. Multiple hit events can be utilized in the Compton Camera method for our detector sy stem design. The other advantage is that the efficiency of this design is not reduced by an a dditional coded aperture in front of the scattering detectors that is used in the conventional hybrid design of imaging system of coded aperture and Compton cameras [43, 44]. For ;1 am arctanm p b In order to achieve resolution of 0.3 radians, the ratio of 0.309mp b is required. According to the design of the Compton camera [10], the distance between the coded aperture and the detector is about 30 cm. The size of hole on the coded aperture is about 9cm. If the distance between th e sources and coded aperture is very large, the angular field of view is arctan 2dd b If the size of detector dd=100cm we foundo1.1903 radian68.2. The opening angle of the field of view for our system is about 140o, which is wide enough for most homeland security applications.

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50 In this dissertation, the coded aperture pattern was generated under constraints on the number of detectors, the size of the system and other requirements as discussed in later Chapters. One of the important items addressed is the lim ited spatial resolution of absorber detectors because the finite size of the crystals and th at ordinary photomultiplier tubes (not position sensitive) were used in the initial system design. This will degrade the angular resolution of the coded aperture camera.

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51 CHAPTER 4 IMAGE RECONSTRUCTION ALGORITHMS Compton cameras do not directly deliver imag es of incoming photons, but rather utilize coincident hits among detectors to encode the directions of the incoming photons. It is thus necessary to apply image reconstruction algorithm s to decode the observation afterwards, which is similar to spatial multiplexing techniques [3]. In general, three kinds of image reconstruction algorithms have been developed: simple back-projection, filtered back-projection, and iterative algorithms. The simple back-projection algorithm and the filtered back-projection algorithm are used to deliver real-time images because they implement individual events, whereas iterative algorithms generally require multiple events in order to reconstruct an image. The Simple Back-Projection Algorithm For each two-hit event, the incident gamma-ra y direction can be constrained on the surface of a cone with the axis defined by a line that connects the position of Co mpton scattering and the position of the first interaction of the scattered photon. The half-angle of the cone is derived from the deposited energies based on the Compton re lationship. In the simple back-projection algorithm, these cones are projected onto the imaging space, which is the hemisphere around the detector, as seen in Figure 4-1. Figure 4-1. The geometry of a Compton scattering event.

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52 The geometry of a scattering ev ent is at the direction of ( ) with scattering angle of and azimuthal angle of where ( s, s) is the possible direction of the incident photon. The formula used for back projection is given below in Eq. 4.1, which converts all possible directions of the incident photon to a unique coordinate. 222 123 12 1 2 2 3cos()[sin()cos()cos()/tan()]sin() (4.1) (-) cos()= (4.2) 2 sin()/sin(); sin()/tan(); 1-sin(); sin(s s sxxx xx where x x x )cos()sin(). Examples of two-hit events induced by 662 keV photons incident at ( s = 0, s= 0) mapped on the hemisphere are presented in Figure 4-2. Each of the rings on the hemisphere corresponds to all possible dire ctions where a photon might be incident upon the camera. -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 sin( )cos( ) sin( )sin( ) cos( ) Figure 4-2 Examples of two-hit event mapped onto hemisphere.

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53 The width of the back-projection cone is determined by the angul ar uncertainty as discussed in Chapter 2. Although the gamma rays from the same direction may pass different cones, the overlaps of these cones along this di rection can be distinguished from the background as seen in Figure 4-3, providing locations of hi gh intensity that represent source locations. The figure shows the simple back-projected image of a point source at 662 keV. (degree) (degree) 0 50 100 150 200 250 300 350 20 40 60 80 100 120 140 160 180 Figure 4-3. The image of a beam of photons one with energy of 662 keV at a polar angle of 30o and an azimuthal angle of =40o. Only two-hit events are used in the simp le back-projection operation. The angular resolution is about 20 The sonogram-like features are attr ibuted to the finite number of absorbing detectors which cover a few regions of scattering angles because each observed scattering angle introduces a sonogram-like curve.

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54 Filtered Back-Projection Algorithm The simple back-projection algorithm is fa st and easy to implement, but its angular resolution is limited by the angular uncertainty Algorithms of the filtered back-projection algorithm have been widely used in computer tomography (CT) image reconstruction [107] to remove blurring features in a point spread f unction (PSF) and improve spatial and contrast resolution. However, the filtered back-project ion algorithm using linear ramp filter in CT systems do not provide good results in Compton cameras because the profiles of the blurred PSF in Compton cameras is different from that in CT systems. In Compton imaging systems, the image plane is expanded by the spherical harmonics rather than the Fourier space, as in CT. In order to take the advantage of the recons truction speed of back-p rojection algorithms and compensate for poor angular resolution, filtered back-projecti on image reconstruction algorithms have been developed. A direct re construction algorithm applied to severely limit scattering directions to only those that are perp endicular to the detector array was developed by Cree and Bones [45]. Analyti cal inversion methods were also studied on conic surface projections using the spherica l harmonics without consideri ng the distribution of possible scattering [46]. An analytical inversion algorithm for the complete data set of all possible scattering angles based on the Klein-Nishina fo rmula was also developed [47]. Since in the Compton imaging system, the image plane is ex panded by the spherical harmonics, the filtered back-projection algorithm is implemented based on the expansion of spherical harmonics series rather than Fourier series for CT. Any function () f on the hemisphere can be transformed into series of spherical harmonics as:

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55 20 *() () (4.3) (21)()! () (cos) 4()! ()()l mm ll lml mm i m ll mm ll sfFY where llm YP e lm FdfY In which (cos)m lP is the associated Legendre polynomial. Ideally, if the Compton relationship for scatteri ng off free electrons is valid and the energy response is the same for different energies, th en the mathematic model of Compton camera is: 2()()(cos) (4.4)sgdgh where () g is the image of a given source() g ; (cos) h is the point spread function with azimuthal symmetry, and is the angle between and According to the spherical convolution theorem [56], in the spherica l harmonics form, this convolution is: 04 (4.5) 21mm ll lGGH l where m lG m lG 0lH are the transformations of() g ,() g and (cos)h in the spherical harmonics domain, respectively. The sphe rical harmonics coefficients of (cos) h are: 2*(cos)() (4.6)mm ll sHdhY. For the azimuthal symmetric(cos) h its spherical harmonics coefficients are zero for all0 m For m=0, we have:

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56 200 0(cos)() (21)(cos)(cos)(cos) 421 (cos)(cos)(cos) 212 4 (4.7) 21ll s l l lHdhY ldhP l dhP l H l 21 where (cos)(cos)(cos) 2lll HdhP Thus, the spherical harmonics coefficients of source are derived as: 21 (4.8) 4mm ll ll GG H In an ideal case where response doe s not depend on the incident angle, (cos)h can be obtained as: 2 22 21( ) (cos) (4.9) 2sin coscos 2 2 dK h where ()K is the Klein-Nishina cross section formula: 0 11 0102 22 01 () sin() (4.10) sin E EE d KZ r dEEE However, due to the limitation in the detector system configuration and the difficulty in detecting small-angle scattering events in practice, an algorithm applied to the limited angle Compton camera data set was developed [48]. This is especially important for application of Compton cameras with limited coverage of scatteri ng angle, such as that in the design presented here. The design presented in this dissertation can only detect th e Compton scattering events of certain scattering angles. This is due to the limited number of absorbing detectors and the

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57 variation in the attenuation of the detection mate rial at different sca ttering directions. The scattered photon energy changes at different scattering angles. Therefore, the measured scattering angle distribution will be different fr om the prediction based on the Klein-Nishina formula. In this dissertation, a de convolution algorithm using the sp herical harmonics will be further investigated. The point sp read function will be numerically calculated based on the KleinNishina formula which takes into account the incomplete coverage of absorbing detector over the scattering angle. Iterative Approach Iterative algorithms are general methods to reconstruct images for Compton cameras [49, 50]. Iterative algorithms allow detailed physical -modeling and noise modeling to be used in image reconstruction and deliver better angula r resolution than that of back-projection algorithms. In general, a Compton camera system consists of two detectors, scatterer and absorber, which are parallel to each other, as shown in Figure 5-4 A true coincident two-hit event (also referred to as a valid event) is recorded when a photon is scattered in the first detector and then absorbed in the second detector. In each valid event we record: (1) scattering position, (2) interaction position of th e scattered photon, and (3) E1 and E2, the energy transferred to the scatterer and absorb er, respectively. For each combination of interaction positions in the two detectors: a scattering angle, the axis 12PP, an apex P1 and E1 and E2 are determined. A mathematical expression for the Compton projection data (ignoring random co incidences) can be given as 1212 1212 00 0 (4.11),PPEE PPEEijkEijkE ijkEgfH

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58 where the Compton projection data and source distribution are represented by 1212 P PEEg and 0ijkE f respectively. The response matrix 1212 0 P PEE ijkEHrepresents the probability that a photon emitted from a voxel (i, j, k, E0) is scattered at position P1 in the scatterer which deposits energy E1 and detected at position P2 of the absorber and deposits energy E2. Figure 4-4. The two coincident hits in Compton camera. The Expectation-maximization algorithm (EM algor ithm), which is the same for all emission imaging systems, is given by [50, 51] 0 1212 1212 00 1212 1212 1212 0 0 12121 (4.12) n ijkE PPEE PPEE n ijkEijkE PPEE PPEE n PPEE ijkE klmEklmE PPEE klmEf g fH H fH The above EM algorithm is implemented by iter ations requiring projec tion of the estimated source distribution and back-pro jection of the ratio between the measured and estimated projection data. However, this method is impo ssible to implement unless there is a method to calculate1212 0 P PEE ijkEH, because the stored response matrices are unreasonable due to their large sizes. P2 ( x2 y 2 z2 ), E2 E0 P1 ( x1, y 1,z1 ) E1

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59 In order to reduce the computer time Barrett and his colleagues applied Maximumlikelihood image reconstruction to list-mode data [108, 109] that was so called MLEM. However, the MLEM algorithm is usually slow in converge. This is especially true for the cases involving response matrixes with large size. The orde red subset expectation maximization (OSEM) algorithm [52] is a possible approach to acce lerate the reconstruction speed. The OSEM algorithm divides the measured data set into several subsets, and uses the reconstructed image of the previous subset as the initial image of th e next subset. The algorithm can provide order-ofmagnitude acceleration over conventional MLEM algor ithms and is relatively easy to implement [52]. Recently, the application of OSEM in Compton cameras has been probed under certain approximations by Kim et al. [53]. The promising results wi ll lead to more studies devoted to this new approach for Compton cameras. In this dissertation, the symmetric approximati on and factorization appr oach is utilized to calculate the 1212 0 P PEE ijkEHbased on much smaller prior stored da ta sets. The OSEM approach will also be investigated. Decoding Coded Aperture Images In coded aperture imaging systems, the en coding process can be converted into the convolution [54, 55]: () ()() and () (4.12) RrOA aa OrOrAAr ba b where () R r is the image observed on the detector plane, and O and A are the source distribution and coded aperture pattern, respectively. Instead of back-projection methods to reconstruct the source distribution, there is a correlation method of decoding that is a way of locating the mask pattern in the projection. The implemen tation of correlation reconstruction is:

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60 (4.13) ORG Therefore, (), (4.14) OOAGNG If, (4.15) AG then, OONG where N represents the noise. In the reconstructed image, the noise is still present, but it is not ill-behaved as that in the back-projection approaches, based on Fourier transforms. In this work, a proposed design of a coded aperture A for a given number of scattering detectors is presented and analyzed. The perfor mance of the correlation reconstruction approach with Monte-Carlo simulation is investigated. In order to combine image reconstruction of multicoincident events, iterative image reconstruction algorithms for the coded aperture approach are also investigated.

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61 CHAPTER 5 LABR3 :CE SCINTILLATION DETECTOR Scintillation crystals have been widely us ed in imaging and spectroscopy of energetic photons ( -rays) at room temperature. The desired properties of scintillation crystals for many spectroscopy applications include high light output, high Z, fast response, low cost, good linearity, and minimal afterglow. Recently, a new cerium doped halide scintillator, LaBr3, has been discovered which has attractive scintillati on properties such as very high light output (~60,000 photons/MeV), and fast principle decay consta nt (30 ns) [57, 58], as seen in Table 5-1. Based on these properties, LaBr3:Ce is a promising scintillator for -ray imaging and spectroscopy, because the high light yield allo ws reduced statistic fluctuation in energy determination and allow application of position sensing in the detector. The fast decay was desired for precision coincident tim ing used in Compton cameras. Table 5-1 Comparison of scintillation crystals. Light Yield Photons/keV Decay Time (ns) /Light Yied BaF2 1.8 0.8 0.44 BrilLanCe*380 63 16 0.25 BrilLanCe*350 49 28 0.57 LSO 27 40 1.48 NaI(TI) 38 250 6.58 GSO 8 60 7.50 BGO 9 300 33.3 LaBr3 has a hexagonal (UCl3 type) structure with P63/m space group [58, 59, 60], as seen in Figure 5-1, and has a density is 5.3 g/cm3. LaBr3 compound melts at 783 C congruently. Therefore LaBr3 crystals can be grown using melt based methods such as Bridgman and Czochralski which are well suited for grow th of large volume crystals [60].

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62 Figure 5-1. LaBr3 Crystal and its Hexagonal structure of LaBr3. Scintillation Mechanisms The superior properties of LaBr3:Ce are attributed to Ce3+[61].The desired scintillation mechanism in LaBr3:Ce is the prompt transfer (faster th an 1 ns) of a free electron and free hole from the ionization track to Ce3+ leading to 4fd excitation and followed by 5df emission with 100% efficiency. However, there are number of processes to transfer electrons to various sites. There are two types mobilization process that are important in the scintillation. First, a hole at the top of the valence band is not stable and will be bound between two anions to form a 2 Xlike molecular complex (X = F, Cl, Br, I which known as kV center) accompanied by strong lattice relaxation [62] that may jump from one site to an adjacent site by thermal activation. Second, the kV center traps an electron from the conduc tion band because it carries positive charge. In this case, a self-tra pped exciton (STE) is created which is a neutral defect and may migrate thermally with a speed faster than that of a kV center [62]. The role of kV and STE centers in the scintillation is illustrated in Figure 5-2. Figure 5-2a shows the self-trapping of a hole into a kV center (indicated by arrow 1). Next the kV center migrates by a thermally activated hopping migration to Br

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63 Figure 5-2. a) Binary kV and electron diffusion, and b) STE migration in the scintillation process. the Ce3+ ion where it is trapped to form Ce4+ or a Ce3+ kV associated complex. Finally the electron is trapped in this center (arrow 2) leading to excitation of Ce3 + followed by 5df photon emission (arrow 3). This process is binary kV and electron diffusion. In this case, the scintillation decay time s is determined not only by the lifetime of the 5d-state of Ce3+ but also by the transfer speed of kV centers to Ce3+ and electrons to Ce4+ or Ce3+ kV The more complex situation occurs when, before being trapped by Ce, kV traps an electron to form an STE, as shown in Figure 5-2b. The S TE is a luminescent defect by itself with typical decay time of several microseconds (arrow 1). The S TE is also a mobile defect that may transfer its energy to Ce3+ (arrow 2) leading to delayed Ce3+ emission (arrow 3), when in the vicinity of Ce3+. In some compounds, the STE emission is que nched at low temperatures, and when the lifetime of the STE is shorter than the time needed to transfer energy, this can be an important scintillation loss factor. Depending on the sp ectral overlap between STE emission and Ce3+ absorption, radiative transfer is also possible. Spectroscopy with LaBr3:Ce Detectors In our design we selected the BrilanCe 380 (LaBr3(Ce)) detector that was manufactured by Saint-Gobain company. In order to maximize light collection, LaBr3:Ce crystals are wrapped in

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64 reflective, white Teflon tape on all faces (ex cept the one that coupl ed to a photomultiplier (PMT)). An optic index matching si licone fluid was also used at the PMT scintillator interface. The energy resolution at 662 keV as function of temperature and Brila nCe 380 detector are shown in Figure 5-2. Figure 5-3. The energy resolution at 662 keV as function of temp erature on left and BrilanCe 380 detector on right. The energy spectrum of 22Na source measured with LaBr3:Ce crystals is show n in Figure 5-4 and the energy resolution is function of energy as shown in Figure 5-5. 0 200 400 600 800 1000 1200 1400 1600 0 500 1000 1500 2000 2500 3000 Energy (keV)Counts/bin22Na 2% Figure 5-4 The energy spectrum of 22Na.

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65 0 200 400 600 800 1000 1200 1400 5 10 15 20 25 30 35 Energy (keV)Energy resolution (keV) Fitting Measured Figure 5-5. The fitting of energy re solution as a function of energy. However, there are number of internal contaminants, such as 227Ac and 238U decay chain, in LaBr3 that create features in spectrum, as seen in a 36,000 second unshielded background spectrum taken with the LaBr3:Ce detector (Figure 5-6). The peak at ~ 1460 keV is the 1436 keV gamma ray that has structure related to a coincide nt x-ray that is absorbed in the detector. The broad feature around 750 to 1000 keV is the 789 keV gamma rays in coincidence with a beta particle. All of these features are attributed to the internal 138La decay. Above the 1436 keV gamma-plus-x-ray peak in energy there are many peaks (1550 keV) associated with the alpha decays from 227Ac. The gross count rate, in this case is 0.58 counts per second. The small bumps between 250-650 keV are external background gamma rays from the 238U decay chain. Timing Properties of LaBr3:Ce 137Cs gamma-ray excited decay curves of LaBr3:5% Ce3+ recorded at 100, 300 and 600 K are shown in Figure 5-7 [61]. A more complete st udy can be found in [61]. They exhibit a fast

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66 0 500 1000 1500 2000 2500 3000 3500 4000 100 101 102 103 104 105 Energy (keV)Counts/bin Bakground 10 hours Figure 5-6 Background spectrum measured with BrilanCe 380 LaBr3 detector in 10 hours. Figure 5-7 Temperature dependence of LaBr3:5% Ce3+ scintillation decay curves. The solid curves are drawn to guide the eye and are not fitted curves. component of 16 ns at 100 and 300 K and 21 ns at 600 K. At 100 K, a slow component with 0.3 s exponential decay constant provides a contribu tion of 40% to the total light yield. The absence of decay time shortening of the fast component with the increase of temperature

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67 indicates that thermal quenching of 5d to 4f emission does not occur. In general, the fluorescent decay times of LaBr3:Ce samples doped 5% Ce were measured using the delayed coincidence method. Overall, these measurements indicate that LaBr3:Ce is a promising scintillator. It has high light output, fast response and shows good energy and timing resolution. It is the desired scintillation material to be used in applica tions of medical imaging, nuclear physics, X-ray diffraction, non destructive evaluation, treaty verification and non-prol iferation monitoring, environmental cleaning, a nd geological exploration.

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68 CHAPTER 6 EXPERIMENT AND HARDWARE In order to evaluate the feasibility of using LaBr3:Ce detectors in Compton camera designs, a bench top Compton camera was setup and test ed. The experimental implementation of the coded aperture camera was difficult. To mimic the coded aperture imaging system without a sufficient number of detectors to create th e MURA was challenging and time consuming. However, the test of the coded aperture camer a may be achieved by scanning the absorbing plane with a few detectors and comparing the results with the modeling and simulations within this dissertation. For investigating the imaging capabilities of th e design of Compton camera, we experimentally implemented the Compton camera design with two LaBr3 detectors. One of the detectors served as scattering and the other sc anned over the scattering angles, as seen in Figure 6-1. Figure 6-1 The sketch of experimental setup. LaBr3 Detector The two used detectors were Brillance 380 de tectors but have differe nt thicknesses and the same radii of 2.5 cm[63]. The thickness of th e absorber was approximately 2.5 cm, while the thickness of the scattere r was about 0.5 cm. The scintillation signal was sensed and amplified by a Photonis XP2060B, 39mm diameter, photomultiplier tube (PMT). The PMTs entrance window 1 AMP DAQ SCA SCA AMP Fast Coincidence 2

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69 was optically coupled to the scintillator by optical couplant. The XP2060 has a bialkali photocathode which ensures a wide wavelength re sponse. The 10 dynode stages was designed to provide significant multiplicati on while retaining good pulse height resolution and linearity at low biases. Low-voltage (~460 V comparing to ~1000v for NaI detector) operation is necessary because of the very high scintillation light output of LaBr3 (60,000 photons/MeV) coupled with its short duration ( = 15ns). LaBr3 detectors achieved better ener gy resolution than that of NaI, as seen in Figure6-2. Figure 6-2. 232Th Spectra from LaBr3:Ce (upper) and NaI(Tl) (lower) The distance between the scattering plane and absorbing plane in the experimental measurements was about 10~20 cm in order in vestigate relationship between the angular resolution and the distance with a relatively high efficiency. Data Acquisition Hardware The electronic readout system was setup with a NI-DAQ 7 PCI card (NI PCI-MIO-16E-1) [64], as seen in Fig, 6.3, and SCB-68-68-Pin shielded connector block [64], as seen in Figure 64. Both pieces of equipment are from National Instruments. The DAQ hardware digitizes signals, performs D/A conversions to generate analog out put signals, and measures and controls digital

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70 I/O signals. E Series devices use the National Instruments DAQ system timing controller (DAQSTC) for time-related functions (used in coinci dence measurements). The DAQ-STC consists of the following timing groups: a) AITwo 24-bit, two 16-bit counters; b) AO Three 24-bit, one 16-bit counter; c) Generalpurpose counter/timer functionsTwo 24-bit counters. The DAQ-STC can independently configure the groups for timing resolutions of 50 ns or 10 s. With the DAQ-STC, a wide variety of internal timing signals to othe r internal blocks can be interconnected. The interconnec tion scheme is flexible and completely software-configurable. The DAQ-STC offers PFI lines to import extern al timing and trigger signals or to export internally generated clocks and triggers. The DAQ-STC also supports buffered operations, such as buffered waveform acquisition, buffered waveform generation, and buffered period measurement. It also supports numerous non-buffered operations, su ch as single pulse or pulse train generation, digital input, and digital output. Figure 6-3. The picture of NI PCI-MIO-16E-1 card and block diagram.

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71 National Instruments measurement devices are packaged with NI-DAQ driver software, an extensive library of functions and VIs can be called from application software, such as LabVIEW or LabWindows/CVI, to program all the features of NI measurement devices. Driver software has an application programming interface (API), which is a library of VIs, functions, classes, attributes, and properties fo r creating applicati ons for a device. The SCB-68 is a shielded I/O connector bl ock with 68 screw terminals for easy signal connection to a National Instruments 68or 100pin DAQ device. The SCB-68 features a general breadboard area for custom circuitry and sockets for interchanging electrical components. These sockets or component pads allow RC filtering, 4 to 20 mA current sensing, open thermocouple detection, and voltage attenuation. Figure 6-4. SCB-68 printed circuit diagram.

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72 In the experiment, three channels were used. Two channels acquire pu lse heights and time from the scattering detector and the absorbing de tector, respectively. The third channel is the trigging signal from a timing coincident unit. Experiment To evaluate the feasibility of using LaBr3(Ce) detectors as both scattering and absorbing detectors in Compton cameras, we set up a bench top system with two LaBr3(Ce) detectors, as seen in Figure 6-1. This setup mimicked a Co mpton camera with one scattering detector and 8 absorbing detectors, as seen in Figure 6-5. In order to reduce the experimental time the separation of the two detectors was reduced to ~11. 6 cm to increase the absolutely efficiency of this bench top. During the experiment a point source of Cs-137 with activity of ~1 Ci was rotated around the center axis at the normal direction of the front detector while th e positions of the two detectors were fixed. Detector 2 was shielded from direct measurement of the source by lead sheets to act as the absorbing (backplane) detector. The source was located off-axis a total of 17.8 cm from the center of the scatte ring detector and was rotated at 45 intervals from 0 to 360 to mimic each of the 8 detectors. At each locatio n, the number of two-hit events collected was greater than 103. Signals output from the preamp lifiers of two detectors were fed to shaping amplifiers. Shaped signals were sent to QAD card and SCAs that provided low level discriminations. The acquisition process was triggered with timing coinci dence signal generated w ith a fast coincident unit from the two SCAs output signals. The DAD was embedded in a computer and controlled with LabVIEW software. In each QAD channel, 40 data points were sampled. The maximum pulse height and base line levels of pre-trigger and post-trigge r were measured online and saved

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73 into a file for post processing. The shaping time of the two shaping amplif iers (AMP) were set to 6 s to assure that the pulse peaks were well resolved. Each detector was energy calibrated separately using a mix of common radiation sources. Figure 6-5. The configuration mimicked in the experiment with two de tectors. The center detector was the primary scattering detector. Spectroscopy The spectra from each detector and the summed spectrum for a 137Cs source are shown in Figure 6-6, in which photon peak and escaped line features appeared at right energy with the similar resolutions of LaBr3(Ce) detectors. It demonstrates our pulse height measurements implemented with our LabVIEW codes are correc t. The line around 38 keV in the spectrum of detector 2 was due to the escaped K photons generated via ionization of K-shell electrons of La in detector 1 and absorbed in the detector 2. The events above 662 keV can be attributed to the high energy background, such as cosmic ray and intrinsic activity in LaBr3(Ce) crystals [6]. The energy resolution of the two-hit ev ents was measured as ~3% at 662 keV, which showed that this imaging system was capable of serving as spectrometer.

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74 0 20 40 60 80 0 20 40 60 Recurrents 0 100 200 300 400 500 600 700 0 100 200 Energy (keV) Det. 1 Det. 2 Det. 1 +Det. 2 Figure 6-6. The energy spectra of coincident events in the two detectors. Image To implement Compton imaging with two-h it coincident events, back-projection and filtered back-projection algorithms were applie d. In Compton cameras, the direction of each incident photon can be constrained onto a conic surface determined with a Compton scattering event. The back-projection image reconstruction method is simply a projection of each of the conic surfaces onto ( ) plane, in which the overlapped regions indicate the emission sources [66, 67]. This method has been widely used b ecause of its simplicity and speed, although it did not provide the best quality of image. The form ulas we used in the back-projection approach were described in [10]. Images obtained with back-projection were s hown in Figure 6-7. In the unfiltered back projection image the point source was evident at ( ) of (32o, 270o), which is near the true source location of (33o, 270o). The ring artifacts can be attributed to the limited coverage of

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75 scattering angles from the eight mimicked detector s, as shown in Figure 6-7. Since there are the artifacts due to limited coverage of scattering angle, the full wi dth at half maximum (FWHM) of the image of the point source varies along differ ent directions of meas urement. The FWHM is approximately 30o (0.52 radians) and is consistent with a prediction based on our previous work [10]. (degree) (degree) 0 50 100 150 0 50 100 150 200 250 300 350 0 1 2 3 4 5 6 7 x 10-5 (degree) (degree) 10 20 30 40 50 250 260 270 280 290 300 0 1 2 3 4 5 6 7 x 10-5 Figure 6-7. The image reconstructed with back-p rojection method on the top and the zoomed in image on the bottom. Since the back-projection ta kes into account the geometri c relationship between the incident photons and scattered photons, the recons tructed images do not represent the real source

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76 distributions and introduce artifacts. To improve the image quality, the scattering cross section of Compton and limited coverage of scattering angles by absorbi ng detectors were need to be considered in image reconstruction that can be partially achieved with filtered back projection algorithms. It has be achieved if the kernel can be represented by a functio n that is depend on the scattering angle but not the inci dent directions of photons [68, 69, 70]. In our case the limited coverage of scattering angles leads to a strong dependency between efficiency and incident directions of photons. Therefore, filtered back projection approach did not apply for our bench top experiment. The iterative methods allows detail modeling of physics of Compton scattering in complex geometries and was used to reconstruct image from the two-hits events recorded in the experiment of the bench top. The response functi on of the bench top setup to two-hit events was approximated as below. 12 0 22 01 i n t 00 01 2 ,, 21i n t022 02 0(,,,,) (,)1(,,)(,,) () (,)(,)1(,,) () (,incoh eff ieff i incoh ScatAbsEE i xyzE phxyzEScat EEPScatEEAbsScatEEAbs EE EEEEPAbsEEEd H EEE dEEE 0 0 0' 0 0 2 0 (6.1) ) (,)E EE EEdE dE EE dE where 0(,,,,)eff x yzEScat is effective solid angle of the scattering detector to the point of (x, y, z) which takes into account the impact of the geometric shape of the scattering detector and the energy of incident photon on the interaction probability; 0(,,)eff iScatEEAbs is effective solid angle of the absorbing detector i to the scattering detector which takes into account the impact of the geometric shape of the absorbing detector and the energy of incident photon on the interaction probability; int 0(,,)iPScatEEAbs is the average probabili ty of photon with energy of 0EE interacting with the scattering detector; (,) EE is the probability of a photon with

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77 energy of E and is measured as E ; int 0 2(,,)iPAbsEEE is the probability of a photon interacting with the absorbing detector i and escaping at the direction of 2 In the image reconstruction, the efficiency of the syst em is needed that can be expressed as: 12 0 12,, 0 {,,,}(,,,) (6.2)i iScatAbsEE effxyzE ScatAbsEEFxyzE H The calculated efficiency 0(,,,)effFxyzE at z = 15.3 cm and E0 = 662 keV was shown in Figure 6-8 which showed the symmetric response around the axis of the scattering detector as we expected. x (cm)y (cm) -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 0.1 0.105 0.11 0.115 0.12 0.125 0.13 0.135 Figure 6-8. The calculated efficiency map of the system as function of th e original position of incident photons. The reconstructed image was shown in Figure 6-9 in which the point source was evident and indicated the angular resolution of the system reduced to about 0.25 radians (FWHM) that was about two times smaller than what we obtai ned with back-projection method as seen in

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78 Figure 6-7. The improvement of reconstructed image was expected when the imaging system was correctly modeled. Figure 6-9. The reconstructed imag e with EML iterative method. Conclusions Based on the available hardware in our Lab. as described above we set up a benchtop and successfully acquitted one hit and two-hit da ta with LabView software. The spectrum of individual detector and coincident spectrum were obtained. The Compton camera approach was successfully implemented on the two-hit data which demonstrated LaBr3 was able to function in Compton camera and spectroscopy of gamma rays.

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79 CHAPTER 7 DESIGNS AND SIMULATION OF HYBRID CAMERA Compton camera imaging is a promising approach to achieve higher efficiency and better angular resolution than that of conventional gamma cameras with mechanical collimators for photons with energy above several hundred keV [71, 72, 73], where Compton scattering is the dominant photon interaction. However, for photons with energy near 100 keV, the efficiency of Compton cameras drops significantly because the photoelectric absorption cross section dominates at this energy in most radiation detector materials. Coded aperture imaging is an alternative approach for imaging photons in this energy range and can result in a higher efficiency than that which can be achieved w ith mechanical collimators [74] and Compton Cameras. In order to image photons across a broa der energy range, we designed and investigated a hybrid imaging system that can be impleme nted as Compton camera and coded aperture camera utlizing an active coded aperture mask that also serves as the Compton scattering layer. Historically, the hybrid systems with additiona l coded apertures have been studied for high energy astrophysics [5] and industry applications in e.g. [76, 77]. In those hybrid systems, coded apertures were made from material with high Z and high density to achieve high attenuation. However, at higher energies of photons, the additional coded aperture masks introduced scattering and decrease detection efficiency. In order to overcome th ese disadvantages in previous designs of hybrid cameras, we presen ted a relatively unstudied hybrid approach in which the coded aperture is composed of active de tection elements, as seen in the discussions of Chapter 3. To achieve high efficiency a nd high attenuation, doped LaBr3(Ce) with ~5% of Ce is a good candidate for both the scattering and absorbi ng detectors because of its high atomic number and density. Furthermore, an energy resoluti on of less than 3% at 662 keV [78] has been

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80 achieved, which is desired for imagers with Compton camera approach and spectrometers. The high light yield and fast decay of light in LaBr3(Ce) provided opportunity for applications requiring fast timing and precision position-sensing [78, 79]. In this design, we aimed at about 0.3 radians angular resolution for homeland app lications to resolve radiation sources with separation about 10 meters and a few tens meters away. We did not use position sensing techniques in each detector, instead investigating the use an indexed ar ray of detectors and a normal PMT to provide position information. The use of non-position sensitive electronics will also allow the full system to be built at a lower cost than a system that utilizes PSPMTs. In this Chapter, we describe the method of optimization of the efficiency and angular resolution of this system. The geometric design of the coded aperture with LaBr3(Ce) detectors is also described. A prototype design of a hybrid gamma camera is proposed and Monte Carlo simulation of this design is presented. The image reconstruction algor ithms investigated are described with detailed modeling of response functions. The lessons we learned from the experimental results and invest igation of the prototype are al so discussed and summarized. Optimization of Compton Camera The optimization of the Compton camera was aimed at two scenarios: highest efficiency for a required angular uncertainty, and the best angular uncertainty for a required efficiency, for particular applications. Unfortunately, these two properties are inversely dependent on one another, thus it is necessary to understand th e optimization that must occur with Compton Camera systems. The optimization was based on the calculation of the efficiency of single Compton events in the scatter plane and the resu lting angular uncertainty. The uncertainty arises from detector position and energy resolution as we ll as the inherent Doppler broadening effect. The probability of single Compton scattering was numerically calculated based on a simple two-layer LaBr3(Ce) configuration wher e the attenuation of LaBr3(Ce) on incident and scattered

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81 photons has been taken into account[10]. It shows that at the thickness of ~1.25 cm the probability of single Compton scatter reache s the maximum for 662 keV photons. For higher energy photons, the thickness for maximum probabil ity is even larger, which indicates that LaBr3(Ce) is a better choice than Si from the efficiency point of view. Contributions for the angular uncertainty co me from the uncertainty in interaction positions. The uncertainties are about the half of th e size of the individual detectors, because we assume no position sensing capabilit y is applied. In general, fo r larger separations, the position uncertainty contributes less to overall angular uncertainty as seen in Chapter 2 and [80]. The contribution of energy resolution to angular uncertainty is a functi on of scatter angle in Chapter 2 and [81]. This calculation incorporates the measured energy resolution as a function of incident gamma-ray energy. For photons with higher energy, the contribution of energy uncertainty is less significant than that fo r lower energy photons since the relative energy resolution improves with E 1. Double differential cross secti on of Compton scattering over bi nding electrons [82] is used to determine the uncertainty due to th e Doppler broadening effects. For LaBr3(Ce) our results show that at scatte ring angles above 30o and below ~150o, the contribution of Doppler broadening effects is less than that at other angles Chapter 3, and [83]. Based on the previous results in Chapter 2, a prototype of Comp ton camera was designed to achieve an angular resolution of about 0.3 radi ans in which a thickness of 1.3 cm was selected for scattering detectors to achieve a high efficiency. The radius of LaBr3(Ce) crystals of both the scatteringand absorbing-layer detectors was sel ected as 1.27 cm, while the thickness of the absorbing detectors was 2.57 cm for absorbing dete ctors to achieve high efficiency in absorbing the scattered photons. The separation between scattering and absorbing detectors was set to 30

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82 cm to contribute uncertainty less than <0.2 ra dians uncertainty, (Figur e 2-13). Considering the angular uncertainties induced fr om energy resolution and Doppler broadening are less than ~0.15 radians, the over all angular reso lution of the imager is expected to achieve ~0.3 radians. Figure 7-1 The configuration of the hybrid gamma camera used for evaluation with Monte Carlo simulation. In comparison with the virtual nine detector s in the benchtop se tup, we proposed and simulated a prototype hybrid im ager that has forty eight sca ttering and one hundred absorbing detectors, the ring artifacts were less significant in the back-proje ction image as shown in Figure 7-1 than that in Figure 6-7. One option to improve the quality of image is an iterative algorithm method, which has been previously applied to reconstruct the image for Compton cameras [71, 91]. Iterative algorithms allow detailed physical-modeling and noi se modeling which deliver better angular resolution than that of filtered back-projec tion algorithms. Detailed physical-modeling of our system is ongoing in which the geometrical shape of detectors will be considered. Therefore,

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83 while this algorithm will be investigated as part of the future work for this system, our research to date has focused on demonstrating the capabiliti es of imaging and spectroscopy with straightfoward algorithms and integrating a Compton camer a with a coded aperture scattering layer. (degee) (degree) 10 20 30 40 50 170 180 190 200 210 220 230 240 250 400 500 600 700 800 900 1000 1100 Figure 7-2. The image obtained in Compton camera approach with back-projection method on the right. In this image, the background level is about 400. The FWHM level at ~800, and the FWHM is about 20o that exceeds the goal for the prototype design. Coded Aperture The coded aperture was implemented under th e constraints of the optimized Compton camera, described previously. For ideal imaging properties it is necessary to record a complete cycle of the basic pattern for ev ery position in the observed field of view (FOV). This can be accomplished by configuring the mask and detector, such as the mosaic of 22 of the basic pattern with 2121 pq mask elements, while the detector is as large as the mask. Our coded

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84 aperture pattern was a basic 5 x 5 (q = 3) mosaic pattern of a Modified Uniformly Redundant Array (MURA) [74]. The FOV is a function of the size of detector dd and distances of source to the aperture a and the aperture to the detector b [74], arctan; (7.1) 2 FOV a the angular resolution can be defined as arctanarctan, (7.2)g mp m ab where m p is the size of an aperture hole. In order to achieve the angular resoluti on of 0.3 radians or better, the ratio pm/b was determined to be 0.31. According to the design and initial models of the Compton camera, the distance between the coded aperture and the detector should then be 30 cm. With this separation, the size of hole on the coded apertu re was determined to be less than 9 cm. In this case, angular field of view wasarctan(/2)ddb If the size of a detector for a real application was dd=100 cm then70o. The open angle of the FOV of about 140o should be wide enough for most homeland security applications, par ticularly for screening vehicles. To implement a coded aperture imaging approach, we selected the one-hit events which were recorded only by the absorbing detectors. In order to reconstruct the image from the shading pattern of {Ai,j i, j=1,2,3,,10 } resolved with the 10 x 10 absorbing detectors, we utilized the cross correlation method 1 ,, ,, ,0 (7.3)n lmlm ijij ijcAB

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85 in which Bl,m is the decoding pattern for the incident directions of { l m=1,2,3,,10} generated from the GEANT4 Monte Carlo simulation package [105]. Prototype H ybrid Gamma Camera and Simulation Based on the considerations above, a prot otype Compton imaging system with LaBr3(Ce) detectors for the scatter and absorber planes was simulated (assuming the use of photodiodes to eliminate photon scatter from the PMTs), as seen in Figure 7-5. In the front layer, there were 48 cylindrical crystals distributed in a Modified Uniformly Redundant Array (MURA) that served as the Compton scattering and coded aperture la yers. The rear 10 X 10 array served as absorbing and position sensing detectors. The shadow of the front detectors on the ab sorbing detector array was calculated based on projection. An example is shown in Figure 7-3. RowColumn 2 4 6 8 10 2 4 6 8 10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Figure 7-3 The shadows of the scattering detect ors on the 10 x 10 array of absorbing detectors when the camera was centered at (0, 0, 0) and irradiated by a point source at (250cm, 0 cm, 1500 cm). As mentioned above, the geometries were optim ized to achieve a high efficiency for the required angular resolution of ~0.3 radians. Ag ain, the distance between the scattering and absorbing layers was selected to be 30 cm; the thicknesses were 1.3 cm for scatter and 2.54 cm for absorber, respectively. The radius of all crystals was 2.54 cm The distance between the

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86 centers of two adjacent elements was 3.81 cm for both layers. All the element sites in the absorbing layer were filled with LaBr3(Ce) detectors while only the opaque element sites were filled with LaBr3 in the front scattering layer. Decode d images with the method described in Chapter 4 showed two point sources at energies of 100 keV and 662 keV are shown in Figures 74, 5. E = 662 keV (degree) (degree) 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 E = 662 keV (degree) (degree) 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Figure 7-4. The image reconstructed by decoded th e shading pattern on the bottom layer resolved with the detector array approach. On the top it was obtained from 2x104 events at 662 keV; on the bottom layer resolved with the detector array approach form 2x105 events at 662 keV.

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87 E = 100 keV (degree) (degree) 10 20 30 40 50 60 70 80 90 0 50 100 150 200 250 300 Figure 7-5. The image reconstructed by decoded the shading pattern from 2x104 events at 100 keV. E= 662 keV (degree) (degree) 20 30 40 50 60 70 170 180 190 200 210 220 230 240 250 Figure 7-6. The reconstructed image of the same two sources at 662 keV with back-projection method implemented in Compton camera approach. For incident photons at the energies of 662 keV and 100 keV, the decoded images are shown in Figures 7-4, 5 Since the decoded image of multiple point sources suffered from coincident correlation, contours of decoded image were plotted which illustrated the evolution of correlation coefficients well. Two point sources with the angular se paration of ~0.3 radians were

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88 resolved at 100 keV, but not at 662 keV, even wi th a factor of 10 increases in exposure time, due to the increase in scattering of higher energy ga mma-rays. The two point sources with separation of ~0.3 radians were not noticeably resolved at 662 keV with Compton camera approach with the back-projection method, as shown in Figure 7-6. Filtered back projection or iterative image r econstruction algorithms (such as MLEM) are needed to improve the image quality and to reso lve the two point sources reliably. To apply filtered back-projection method, we need to assu me that imaging system can be represented as 2()()(cos), (7.4)sgdgh in this formula g`( `) and g( ) were the observed and source a ngular distributions, respectively. The filtered back-projection method was implemen ted on SO(3) the group of rotations in three dimensions. Fourier Transforms and represented as 21 (7.5) 4mm ll ll GG H where 2 20 '*21 = () () 2 ()() (')() (21)()! () (cos), 4()!l mm lll lml mm ll s mm ll s mmim lll HfF Y GdgY GdgY llm YP e lm and (cos)m lP is the associated Legendr e polynomial. The kernel h(cos( )) was only a function of the angle between ` and The formula used to derived this kernel was

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89 m 0 01 m 01(,) (,) (,) 1 ,() 1 (cos), (7.6) (1 ) 2sin 2eaninin E outoutout EE eanoutout EEd L NN d inoutin inouteK e h e where 12 22 2 222 1211 if {[,]} sin coscos 2 11 () ; sin 4sin()sin()4sin 2 if {[0,][,]} d d d K d ff 0 11 0102 22 01 sin(); sin E EE d Zr dEEE is the angle between (,)inin and (,)outout ; 242 -2 -1 12 221 () ; (1cos)(1cos) = arccos(1-/2); = arccos(1-); ; f E mc m(,)eaninind is the mean distance for a photon, incident from direction (,)inin to pass before scattering; (,) outoutoutL is the attenuation-path-l ength for a scattering phot on escaping at direction (,)outout ; inoutis the solid angle of an absorbing detector ( out ) subtended by the scattering detector ( in ); N is the number of detectors.

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90 These formulae take into account the attenuation in detector for both inci dent and scattering photons at different scattering an gles and limited coverage of scattering angles [93] that corresponded to the specified locations of differ ent detectors. The filtered back-projection was implemented with the Soft 2. 0 software package [94]. ( de g ree ) (degree) 50 100 150 50 100 150 200 250 300 350 ( de g ree ) 50 100 150 50 100 150 200 250 300 350 Figure 7-7 The image reconstructed with back-pro jection method is on the left. The image on the right is obtained with filter ed back-projection method. The image reconstructed with back-projecti on method is filled with artifacts. It is understandable because in our experiment with the bench top system, the back-projection image indicated that this kernel was strongly dependent on both ` and Therefore, the image obtained with the filtered back -projection method has other miss -resolved regions as seen in Figure 7-7. To improve the quality of image, an iterativ e algorithm method was one of the choices, and has been previously applied to reconstruct th e image for Compton cameras [80]. The response function of the bench top setup to two-hit events was approximated as

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91 12 0 2 02 01 i n t 00 01 2 ,,, 21i n t022 02 0 2 0(,,,,) (,)1(,,)(,,) () (,)(,)1(,,) () (,) (,)incoh eff eff incoh ijEE xyzE EE phxyzEi EEPiEEjiEEj EE EEEEPjEEEd H EEE dEEE EE dE 0 0' 0 0 (7.7)E EEdE dE Since we were not able to distinguish which detector was interacted first among the two hit detectors, the response function of this Comp ton camera was proportional to the summation of the two cases: 1) an incident photon hit detector i first; and 2) the photon hit j first. 12 12 12 000,,,,,,,,, (7.8)ijEEijEEjiEE xyzE xyzE xyzEHHH 0(,,,,)eff x yzEi is the effective solid angle of the detector i to the point of (x, y, z) which takes into account the im pact of the geometric shape of the detector i and the energy of incident photon on the interaction probability; 0(,,)effiEEj is effective solid angle of the absorbing detector j to the detector i which takes into account the impact of the geometric shape of the detectors and the energy of incide nt photon on the interaction probability; int0(,,) PiEEj is the average probability of a photon with energy of 0EE interacting with detector i ; (,) E E is the probability of photon with actual energy of E measured as E ; int0 2(,,) PjEEE is the probability of a photon interacti ng with detector j and escap ing along the direction of 2 In our calculation, we assumed that on ly one interaction, either phot oelectric absorption or Compton scattering, occurred and located in the center of each hit detector (to account for the fact we are not utilizing position sensitive electronics). In the image reconstruction, the efficiency (Feff) of the system is needed that can be expressed as: 12 0 12,,, 0 {,,,}(,,,) (7.9)ijEE eff xyzE ijEEFxyzEH

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92 The calculated efficiency 0(,,,)effFxyzEat z = 1500 cm and E0 = 100 keV is shown in Figure 78. x (cm)y (cm) -2000 -1000 0 1000 2000 -2000 -1500 -1000 -500 0 500 1000 1500 2000 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 x 10-4 Figure 7-8. The efficiency of the hybrid camera as function of the original location of incident photons with 100 keV on XY plan at z= 1500 cm. The reconstruction image of 100 keV photons from two-hit events is shown in Figure 7-12. The two point sources were evident with the high est intensity, but artifacts were significant. Compton Camera @ 100 keV 0 500 1000 1500 -1000 -500 0 500 1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 7-9. The reconstructed image of 100 keV photons from two-hit events.

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93 Discussion In comparison with conventional hybrid gamma camera, our design has three major advantages. First, our design does not induce additional background from scattering on an inactive coded aperture mask. Seco nd, the active coded aperture allo ws us to utilize the recorded hits to improve the opaqueness of the mask elements by eliminating the ev ents with double hits (one in scattering detector and one in absorbi ng detector layer). These two advantages were inherited from active coded aperture elements th at were evaluated in 1980 for a coded aperture imager in 50 500 MeV [92]. Third, the efficien cy of the hybrid camera in our design is not affected by the attenuation of the additional coded aperture in front of the scattering detectors used in conventional hybrid imaging system. The coded aperture approach was successfu lly applied for 100 keV photons, but not for 662 keV photons. Our simulation showed that the modul ation ratios (defined as the ratio between the difference of the maximum and the minimum c ounts and the mean count) were 2 and 0.4 for 100 keV and 662 keV photons, respectively. These results suggest that the coded aperture approach is capable of finding fa inter sources at 100 keV because of more significant modulation than that at 662 keV. To compare the efficiencies of the Compton camera and coded aperture, we calculated the ratios of events with one-hit at the absorbing layer and events with two-hits of any two detectors which were found to be 0.007 and 0.2 for 100 keV and 662 keV photons, respectively. This indicates that the Compton Camera approach is applicable for photons above ~500 keV, while the coded aperture method best serves photon ener gies less than 500 keV, which was consistent with the image results presented in Figures. 7-4, 5 and 7-6. The angular resolution of this hybrid system, ~0.3 radians, can be achieved with simple back-projection reconstruction method, which wa s determined by the angular uncertainty for a

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94 single source. Advanced image reconstruction algorithms combined detail modeling improved the spatial and contrast resolutions of image further, as seen in Figure 7-9 Conclusions Our hybrid camera prototype with LaBr3(Ce) detectors was capable of serving as both imager and spectrometer in a broad energy rang e from about one hundred keV to a few MeV. The angular resolution of ~0.3 radians wa s achievable with simple back-projection reconstruction method. The cycle cross correlati on was successfully applied in constructing the image in the coded aperture approach implemen ted with one hit events. The shadow patterns used for coded aperture decoding were generated via Monte Carlo simula tion at the reasonable expense of computer time when limited directions are involved and the required angularresolution was about ~10o. The feasibility of this design wa s demonstrated by the experimental results of the bench top c onfiguration with two LaBr3:(Ce) detectors. In addition, iterative image algorithms were developed that improve d image quality significantly. In the future, we will investigate the possi bilities and advantages of applying position sensing techniques to LaBr3(Ce) detectors, such as use of a position sensitive PMT or APD. The filtered back-projection algorithm will be furthe r investigated for a prototype with increased coverage of scattering angles. Co mbining one-hit data and two-hit data will also be studied, as well as combining coded aperture and Compton images.

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95 CHAPTER 8 DESIGN OF A COMPTON IMAGING CAME RA FOR MEDICAL APPLICATIONS Introduction With development of 3D conformal delivering techniques of radiation dose, such as IMRT and IGRT approaches with medial of photon and proton beams, radiation therapy has become a more and more favored method to combine with chemotherapy and surgery in tumor control. With a sharp distal fall off in depth dose distribution, proton therapy provides a superior conformal dose compared with that of photon beams which is necessary to treat the tumor in the vicinity of critical organs, such as spinal cord, as seen in Fi gure 8-1 [110]. Due to the large gradient of dose, miss-location in dose deliveri ng leads to significant change in treatment outcomes [95, 96]. In order to assure the outcome, advanced treatment planning systems and dose verification methods are crucial. The accurate and detail physical modeling assured the accuracy and precision in the calculation of the stopping power of tissues, such as that used in Monte Carlo simulation approach that is the techni que near horizon of clin ical application [97]. However, uncertainty in dose delivering is unavoid ably induced in clinical applications from uncertainties of stopping power calculated base d on the electron density derived from CT numbers, motion of patients, patie nt setup, and etc. Verification of dose delivering during or after treatment is highly desirable but it is still an on-going research area. Gamma ray emission from patients during or after treatment can disclose the trace of the proton beam. There is a promising and ongoing re search area in which dose distribution is reconstructed after treatment with positron emission tomography (PET) by imaging nuclear reaction products of positron emitters [98]. Howe ver, recent findings showed that biological wash out effects were difficult to model and im pacted the precision of the approach with PET after treatment [99, 100, 101, and 102]. Furthermore, the work load and time-consuming

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96 acquisition process of PET limits this approach Imaging the prompt gamma emission during the treatment overcome those shortages with PET after treatment. Figure 8-1. The comparison the dose de livery with proton and photon beams. The prompt gamma rays are emitted due to inelastic scattering of protons with nuclei, neutron capture, and decay of radioisotopes generated via nucleic reaction induced by high energy protons as well known. The energy spectr um of the gamma emission is shown in Figure 8-2 and was obtained via Mont e Carlo simulation based on MCNPX 2.5. Among the photons there are many gamma lines. Two gamma ray lines of 511 keV and 2.2 MeV are particularly interesting, in that they are associated with the positron emission and neutron capture, respectively. Figure 8-2. The energy spectrum of the prom pt gamma emission induced by 200 MeV proton beam in water.

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97 Although, there is large number of photons emitted during treatment with proton beam especially for photons with energies above 1 MeV, as seen in Figure 8-3, it is challenging to image gamma rays with energies above a few hundred keV because of their penetration power. Mechanical collimators have been widely app lied for imaging photons below a few hundred keV but its efficiency decreases and angular resolution degrades as the energy of photons increasing. There is an alternative approach to image high energy photons with high efficiency and good resolution is the Compton camera approach whic h has been explored in single photon emission tomography (SPECT) and gamma-ray astrophysics. For SPECT, low Z Si material with good energy resolution is used as scattering material in order to reduce the Doppler broadening effects in imaging photons around 140 keV. For photons in high energy range, such as above 500 keV, the Doppler broadening effects are reduced a nd have insignificant impact on the angular resolution of Compton cameras because the en ergy and momentum of bounded electrons are very small compared to that of the incident photons [29]. The new scintillation material LaBr3 with high atomic number and density provides high efficiency at a reasonable thickness. Furthermor e, the good energy resolution of ~3% at 662 keV achieved in LaBr3 detectors makes LaBr3 to be a desirable material for Compton cameras. With the development of position sensing readout in scintillatio n detectors, pixelated LaBr3 crystals have been developed for the application of TOF PET by Kuhn, et al. [103, 104]. The improved precision in position sensing allows LaBr3 to be applied in the high resolution Compton cameras. High Resolution Compton Cameras for High Energy Photons In order to achieve a high resolution, pixelated LaBr3 crystals were used for scattering and absorbing detectors to reduce the uncertainty in locating scattering and absorbing positions. In our design each LaBr3 crystal module used in front layer has the size of 2.5cm x 2.5cm x 0.5cm

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98 that was segmented into 4 mm x 4 mm x 2 mm on its top to enhance the spatial resolution based on the differential response of PSPMT that receives light. Each detector in the rear layer has the size of 2.5cm x 2.5cm x 3.0cm and was segm ented into 4 mm x 4 mm x10 mm. The position resolution in locating in teraction is about 2mm laterally a nd 2.5mm vertically in the front detectors while the resolutions are 2mm and 15 mm in the rear detectors. The efficiency and angular uncertainty of this Compton camera was investigated for photons with energies of 511 keV to 2 MeV based on numerical calculation. The geometry of the detectors and distance between detectors were optimized to achieve hi gh efficiency or high angular resolution. The configuration of this design was combination of simplexes to assurance that the scattered photons have more chance observed at 25o-60o scattering angles for incident photons from the region of interested which located in the center of the camera. The sizes of detectors and pixel were shown in Figure 8-3. 2. 54 c m ~ 2 4 c m ~2.4 cm 0.4 cm 0. 5~ 1.3 c m 0.4 cm 2. 54 c m ~ 2 4 c m ~2.4 cm 0.4 cm 0. 5~ 1.3 c m 0.4 cm2. 54 c m ~ 2 4 c m ~2.4 cm 0.4 cm 0. 5~ 1.3 c m 0.4 cm ~ 2 4 c m ~2.4 cm 0.4 cm 0. 5~ 1.3 c m 0.4 cm ~ 2 4 c m ~2.4 cm 0.4 cm 0. 5~ 1.3 c m 0.4 cm Figure 8-3. The configuration of the Compton camera is on the left. The sizes of detectors and the pixel are on the right.

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99 During designing, we toke into account th e relationships betw een the geometries, efficiency, as seen in Figure 8-4, and angular uncertainty in order to optimize the thickness of crystals and separation of detectors to achieve the highest efficiency for a required angular resolution and vice versa. Th e feasibility of using LaBr3 to build Compton camera was evaluated with the experiment of a bench top setup in Chapter 6. A prototype of Compton cameras was presented and simulated. Image reconstruction al gorithms of ordered subset EM (OSEM) were applied based on physical modeling of the designed camera [53]. 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Thickness (cm)EfficiencySingle Compton Scattering 511 keV Si 511 keV LaBr3 2 MeV Si 2 MeV LaBr3 Figure 8-4. The efficiency of si ngle Compton scattering as functi on of thickness of the detector. Compton Camera Approach In general, a Compton camera approach is implemented based on the observation of the scattering of initial photons and ab sorbing of the scattered photons. Therefore, the efficiency of a Compton camera is determined by the efficiency of single Compton scat tering and the observing efficiency of the scattered photons. LaBr3 crystal as scattering dete ctor has advantages over Si

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100 (the conventional scattering material) in efficien cy of single Compton scattering at the thickness of less than 1.5 cm for photons at 511 keV (Fi gure 8-5). Above 2 MeV this efficiency advantage extends to a larger range of thickness from 0 to 3.5 cm. 0 50 100 150 200 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Scattering angle (degree)Normalized efficienc to the eak @ 2 MeV 2 MeV 511 keV Figure 8-5. The relative efficiency as function of scattering angle for LaBr3 Compton imaging system. The observed efficiency of the scattered phot ons depends on where th e absorbing detectors were placed because the probability of scatte ring depends on the scattering angle. The calculation shows that th e probability is higher for scattering angle 40o for gamma rays at 511 keV while that is more forward to 20o for 2 MeV, as seen in Figure 8-6. However, taking into account the angular fiel d of view of ~90o, the sensitivity of the efficiency to incident angles can

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101 be reduced by increasing coverage of absorbing detector. That helps to suppress the artifacts in reconstructed images, especially for low statistic (poor count) cases. The angular uncertainty in the determination scattering angle is an indicator of angular resolution that is attributed to uncertainty in pos itioning the interaction sites, uncertainty in the measurement of energies, and D oppler broadening. According to Figure 8-6, the separation of 10 cm between detectors in the same layer can assu rance that the angular un certainty induced from positioning uncertainty is less than 0.04 radian s. The angular uncertainty induced from uncertainty in energy measurement can be cons trained below 0.06 radians for 511 keV and 0.02 radians for 2 MeV gamma rays when the gamma rays are scattered with 10o to 60o, respectively, as seen in Figure 8-7. For 511-keV gamma rays, the lower limit of angular uncertainty is 0.03 radians due to the Doppler broadening effects, as shown in Figure 8-8 (the uncertainty drop above 165 degrees was attributed to truncated of energies of scattered photons above the energy of incident photons), that is 0.02 radians for 2 MeV gamma rays. 0 50 100 150 200 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Scattering angle (degree)Angular uncertainty (radian)20 cm 2 cm Figure 8-6. The angular uncertainty induced from positioning as function of the distance between detectors.

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102 0 50 100 150 200 10-2 10-1 100 101 Scattering angle (degree)Angular uncertainty (radian) 100 keV 300 keV 511 keV 1 MeV 2 MeV Figure 8-7. The angular uncertain ty induced from uncertainty in measurement of energies as function of scattering angle. Due to Doppler broadening 0 50 100 150 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Scattering angle (degree)Angular uncertainty (radian) 2.2 MeV 0.511 MeV Due to Doppler broadening 0 50 100 150 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Scattering angle (degree)Angular uncertainty (radian) 2.2 MeV 0.511 MeV Due to Doppler broadening 0 50 100 150 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Scattering angle (degree)Angular uncertainty (radian) 2.2 MeV 0.511 MeV Figure 8-8. The angular uncertainty induced from Doppler broadening.

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103 Image Reconstruction Image reconstruction algorithms applied on the Compton camera included direct back projection, filtered back proj ection and iterative approaches. The back projection approaches were usually applied to obtain angular projec tion image of emission sources in 2D when the point spread function is approximate ly independent of incident direct ion. In order to reconstruct image in 3D, iterative algorithms were conventional choices in which detail modeling of the Compton camera in physics is allowed. Expect ation maximum of likelihood (EML) method as iterative approach has been wildly used in Compton cameras [53]. The general form of imaging process in Compton cameras can be represented as 1212 121200 0 (8.1)PPEE PPEE xyzExyzE xyzEgfH An approximation of the response function of the system is represented as where P1 and P2 are the two pixels points in one or two arbitrary detectors; (E1,E2) is probability of measuring a photon with the energy of E1 at energy E2; Pabsorbing( P1,E,P2) is the absorption probability of a photon with the energy of E travelling from point P1 to P2; 1212 0 22 01 1 1 102 01 2 21 2022 02 12 01(,,,,)(,,,) (,)1(,,) () (,)(,)1(,,) () (,) (incoh Absorbing Absorbing incoh PPEE Absorbing xyzE phPxyzEPxyzPEEPPEEP EE EEEEPPEEEd H EEE PP dEE 0 0 0' 0 0 2 0 2 02 2 2 201 01 2 0 21,) (,) 1(,,,,)(,,,) (,)1(,,) () () (,)E EE EE incoh Absorbing Absorbing incohdE dE E EE dE PxyzEPxyzPEEPPEEP EE EEE PP 0 0 212 1022 2 0 0 0 1 (8.2) (,)(,)1(,,) (,) (,)E Absorbing EE phdE EEEEPPEEEd dE dEEE EE dE

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104 1(,,,)eff x yzP is effective solid angle of the pixel 1 to the point of (x, y, z) which takes into account the impact of the geometric shape of the detector, location of the two pixels, and the energy of incident photon on the interaction probability; 12(,)effPP is effective solid angle between pixel 1 and pixel 2, which takes into ac count the impact of the geometric shape of the detectors, location of the tw o pixels, and the energy of the scattered photon based on the interaction probability. In our modeling the response function, we assumed interaction located at the center of the hit pixel. The EML for the Compton camera can be represented by: However, the large size of the response matrix of Compton cameras, there is great advantage to apply list mode approach where only the observed two-hit events appeared in summation[52, 53]: Another acceleration approach in image reconstruc tion is promising is the ordered subset where the detector bins we re divided in to nG subsets {S : = 1, 2, ..., nG }. Each iteration step divided into nG sub-steps and each sub-step involving a sut-data set whose size is nG fraction of origin data set. The OSEM iteration is represented by 0 1212 1212 0 0 1212 1212 0 1212, ,1 (8.5)n xyzE PPEE PPEE n xyzE xyzE PPEE PPEES xyzE PPEESf g fH HP 0 1212 1212 00 1212 1212 1212 0 0 12121 '''''' ''' (8.3) n xyzE PPEE PPEE n xyzE xyzE PPEE PPEE n PPEE xyzE xyzExyzE PPEE xyzEf g fH H fH 0 1212 1212 0 0 1212 1212 1212 0 1212 0 12121 {:0} '''''' ''' (8.4) PPEEn xyzE PPEE PPEE n xyzExyzE PPEE PPEE n PPEEg xyzE xyzExyzE PPEE xyzEf g fH H fH 1212 01212'''''' '''PPEE n x yzExyzEPPEES xyzEPfH

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105 Results and Discussion To evaluate the validation of the investiga tion above in guild of our design, we propose a prototype design, as seen in Figur e 8-3 that is composed of two layers. Each of the layers is composed of 7 detectors of LaBr3. The thickness of the detectors in the front layer was 0.5 cm to achieve approximately 0.25 cm of spatial resolution vertically. The detectors in the rear layer have thickness of 2.54 cm to achieve high effi ciency of absorption. The separation of the detectors in the same layer was 10 cm, while the distance between the two layers was 15 cm~20 cm to reduce the angul ar uncertainty induced from the uncertainty of positioning vertically in the absorbing detector s because of their large thickness. In the image reconstruction, the efficiency of the system is n eeded that can be expressed as: 1212 0 1212(,,) (8.6)PPEE eff xyzE PPEEFxyzH It is a function of the original location and energy of incident photons, as shown in Figure 8-10 as an example of the efficiency map at XY plan of z= 15 cm for photons with energy of 511 keV with arbitrary unity because we did not normalize it. y = 10 cmz = 15 cm x y y = 10 cmz = 15 cm x y x (cm)y (cm) -2 -1 0 1 2 8 9 10 11 12 0.5 1 1.5 2 2.5 3 3.5 4 x 10-5 Figure 8-9. The point source and the Camera setup for simulation on the left. The point source reconstructed with OSEML from two-hit events on the right.

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106 x (cm)y (cm) -10 -5 0 5 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 2.62 2.64 2.66 2.68 2.7 2.72 x 106 Figure 8-10 The map of the Compton camera as f unction of the original location of incident photons on XY plan at z= 15 cm. The Simulations were conducted with Geant4 (v 4.92) toolkit where the deposited energies of two-hit events were recorded. The interaction locations were determined into individual pixel. The reconstructed image from a point source as shown in Figure 8-9 indicated that the spatial resolution at 15 cm depth is about 5mm. Since th e large size of scattering detector array, 3-D image reconstruction was proper and the 3-D imag e of a point source reco nstructed with OSEML was shown in Figure 8-11. In order to evalua te the acceleration rate with OS approach, the subset sizes of 100 and 1000 events were applied and the converge proc esses were shown in Figure 8-12. It indicated that the significant a cceleration in converge speed with smaller size of

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107 -5 0 5 5 10 15 0 0.5 1 x 10-7 -5 0 5 5 10 15 0 0.5 1 x 10-7 -5 0 5 5 10 15 0 0.5 1 x 10-7 -5 0 5 5 10 15 0 0.5 1 x 10-7 -5 0 5 5 10 15 0 1 2 x 10-7 -5 0 5 5 10 15 0 0.5 1 x 10-7 -5 0 5 5 10 15 0 0.5 1 x 10-7 x (cm) y(cm) Insensity -5 0 5 5 10 15 0 0.5 1 x 10-7 -5 0 5 5 10 15 0 0.5 1 x 10-7 slice 3 slice 2 slice 1 slice 4 slice 5 slice 6 slice 7 slice 8 slice 9 Figure 8-11. 3-D image reconstruction of a point source with OSEML algorithm. The different slices correspond to different depths. Figure 8-12. The converge seed of OSEML algorith m increased with decreasing of the size of subset.

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108 subset. Since in medical applic ation continuously distributed em ission sources we re common, we evaluated the performance of our designed camera by simulation a line source. The reconstructed images, shown in Figure 8-14, indicated that our designed camera was capable to resolve continue sources with reas onable accuracy. For 2.2 MeV photons, the image quality was degraded by poor statistics. The low efficiency in detection of high energy photons, such as 2.2 MeV, was attributed to the lower efficiency on single Compton scattering and the adjacent two-hit events generated by high energy recoiled electrons. In order to improve the efficiency and angular resolution, we may increase the number density of detectors in both scattering an d absorbing layers. x (cm)y (cm) -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 x (cm)y (cm) -10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure 8-13. The images reconstructed with OSEML algorithm for 2x107 incident photons at 511 keV on the left and 2.2 MeV on the right. The other approach is to a dd another Compton camera with the same configuration as shown in Figure 8-3. The two modules are arrange d orthogonally, as seen in Figure 8-14. This arrangement may improve the spatial resolution in the both directions of lateral and depth,

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109 because source position change along either di rection can introduce the maximum change of incident angle to either of the module. Figure 8-14. Two orthogonal Compton cameras w ith the same configuration of Figure 8-4. Conclusions The prototype Compton camera was designed base d on the considerations of the efficiency and angular uncertainty. The evaluation of this de sign with Monte Carlo s howed that imaging 0.5 2.2 MeV gammas can be achieved. The imag e reconstruction algorithm of OSEML was developed for this design and 3D image recons truction was accomplished. The OS approach did speed up the converge speed in image reconstructi on process. The spatial resolution of ~5 mm resolution was achievable at the depth of 15 cm. LaBr3 can be used in Compton camera as both scattering and absorbing detectors for imaging high energy photons. In order to improve the efficiency and angular resolution, we may increase the density of detectors in both scattering and ab sorbing layers. The other appro ach is to add another Compton

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110 camera with the same configuration but put orth ogonally that will improve the spatial resolution in the both directions of lateral and depth, as seen in Figure 8-15.

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111 CHAPTER 9 CONCLUSIONS & FUTURE WORKS Imaging and spectroscope of gamma ray have key applications for environment and medicine. The availability of LaBr3:Ce crystals with their high light yield, fast decay provides an new opportunity for developing gamma ray im agers and spectrometers with superior performance. In my dissertation, firstly, we investigated with numerical calculations of the efficiency and angular uncertainty of Co mpton cameras that may be built with LaBr3. It showed that in high energy range Compton cameras of LaBr3:Ce can achieved higher efficiency with less thickness than that of Si the c onventional material used as sca ttering material. Further more, the angular Doppler broadening effect s was significantly reduced when the energies of incident photons increased to above 500 keV that means that LaBr3:Ce is an excellent material to build Compton cameras. The relationship between the e fficiency, angular uncertainty, and geometries of detectors were presented also that could be used for optimize the geometries, such as the sizes of detector and separatio n between detectors of Compton cameras. Secondly, the feasibility of using LaBr3 in Compton cameras was evaluated with the experiment of the benchtop where LabView software controlled data acquisition card was used to sample the pulse profile from each detector and pulse height was measured online. After calibrated the energy of the benc htop with series of radioactiv e sources, the energy deposited was determined in each detector. The energy spec tra of individual detector and summation of all hit detectors were constructed. Image of a point source of Cs 137 was reconstr ucted with back-projection, filtered backprojection, iterative method of EM. Ring artifacts were evident in the image obtained with backprojection method. The filter back-projection method may apply to image systems with the response that were independent of the directions of incident p hotons. The low quality of image

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112 and artifacts in reconstructed image with filte red back-projection method was obtained. It was attributed to that the response, in our case, was significantly de pendent on incident directions because of the limited coverage of scattered pho tons observed with the absorbing detectors. Iterative method of EML did show the promis ing of good quality of reconstructed images. The angular resolution was improved from ~0.3 radians to ~ 0.1 radians. Further more the contrast resolution of the reconstructed image wa s improved also, because the remove of artifacts due to physical modeling of the camera. However, ar tifacts were still existed that was attributed to the deviation between the real camera and ap proximation in its modeling because the complex geometry of the detectors. Based on our studies of Compton cameras of LaBr3 above, a novel design of a hybrid image system was presented for the applications of environmental and ho me land security with LaBr3:Ce. This system composed of Compton camer a and coded aperture camera. In this design an angular uncertainty of ~0.3 radians was achieved. In our design we used LaBr3:Ce for both scattering and absorbing detectors. The one-hit records of the absorbing detectors were utilized for implementation of coded aperture camera in which image was decoded with cycle cross correlation method or iterative method of EM. Ag ain, the iterative did proved better image quality than that of directive decoded that was simple and fast. The two-hit events were recorded as coinci dent two hits of two detectors which were utilized for implementation of Compton cameras. To reconstruct the image, we developed the image reconstruction algorithms of simple back projection and OSLEML. With the simple back projection algorithm, the angular resolution of re construction image was similar to the angular uncertainty about 0.3 radians, while the resolution was improv ed to about 0.1 radians with

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113 OSLEML algorithm. The OSLEML method did speed up converge, but different selections of subsets may lead to local minimum because the biased sampling of data set in ordered subsets. Our hybrid camera we used so called active el ements as the coded apertures that have advantage to improve the oblique of aperture by removing the multiple hits records. Our design did not use passetive aperture in the front Compton cameras which introduced scattering background to Compton cameras as that in c onventional hybrid camera. The coded aperture image approach showed high efficiency and hi gh resolution in the detection of low energy photons in the range of about 100 keV. The Compton camera appr oach showed high efficiency and high resolution in the detection of high en ergy photons in the range of about 500 keV. Combination the two approaches allowed us to ac hieve better quality of reconstructed image at the expense computation time. Proton therapy with its capability of deliver shape dose distribution has gained more and more attention. Each year more and more Proton therapy facilities were built and planned to be built. However, the issue of verification of dose delivered became more crucial for proton therapy because the shape dose distributions. In order to address the issues we studied the interaction between proton beam and water w ith Monte Carlo simula tion (MCNPX) and found prompt gamma ray emission duri ng proton therapy treatment is closely related to energy deposition of proton beam. We pr oposed to image the gamma ray emission as means for dose verification in proton therapy in vivo. In order to achieve high spatial resolution for medical applications, we presented a novel design of Compton camera with pixelated LaBr3:Ce that allowed position sensing in each individual dete ctors and significantly reduced the angular uncertainty induce from errors in the locations of interactions. In this design spatial resolution of ~ 5mm was achieved for point sources at 15 cm depth based our Monte Carlo simulation with

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114 Geant4 toolkits. Because large ar ea of scattering detector array, the gamma ray emission sources were able reconstructed in 3-D that was achieved with image recons truction algorithm of OSEML. The combination of the design Compton camera and the developed OSLEML image reconstruction algorithm showed de sirable performance in resolving the continue sources was demonstrated with line sources. Generally, a Compton camera must be a spectrometer because the image process dependent on the energy resolution id each dete ctor in the camera. In principle, the source distributions in space and energy can be reconstruc ted. In deed, the response functions of the Compton image systems depended on the ener gy of incident photons. Therefore, the simultaneous reconstruction of the image and energy spectrum of ga mma ray sources was straight forward with the algorithm of OSLEML. However, the high dimension of response matrixes and their huge sizes made this simulta neous approach difficult and time consuming. With the development of computer architectures, this difficulty may be solved with application GPC or cell machine etc. Although it was difficult, it was still worth to de velop this simultaneous approach, because this approach was required form applications where the energies of incident photons were unknown, such as gamma em ission in proton therapy treatment. For high resolution applications, position sensi ng in each individual de tector was critical. The pixelated LaBr3:Ce was the one possible approach to achieved the position sensing. The mircocolumn LaBr3:Ce may be another promising appro ach to achieve po sition sensing.

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115 APPENDIX A CODES FOR HYBRID CAMERA IN GEANT #include #include #include "DetectorConstruction.hh" #include "DetectorMessenger.hh" #include "G4Material.hh" #include "G4Box.hh" #include "G4Tubs.hh" #include "G4LogicalVolume.hh" #include "G4PVPlacement.hh" #include "G4PVReplica.hh" #include "G4UniformMagField.hh" #include "G4GeometryManager.hh" #include "G4PhysicalVolumeStore.hh" #include "G4LogicalVolumeStore.hh" #include "G4SolidStore.hh" #include "G4MultiFunctionalDetector.hh" #include "G4SDManager.hh" #include "G4VisAttributes.hh" #include "G4Colour.hh" //========================== ================== ============= DetectorConstruction::D etectorConstruction() :ScatterMaterial(0),AbsorberMaterial(0),GapMaterial(0),defaultMaterial(0),

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116 solidWorld(0),logicWorld(0),physiWorld(0), solidCamera(0),logicCamera(0),physiCamera(0), solidLayer(0),logicLay er(0),physiLayer(0), solidScatter(0), solidAbsorber(0),solidGap (0),logicGap (0),physiGap (0), magField(0) { // default parameter values of the Cameraimeter AbsorberThickness = 2.54 *cm; AbsorberRadius = 2.54/2 *cm; ScatterThickness = 1.3 *cm; ScatterRadius = 2.54/2 *cm; Distance_Z = 30. *cm; Distance_Y = AbsorberRadius*5; GapThickness = 60.0*cm; NbOfLayers = 1; NbOfScatters = 40; NbOfAbsorbers = 100; CameraSizeXY = (ScatterRadius*8 + AbsorberRadius*10)*2; ComputeCameraParameters(); // materials DefineMaterials(); SetScatterMaterial( "LaBr3");

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117 SetAbsorberMaterial( "LaBr3" ); SetGapMaterial( "Air" ); // create commands for interactive definition of the Cameraimeter detectorMessenger = new DetectorMessenger(this); } //========================== ================== ============= DetectorConstruction::~DetectorConstruction() { delete detectorMessenger;} //========================== ================== ============= G4VPhysicalVolume* Detector Construction::Construct() { return ConstructCameraimeter(); } //========================== ================== ============= void DetectorConstruction::DefineMaterials() { //This function illustrates the possi ble ways to define materials G4String symbol; //a=mass of a mole; G4double a, z, density; //z=mean number of protons;

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118 G4int iz, n; //iz=number of protons in an isotope; // n=number of nucle ons in an isotope; G4int ncomponents, natoms; G4double abundance, fractionmass; // // define Elements G4Element* H = new G4Element( "Hydrogen" ,symbol= "H" z= 1., a= 1.01*g/mole); G4Element* C = new G4Element( "Carbon" ,symbol= "C" z= 6., a= 12.01*g/mole); G4Element* N = new G4Element( "Nitrogen" ,symbol= "N" z= 7., a= 14.01*g/mole); G4Element* O = new G4Element( "Oxygen" ,symbol= "O" z= 8., a= 16.00*g/mole); G4Element* Si = new G4Element("Silicon" ,symbol= "Si" z= 14., a= 28.09*g/mole); G4Element* Br = new G4Element( "Bromine",symbol= "Br" z= 35., a= 79.904*g/mole); G4Element* La = new G4Element( "Lanthanum" ,symbol= "La" z= 57., a= 138.90547*g/mole); // // define simple materials new G4Material("Aluminium" z=13., a=26.98*g/mole, density=2.700*g/cm3); new G4Material("liquidArgon" z=18., a= 39.95*g/mole, density= 1.390*g/cm3); new G4Material("Lead" z=82., a= 207.19*g/mole, density= 11.35*g/cm3); // // define a material from elements. case 1: chemical molecule G4Material* LaBr3 = new G4Material("LaBr3",density= 5.300*g/cm3, ncomponents=2); LaBr3->AddElement(La, natoms=1);

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119 LaBr3->AddElement(Br natoms=3); // define a material from elements. case 2: mixture by fractional mass // G4Material* Air = new G4Material("Air" density= 1.290*mg/cm3, ncomponents=2); Air->AddElement(N, fractionmass=0.7); Air->AddElement(O, fractionmass=0.3); // vacuum G4Material* Vacuum = new G4Material("Galactic" z=1., a=1.01*g/mole,density= universe_mean_density, kStateGas, 2.73*kelvin, 3.e-18*pascal); G4Material* beam = new G4Material("Beam" density= 1.e-5*g/cm3, ncomponents=1, kStateGas, STP_Temperature, 2.e-2*bar); beam->AddMaterial(Air, fractionmass=1.); G4cout << *(G4Material::GetMaterialTable()) << G4endl; //default materials of the World defaultMaterial = Air; ScatterMaterial = LaBr3; AbsorberMaterial = LaBr3; } // ================ ========================= ================

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120 G4VPhysicalVolume* DetectorConstruction::ConstructCameraimeter() { G4double pi=3.14159265; // Clean old geometry, if any // G4GeometryManager::GetInstance()->OpenGeometry(); G4PhysicalVolumeStore::GetInstance()->Clean(); G4LogicalVolumeStore::GetInstance()->Clean(); G4SolidStore::GetInstance()->Clean(); // complete the Camera parameters definition ComputeCameraParameters(); // // World // solidWorld = new G4Box( "World" //its name Worl dSizeXY/2,WorldSizeXY/2,WorldSizeZ/2); //its size logicWorld = new G4LogicalVolume(solidWorld, //its solid defaultMaterial, //its material "World" ); //its name physiWorld = new G4PVPlacement(0, //no rotation G4ThreeVector(), //at (0,0,0)

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121 logicWorld, //its logical volume "World" //its name 0, //its mother volume true, //no boolean operation 0); //copy number // // Camera solidCamera=0; logicCamera=0; physiCamera=0; if (CameraThickness > 0.) { solidCamera = new G4Box("Cameraimeter" //its name CameraSizeXY/2,CameraSizeXY/2, CameraThickness/2); //size logicCamera = new G4LogicalVolume(solidCamera, //its solid defaultMaterial, //its material "Cameraimeter" ); //its name physiCamera = new G4PVPlacement(0, //no rotation G4ThreeVector(0,0,WorldSizeZ/2-CameraThickness/2), //at (0,0,0) logicCamera, //its logical volume "Cameraimeter" //its name logicWorld, //its mother volume true, //no boolean operation 0); //copy number }

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122 // // Scatter if (ScatterThickness > 0.) { solidScatter = new G4Tubs( "Scatter", //its name 0.0, ScatterRadius, Scatte rThickness/2,0.0,2*pi); //size G4int PS[40]= { 1, 4, 6, 9, 11, 12, 16, 17, 20, 21, 25, 26, 28, 31, 33,

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123 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 49, 51, 54, 56, 57, 61, 62, 65, 66, 70, 71, 73, 76,

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124 78, 81}; G4int iy; G4int ix; for(size_t i=0;i<40;i++) { char IDS[20]; sprintf(IDS, "%d" ,i+1); logicScatter[i] = new G4LogicalVolume(solidScatter, //its solid ScatterMaterial, //its material IDS); //its name iy=ceil(PS[i]/9); ix=PS[i]-9*(iy); G4cout<< "Xs= << 2.5*ScatterRadius*(ix)-2.5*ScatterRadius*4<< Ys= <<2.5*ScatterRadius*(iy)-2 .5*ScatterRadius*4.5<< Zs = <
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125 true, //no boulean operat 0); //copy number } } // // Absorber if (AbsorberThickness > 0.) { char IDA[20]; solidAbsorber = new G4Tubs( "Absorber", //its name 0.0, AbsorberRadius, AbsorberThickness/2,0.0,2*pi); G4int ii=100; for(int i=0;i<10;i++) { for(size_t j=0;j<10;j++) { sprintf(IDA,"%d" ,ii); ii++; logicAbsorber[i*10+j] = new G4LogicalVolume(solidAbsorber, //its solid AbsorberMaterial, //its material AbsorberMaterial->GetName()); //name

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126 G4cout<< Xa= "<< 2.5*AbsorberRadius*(i)-2 .5*ScatterRadius*4.5<< Ya=" <<2.5*AbsorberRadius*(j)-2 .5*ScatterRadius*4.5<<" Za = <SetVisAttributes (G4VisAttributes::Invisible); G4VisAttributes* simpleBoxVisAtt= ne w G4VisAttributes(G4Colour(1.0,1.0,1.0)); simpleBoxVisAtt->SetVisibility(false);

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127 logicCamera->SetVisAttributes(simpleBoxVisAtt); // with the interactive expansion / contraction geometry system of the // vis/OpenInventor driver : {G4VisAttributes* simpleBoxVisAtt= new G4VisAttributes(G4Colour(0.5,1.0,0.15)); simpleBoxVisAtt->SetVisibility(false); logicCamera->SetVisAttributes(simpleBoxVisAtt);} {G4VisAttributes* atb= new G4 VisAttributes(G4Colour(1.0,.5,0.1)); atb->SetForceSolid(true); for(int i=0;i<40;i++) { logicScatter[i]->SetVisAttributes(atb); } } {G4VisAttributes* atb= new G4Vi sAttributes(G4Colour(0.5,2.0,0.1)); atb->SetForceSolid(true); for(int i=0;i<100;i++) { logicAbsorber[i]->SetVisAttributes(atb); } } // return physiWorld; }

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128 //========================== ================== ============= void DetectorConstruction ::PrintCameraParameters() { G4cout << "\n----------------------------------------------------------" << "\n---> The camera is << NbOfScatters << scatters of: [ << ScatterThickness/mm << "mm of << ScatterMaterial->GetName() << + << NbOfAbsorbers<< absorbers of: [" <GetName() << "\n---------------------------------------------------------\n" ; } //========================== ================== ============= void DetectorConstruction::SetScatte rMaterial(G4String materialChoice) { // search the material by its name G4Material* pttoMaterial = G4Material::GetMaterial(materialChoice); if (pttoMaterial) ScatterMaterial = pttoMaterial; } //========================== ================== ============= void DetectorConstruction::SetAbsorberMaterial(G4String materialChoice) { // search the material by its name G4Material* pttoMaterial = G4Material::GetMaterial(materialChoice);

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129 if (pttoMaterial) AbsorberMaterial = pttoMaterial; } //========================== ================== ============= void DetectorConstruction::SetGapM aterial(G4String materialChoice) { // search the material by its name G4Material* pttoMaterial = G4Material::GetMaterial(materialChoice); if (pttoMaterial) GapMaterial = pttoMaterial; } //========================== ================== ============= void DetectorConstruction::Set ScatterThickness(G4double val) { // change Scatter thickness and recompute the Cameraimeter parameters ScatterThickness = val; } //========================== ================== ============= void DetectorConstruction::Set AbsorberThickness(G4double val) { // change Absorber thickness and reco mpute the Cameraimeter parameters AbsorberThickness = val; } //========================== ================== ============= void DetectorConstruction::S etGapThickness(G4double val)

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130 { // change Gap thickness and recompute the Cameraimeter parameters GapThickness = val; } //========================== ================== ============= void DetectorConstruction::S etCameraSizeXY(G4double val) { // change the transverse size and reco mpute the Cameraimeter parameters CameraSizeXY = val; } //========================== ================== =============. void DetectorConstruction::S etNbOfLayers(G4int val) { NbOfLayers = val; } //========================== ================== ============= #include "G4FieldManager.hh" #include "G4TransportationManager.hh" void DetectorConstruction::Set MagField(G4double fieldValue) { //apply a global uniform magnetic field along Z axis G4FieldManager* fieldMgr = G4TransportationManager::GetTrans portationManager()->GetFieldManager();

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131 if(magField) delete magField; //delete the existing magn field if(fieldValue!=0.) // create a new one if non nul { magField = new G4UniformMagField(G4ThreeVector(0.,0.,fieldValue)); fieldMgr->SetDetectorField(magField); fieldMgr->CreateChordFinder(magField); } else { magField = 0; fieldMgr->SetDetectorField(magField); } } //========================== ================== ============= #include "G4RunManager.hh" void DetectorConstructi on::UpdateGeometry() { G4RunManager::GetRunManager()->Define WorldVolume(Construc tCameraimeter()); }

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132 APPENDIX B CODES FOR COMPTON CAMER IN GEANT #include #include #include "DetectorConstruction.hh" #include "DetectorMessenger.hh" #include "G4Material.hh" #include "G4Box.hh" #include "G4Tubs.hh" #include "G4LogicalVolume.hh" #include "G4PVPlacement.hh" #include "G4PVReplica.hh" #include "G4UniformMagField.hh" #include "G4GeometryManager.hh" #include "G4PhysicalVolumeStore.hh" #include "G4LogicalVolumeStore.hh" #include "G4SolidStore.hh" #include "G4MultiFunctionalDetector.hh" #include "G4SDManager.hh" #include "G4VisAttributes.hh" #include "G4Colour.hh" //========================== ================== =============

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133 DetectorConstruction::D etectorConstruction() :ScatterMaterial(0),AbsorberMaterial(0),GapMaterial(0),defaultMaterial(0), solidWorld(0),logicWorld(0),physiWorld(0), solidCamera(0),logicCamera(0),physiCamera(0), solidLayer(0),logicLay er(0),physiLayer(0), solidScatterPixel(0), solidAbsorberPixel(0),solidGap (0),logicGap (0),physiGap (0) { // default parameter values of the Cameraimeter N_X_Pixel_Abs = 6; N_Y_Pixel_Abs = 6; N_X_Pixel_Scat =6; N_Y_Pixel_Scat =6; NbOfAbsorbers = 7; NbOfScatters= 7; AbsorberThickness = 2.54 *cm; AbsPixelThickness = AbsorberThickness; AbsPixelSizeXY = 0.4 *cm; AbsorberSizeXY = AbsPixelSizeXY*N_X_Pixel_Abs; ScatterThickness = 0.5 *cm; ScatPixelThickness = ScatterThickness; ScatPixelSizeXY = 0.4 *cm; ScatterSizeXY = ScatPixelSizeXY*N_X_Pixel_Scat;

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134 Distance_Z = 15.0 *cm; Distance_Scatter = 10.0 *cm; Distance_Absorber = 10.0 *cm; GapThickness = 30.0*cm; NbOfAbs_Pixel = N_X_Pixel_Abs*N_X_Pixel_Abs*NbOfAbsorbers; NbOfScat_Pixel = N_X_Pi xel_Scat*N_X_Pixel_Scat*NbOfScatters; CameraSizeXY = Distance_Scatter*3; CameraThickness = 1.2*(ScatterT hickness + AbsorberThickness+Distance_Z); ComputeCameraParameters(); // materials DefineMaterials(); SetScatterMaterial( "LaBr3"); SetAbsorberMaterial( "LaBr3" ); SetGapMaterial( "Air" ); // create commands for interactive definition of the Cameraimeter detectorMessenger = new DetectorMessenger(this); } //========================== ================== ============= DetectorConstruction::~DetectorConstruction() { delete detectorMessenger;} //========================== ================== ============= G4VPhysicalVolume* Detector Construction::Construct() {

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135 return ConstructCamera(); } //========================== ================== ============= void DetectorConstruction::DefineMaterials() { //This function illustrates the possi ble ways to define materials G4String symbol; //a=mass of a mole; G4double a, z, density; //z=mean number of protons; G4int iz, n; //iz=number of protons in an isotope; // n=number of nucleons in an isotope; G4int ncomponents, natoms; G4double abundance, fractionmass; // // define Elements G4Element* H = new G4Element( "Hydrogen" ,symbol= "H" z= 1., a= 1.01*g/mole); G4Element* C = new G4Element( "Carbon" ,symbol= "C" z= 6., a= 12.01*g/mole); G4Element* N = new G4Element( "Nitrogen" ,symbol= "N" z= 7., a= 14.01*g/mole); G4Element* O = new G4Element( "Oxygen" ,symbol= "O" z= 8., a= 16.00*g/mole); G4Element* Si = new G4Element("Silicon" ,symbol= "Si" z= 14., a= 28.09*g/mole); G4Element* Br = new G4Element( "Bromine",symbol= "Br" z= 35., a= 79.904*g/mole); G4Element* La = new G4Element( "Lanthanum" ,symbol= "La" z= 57., a= 138.90547*g/mole); new G4Material("Aluminium" z=13., a=26.98*g/mole, density=2.700*g/cm3); G4Material* LaBr3 =

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136 new G4Material("LaBr3",density= 5.300*g/cm3, ncomponents=2); LaBr3->AddElement(La, natoms=1); LaBr3->AddElement(Br natoms=3); // define a material from elements. case 2: mixture by fractional mass G4Material* Air = new G4Material("Air" density= 1.290*mg/cm3, ncomponents=2); Air->AddElement(N, fractionmass=0.7); Air->AddElement(O, fractionmass=0.3); // define a material from elements and/or others materials (mixture of mixtures) G4Material* Aerog = new G4Material("Aerogel" density= 0.200*g/cm3, ncomponents=3); Aerog->AddMaterial(SiO2, fractionmass=62.5*perCent); Aerog->AddMaterial(H2O fractionmass=37.4*perCent); Aerog->AddElement (C fractionmass= 0.1*perCent); // vacuum G4Material* Vacuum = new G4Material("Galactic" z=1., a=1.01*g/mole,density= universe_mean_density, kStateGas, 2.73*kelvin, 3.e-18*pascal); G4Material* beam = new G4Material("Beam" density= 1.e-5*g/cm3, ncomponents=1, kStateGas, STP_Temperature, 2.e-2*bar); beam->AddMaterial(Air, fractionmass=1.); G4cout << *(G4Material::GetMaterialTable()) << G4endl;

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137 //default materials of the World defaultMaterial = Air; ScatterMaterial = LaBr3; AbsorberMaterial = LaBr3; } //========================== ================== ============= G4VPhysicalVolume* DetectorConstruction::ConstructCamera() { G4double pi=3.14159265; // Clean old geometry, if any // G4GeometryManager::GetInstance()->OpenGeometry(); G4PhysicalVolumeStore::GetInstance()->Clean(); G4LogicalVolumeStore::GetInstance()->Clean(); G4SolidStore::GetInstance()->Clean(); // World // solidWorld = new G4Box( "World" //its name Worl dSizeXY/2,WorldSizeXY/2,WorldSizeZ/2); //its size logicWorld = new G4LogicalVolume(solidWorld, //its solid defaultMaterial, //its material "World" ); //its name physiWorld = new G4PVPlacement(0, //no rotation

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138 G4ThreeVector(), //at (0,0,0) logicWorld, //its logical volume "World", //its name 0, //its mother volume true, //no boolean operation 0); //copy number // Cameraimeter solidCamera=0; logicCamera=0; physiCamera=0; if (CameraThickness > 0.) { solidCamera = new G4Box("Camera", //its name CameraSizeXY/2,CameraSizeXY/2, CameraThickness/2); //size logicCamera = new G4LogicalVolume(solidCamera, //its solid defaultMaterial, //its material "Camera" ); //its name physiCamera = new G4PVPlacement(0, //no rotation G4ThreeVector(0,0,0), //at (0,0,0) logicCamera, //its logical volume "Camera", //its name logicWorld, //its mother volume true, //no boolean operation 0); //copy number } //

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139 // Scatter // G4double xp,yp,zp; G4int i_Pixel_Scat=0; char IDS[20]; G4double XScat, YScat, ZScat; ZScat = -CameraThickness/2 + ScatPixelThickness/2; if (ScatterThickness > 0.) { solidScatterPixel = new G4Box( "Scatter" //its name ScatPi xelSizeXY/2, ScatPixelSize XY/2,ScatPixelThickness/2); //size for(size_t i_Scat=0; i_Scat < NbOfScatters;i_Scat++) { if (i_Scat>0) { XScat=Distance_ Scatter*cos(pi/3*i_Scat); YScat=Distance_Scatter*sin(pi/3*i_Scat); } else { XScat=0.0; YScat=0.0; }

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140 XScat= -ScatterSizeXY/2 + XScat + ScatPixelSizeXY/2; YScat= -ScatterSizeXY/2 + YScat + ScatPixelSizeXY/2; for(size_t ix=0; ix < N_X_Pixel_Scat;ix++) { for(size_t iy=0; iy < N_Y_Pixel_Scat;iy++) { sprintf(IDS, "%d" ,i_Pixel_Scat+1); logicScatter[i_Pixel_Scat] = new G4LogicalVolume(solidScatterPixel, //its solid ScatterMaterial, //its material IDS); //its name xp= XScat + ix*ScatPixelSizeXY*1.001; yp= YScat + iy*ScatPixelSizeXY*1.001; zp= ZScat; G4cout<< "Xs= << xp/mm << Ys= << yp/mm << Zs = <
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141 } } } // // Absorber // if (AbsorberThickness > 0.) { G4int i_Pixel_Abs=0; char IDA[20]; G4double XAbs, YAbs, ZAbs; ZAbs = ZScat + Distance_Z; solidAbsorberPixel = new G4Box("Absorber" //its name AbsPixelSizeXY/2, AbsPixelSizeXY/2, AbsPixelThickness/2); for(size_t i_Abs=0; i_Abs0) { XAbs=Distance_Absorber*cos(pi/3*i_Abs); YAbs=Distance_Absorber*sin(pi/3*i_Abs); } else {

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142 XAbs=0.0; YAbs=0.0; } XAbs= -AbsorberSizeXY/2 + XAbs + AbsPixelSizeXY/2; YAbs= -AbsorberSizeXY/2 + YAbs + AbsPixelSizeXY/2; for(size_t ix=0; ix GetName()); //name xp= XAbs + 1.001*AbsPixelSizeXY*ix; yp= YAbs + 1.001*AbsPixelSizeXY*iy; zp= ZAbs; G4cout<<" Ya= << xp/mm << Ya="<
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143 0); //copy number i_Pixel_Abs++; } } } } PrintCameraParameters(); // Visualization attributes // logicWorld->SetVisAttributes (G4VisAttributes::Invisible); G4VisAttributes* simpleBoxVisAtt= ne w G4VisAttributes(G4Colour(1.0,1.0,1.0)); simpleBoxVisAtt->SetVisibility(false); logicCamera->SetVisAttributes(simpleBoxVisAtt); {G4VisAttributes* simpleBoxVisAtt= new G4VisAttributes(G4Colour(0.5,1.0,0.15)); simpleBoxVisAtt->SetVisibility(false); delete logicCamera->GetVisAttributes(); logicCamera->SetVisAttributes(simpleBoxVisAtt);} {G4VisAttributes* atb= new G4 VisAttributes(G4Colour(1.0,.5,0.1)); atb->SetForceSolid(true); for(int i=0;iSetVisAttributes(atb); }

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144 } {G4VisAttributes* atb= new G4Vi sAttributes(G4Colour(0.5,2.0,0.1)); atb->SetForceSolid(true); for(int i=0;iSetVisAttributes(atb); } } return physiWorld; } //========================== ================== ============= void DetectorConstruction ::PrintCameraParameters() { G4cout << "\n----------------------------------------------------------" << "\n---> The camera is << NbOfScat_Pixel << scatter pixels of: [ << ScatterThickness/mm << "mm of << ScatterMaterial->GetName() << + << NbOfAbs_Pixel<<" absorber pi xels of: [" <GetName() << "\n---------------------------------------------------------\n" ; } //========================== ================== =============

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145 void DetectorConstruction::SetScatte rMaterial(G4String materialChoice) { // search the material by its name G4Material* pttoMaterial = G4Material::GetMaterial(materialChoice); if (pttoMaterial) ScatterMaterial = pttoMaterial; } //========================== ================== ============= void DetectorConstruction::SetAbsorberMaterial(G4String materialChoice) { // search the material by its name G4Material* pttoMaterial = G4Material::GetMaterial(materialChoice); if (pttoMaterial) AbsorberMaterial = pttoMaterial; } //========================== ================== ============= void DetectorConstruction::SetGapM aterial(G4String materialChoice) { // search the material by its name G4Material* pttoMaterial = G4Material::GetMaterial(materialChoice); if (pttoMaterial) GapMaterial = pttoMaterial; } //========================== ================== ============= void DetectorConstruction::S etCameraSizeXY(G4double val) {

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146 // change Scatter thickness and recompute the Cameraimeter parameters CameraThickness = val; } //========================== ================== ============= void DetectorConstruction::Set ScatterThickness(G4double val) { // change Scatter thickness and recompute the Cameraimeter parameters ScatterThickness = val; } //========================== ================== ============= void DetectorConstruction::Set AbsorberThickness(G4double val) { // change Absorber thickness and reco mpute the Cameraimeter parameters AbsorberThickness = val; } //========================== ================== ============= void DetectorConstruction::S etGapThickness(G4double val) { // change Gap thickness and recompute the Cameraimeter parameters GapThickness = val; } //========================== ================== ============= void DetectorConstruction::SetScatterDistance(G4double val)

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147 { // change the transverse size and reco mpute the Cameraimeter parameters Distance_Scatter = val; } void DetectorConstruction::Set AbsoberDistance(G4double val) { // change the transverse size and reco mpute the Cameraimeter parameters Distance_Absorber = val; } //========================== ================== ============= #include "G4RunManager.hh" void DetectorConstructi on::UpdateGeometry() { G4RunManager::GetRunManager()->De fineWorldVolume(ConstructCamera()); }

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148 APPENDIX C AN EXAMPLE OF IMAGE RECONSTRUCTION CODES global E_LaBr3 Tot_w_LaBr3 ph_ab_LaBr3 density_LaBr3 Height_A Height_S f0 NDetectors V_Detector V_Center width_X width_Y NB NBZ V4 global xs ys zs NbOfScatters Height _S Height_A XYZ Part1_S Part1_A global N1 N2 E1 E2 NbOfEvents_OS [E_LaBr3 Coh_LaBr3 Incoh_LaBr3 ph_ab_LaB r3 Nu_p_LaBr3 Ele_p_LaBr3 Tot_w_LaBr3 Tot_wo_LaBr3]=textread( 'LaBr3_ph.m' '%f %f %f %f %f %f %f %f' 94); [N01 E01 N02 E02]=textread( 'line_2.2MeV_2' '%d %f %d %f' 2000000); N1=N01; N2=N02; E1=E01; E2=E02; NEV=numel(N1); NbOfScatters=252; density_LaBr3=5.2; NbOfAbsorbers = 7; N_iterative=20; width_X=6*0.4; width_Y=6*0.4; NDetectors=252*2; Height_A=2.54; Height_S=1.3; V4=[[width_X/2, width_Y/2,0]

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149 [-width_X/2, width_Y/2,0] [-width_X/2,-width_Y/2,0] [ width_X/2,-width_Y/2,0]]; [Vscat Vabs V_Center]=Dposition(); V_Detector=[Vscat Vabs]; E_Source=2200/1000; LX=20.; LY=20.; LZ=5.; NB=51; NBZ=1; f=zeros(NB,NB,NBZ)+1; f0=f; ff=zeros(N_iterative,NB,NB,NBZ); SUM1=zeros(NB,NB,NBZ); NN=floor(NB/2); NNZ=floor(NBZ/2) xs=[-NN:NN]*LX/NB; ys=[-NN:NN]*LY/NB; zs=Vscat(1,3)-15+[-NNZ:NNZ]*LZ/NBZ; XYZ=zeros(NB*NB*NBZ,3); ii=1;

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150 for iz=1:NBZ for iy=1:NB for ix=1:NB XYZ(ii,:)=[xs(ix),ys(iy),zs(iz)]; ii=ii+1; end end end SUM1=real(SUM_DEN(E_Source)) [P_Scat1 P_Abs1]=SUM_32P1(E_Source); ND=find(abs(ceil(N01/36 )-ceil(N02/36))>=1); N1=N01(ND); N2=N02(ND); E1=E01(ND); E2=E02(ND); NbOfEvents=numel(ND); NbOfOsEV=1000; NbOfSet=floor(NbOfEvents/NbOfOsEV); Part1_S=P_Scat1(ND,:); Part1_A=P_Abs1(ND,:); T_total=0.0; for I_iterative=1:N_iterative for i_Set=1:NbOfSet

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151 NbOfEvents_OS=NbOfOsEV; Index_Start=(i_Set-1).*NbOfOsEV+1; Index_End=i_Set.*NbOfOsEV+1; Part1_S=P_Scat 1(ND(Index_Start:Index_End),:); Part1_A=P_Abs1 (ND(Index_Start:Index_End),:); N1=N01(ND(Index_Start:Index_End)); N2=N02(ND(Index_Start:Index_End)); E1=E01(ND(Index_Start:Index_End)); E2=E02(ND(Index_Start:Index_End)); SUM32=SUM_32P2_OS(E_Source) f=f0./SUM1.*SUM32; f0=f.*NbOfOsEV./sum(sum(sum(f))) end DF(I_iterative)=sum(sum(sum(abs(f-f00)))); f00=f; ff(I_iterative,:,:,:)=f; T_total=T_total+toc; end

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152 APPENDIX D AN EXAMPLE OF RESPONSE MATRIXES GENERATION CODES function Coeff=SUM_DEN(E_Source) global V_Detector E0 E_LaBr3 NB NBZ xs ys zs Tot_w_LaBr3 ph_ab_LaBr3 density_LaBr3 Radius Height_A Height_S V_Center global J_Br_Q J_La_Q Q XYZ NbOfSca tters width_X width_Y V_Second mc2=0.511; sc=137.0387; width=width_X; NEB=10; Nf=9; Coeff=zeros(NB,NB,NBZ); D1=[36:36:252]-18; D2=D1+252; D=[D1,D2]; mu_s_in=mu(E_Source); for i=1:14-1 j0=i+1; for j=j0:14 IEE=1; while IEE<3 if IEE==1 i_Scat=D(i); i_Sec=D(j);

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153 else i_Scat=D(j); i_Sec=D(i); end IEE=IEE+1; V_ Scatter=V_Center(ceil(i_Scat/36),:); V_S econd=V_Center(ceil(i_ Sec/36),:); if i_Scat
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154 LSA=PassLengthNDE(V1,V2,ID); Ls_out = LSA(1); La_in = LSA(2); VSout=V_Second-V_Scatter; Ls_in=PassLengthN3DNDE(V_Scatter,i_Scat); P_S_in=exp(-mu_s_in.*Ls_in).*(Ls_in>0)+(1-exp(mu_s_in.*height_scat)).*(Ls_in==0); VSin=[V_Scatte r(1)-XYZ(:,1),V_Scatter(2)-XYZ(: ,2),V_Scatter(3)-XYZ(:,3)]; VSinMVSout=[VSin (:,1)*VSout(1),VSin(:,2)*VSout(2),VSin(:,3)*VSout(3)]; cos_theta_S=(sum(VSi nMVSout,2)./sqrt(sum(VSin.*VSin,2).*sum(VSout.*VSout))); alpha0=E_Source/.511; Nff=find(cos_theta_S==1); if numel(Nff)>0 cos_theta_S(Nff)=0.99999; end er=1.0./(1+alpha0.*(1-cos_theta_S)); E_Scat=E_Source.*er; P1=sqrt(E_Source.*E_Source+E_Scat.*E_Scat +2.0*E_Source.*E_Scat.*cos_theta_S); pz=-(E_Source-E_Scat-E_Source.*E_Scat.*(1-cos_theta_S)/mc2)./P1; q=abs(pz*sc); NS=find(q<=100); NL=find(q>100);

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155 J(NS)= interp1q(Q',J_La_Q',q(NS))+ 3. *interp1q(Q',J_Br_Q',q(NS)); J(NL) = 0.0; st=sin(acos(cos_theta_S)); ver=1./er; sigma_KN_DB= er.*er.*(er+ver-st.*st).*E_Source./P1.*J'./E_Scat; CrossS=sigma_KN_DB.*st/19.0; mu_s_out=mu(E_Scat); P_S_out=exp(-mu_s_out.*Ls_out); P_A_in=exp(-mu_s_out.*La_in).*(La_in>0)+(1-exp(mu_s_out.*height_sec)).*(La_in==0); E000=E_Scat; alpha=E000/.511; height=height_scat; Dist_sqoo=sum(VSin.*VSin,2); cos_theta_inoo=(VSin(:,3)./sqrt(Dist_sqoo)); Omiga_Top=width*height*sqrt(1-cos_theta_inoo.*cos_theta_inoo); Omiga_Side=width*width*abs(cos_theta_inoo); Omiga_in=(Omiga_Top+Omiga_Side)*36./Dist_sqoo; %-----------------------------------------------------------------height=height_sec; Vin=V_Second-V_Scatter; Dist_sq=sum(Vin.*Vin); cos_theta_in=(Vin(:,3)/sqrt(Dist_sq));

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156 Omiga_Side=width.*height.*sqrt(1-cos_theta_in.*cos_theta_in); Omiga_Top=width.*width.*abs(cos_theta_in); Om iga_out=(Omiga_Top+Omig a_Side)*36./Dist_sq; Part1=P_S_out.*P_A_in.*Omiga_out; E02=zeros(NB*NB*NBZ,NEB); for ieng=1:NEB Eo2(:,ieng)=ieng.*E_Scat/NEB; end for m=1:NEB E_Sec=Eo2(:,m); E_out=E_Scat-E_Sec; Vp=(E_Scat./(1+2*alpha)<=E_out).*(E_out0 E00=E_Scat(NP); E_outp=E_out(NP); alphap=alpha(NP); cos_theta_A_out0=1.-(E00-E_outp)./(E_outp.*alphap); theta_A_out0=acos(cos_theta_A_out0); CrossS_Sec0=DBKNN(the ta_A_out0,E00,E_outp); DV=sqrt(sum(VSout.*VSout)); theta_p=acos(VSout(3)./DV); DD=sqrt(VSout(1)*VSout(1)+VSout(2)*VSout(2));

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157 if DD==0 phi_p=0.0; else cos_phi_p=VSout(1)./DD; phi_p=acos(cos_phi_p); phi_p=phi_p.*(VSout(2)>=0)+ (2*pi-phi_p).*(VSout(2)<0); end NNP=numel(NP); phi_pV=zeros(NNP,1); theta_pV=zeros(NNP,1); phi_pV(:,1)=phi_p; theta_pV(:,1)=theta_p; [theta_A_out,phi_A_out]= angleprojectN(Nf,t heta_A_out0,theta_pV,phi_pV); phi_A_out=phi_A_out/180*pi; XA=sin(theta_A_out).*cos(phi_A_out); YA=sin(theta_A_out).*sin(phi_A_out); ZA=cos(theta_A_out); IDp=zeros(NNP,Nf,1); V1p=zeros(NNP,Nf,3); V2=[XA,YA,ZA]; for ii=1:Nf V1p(:,ii,1)=V_Second(1); V1p(:,ii,2)=V_Second(2);

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158 V1p(:,ii,3)=V_Second(3); IDp(:,ii)=i_Sec; end V1=reshape(V1p,NNP*Nf,3); ID=reshape(IDp,NNP*Nf,1); La_out0= PassLengthN(V1,V2+V1,ID); La_out=reshape(La_out0,NNP,Nf); Coefexp=zeros(NNP,Nf); mu_A_out=mu(E_outp); for iii=1:Nf Coefexp(:,iii)=m u_A_out.*La_out(:,iii); end P_A_outp=sum(exp(-Coefexp),2)*2*pi/Nf; P_A_out=Vp; P_A_out(NP)=P_A_outp; CrossS_Sec=Vp; CrossS_Sec(NP)=CrossS_Sec0; % twice Comptom Scattering Part1_S=Part1.*CrossS_Sec.*P_A_out; else Part1_S=zeros(NB*NB*NBZ,1); end % Once Compton Scattering Once photoelectric absorbing

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159 CrossS_A=interp1q(E_LaBr3,ph_ab_LaBr3,E_Scat); Pa rt1_A=Part1.*CrossS_A.*E_reps(E_Scat,E_Sec, i_Sec); % twice Comptom Scattering pp=Omiga_in.*CrossS; F1=P_S_in.*reshape(pp,NB,NB,NBZ); P_Scat_Scat=F1.*reshape (Part1_S,NB,NB,NBZ); % Once Compton Scattering Once photoelectric absorbing P_Scat_Abs=F1.*reshape (Part1_A,NB,NB,NBZ); Coeff=Coeff+P_Scat_Scat+P_Scat_Abs; end end end end end

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168 BIOGRAPHICAL SKETCH I graduated with B.S. from Yunnan University in physics and M.S. in laser physics from Zhejiang University. After working in Physics department, Yunnan University as teacher and research scientist, I was enrolled in Ph.D. progr am in Institute of High Energy Physics, Chinese Academy of Sciences. I was rewarded Ph.D degree on particle and nuclear physics in 1999. Since 2005 I have been enrolled in medical physics program in Nuclear & Radiological Engineering department in University of Florid a. I received M.S. in medical physics in July 2008.