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Photon Statistics in Scintillation Crystals

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Photon Statistics in Scintillation Crystals PHOTON STATISTICS IN SCINTILLATION CRYSTALS by Vaibhav Joga Singh Bora BY: = A Dissertation Submitted to the Faculty of the COLLEGE OF OPTICAL SCIENCES In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2015 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dis- sertation prepared by Vaibhav Joga Singh Bora entitled Photon Statistics in Scin- tillation Crystals and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. Date: 15 May 2015 Harrison H. Barrett Date: 15 May 2015 Lars Furenlid Date: 15 May 2015 Eric Clarkson Date: 15 May 2015 H. Bradford Barber Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. Date: 15 May 2015 Dissertation Director: Harrison H. Barrett 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. This work is licensed under the Creative Commons Attribution-No Derivative Works 3.0 United States Li- cense. To view a copy of this license, visit http://creativecommons.org/licenses/by- nd/3.0/us/ or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA. SIGNED: Vaibhav Joga Singh Bora 4 ACKNOWLEDGEMENTS I would like to thank Harry for all the guidance, patience and time he invested into me and my PhD. Lars Furenlid, Eric Clarkson and Brad Barber made themselves very approachable and always took out time to answer all my questions, and for discussions about all things under the sun. I would like to thank Tom Milster who advised and guided me on a couple of very rewarding optics projects during my PhD. Radiation monitoring Devices, Boston has manufactured, and shared with us the latest new scintillation materials. I am very thankful for their support for my dissertation. David Fastje tremendously helped me with the experiments. He made some very nice measurements which are a part of this thesis. I would like to thank Helen, Esen, Cecile, Jin, Ronin, Joy, Ling, Xin, Nasrin, Maria, Chris, Kyle, George, Daniel, Luca, Abhinav, Heather, Brian, Steven and Jared for sharing their time, letting me pick their brain and helping me along with technical advise, life guidance, or kind words. My PhD experience would have been hollow without all of you. I would also like to Thank Merry Warner, Christy and Liz Hague for helping me buying all the lab supplies and keep the lab running. 5 DEDICATION I would like to dedicate my PhD thesis to my family. To my sweetheart Lakshmi, who moved twice so that I could enroll and complete my PhD, my daughter Kavya, who has brought so much joy to our lives, my parents Joga Singh and Chandra who have raised me to be the person I am today, my sisters, Anjana and Vaishali, who have always looked out for me and are just awesome and my in-laws Gopalakrishnan and Visalakshi who have encouraged and supported me throughout my Phd. I would also like to give a big shout-out to Anirban, Anubhab and Niladri who opened their homes and hearts to me. Thanks for all the great dinners and discus- sions. Lastly, my Toyota Matrix, who through our 200K miles journey has not failed me once. 6 TABLE OF CONTENTS LISTOFFIGURES................................ 10 LISTOFTABLES................................. 15 ABSTRACT.................................... 16 CHAPTER 1 Introduction ............................ 18 1.1 Single Photon Emission Computed Tomography ............ 18 1.2 Gamma-ray spectrometers and gamma-ray imaging detectors . 20 1.3Statisticsingamma-rayimaging..................... 22 1.3.1 Fanofactor............................ 23 1.4MotivationformeasuringFanofactor.................. 23 1.5Gamma-rayinteractionsinmatter.................... 25 1.5.1 Photoelectricinteraction..................... 26 1.5.2 Comptoninteraction....................... 28 1.5.3 Pairproduction.......................... 29 1.6Typesofgamma-raydetectors......................31 1.6.1 Gasdetectors........................... 31 1.6.2 Semiconductor detectors ..................... 32 1.6.3 Scintillation detectors ....................... 33 1.7Energyresolution............................. 34 1.7.1 Why we need to estimate energy in a gamma-ray imaging detector.............................. 35 CHAPTER 2 Inorganic Scintillation Detectors ................. 37 2.1 Physics of scintillation crystals ...................... 37 2.1.1 Gamma-rayinteractioninmatter................ 38 2.1.2 Ionization............................. 38 2.1.3 Carrierthermalisation...................... 39 2.1.4 Captureatdopantsite...................... 39 2.1.5 Radiativeemission........................ 39 2.2 Properties of scintillation gamma-ray detectors ............. 40 2.2.1 Lightyield............................. 40 2.2.2 Duration of scintillation pulse .................. 41 2.2.3 Density.............................. 41 2.2.4 Opticalproperties......................... 42 7 TABLE OF CONTENTS –Continued 2.2.5 Emissionspectra......................... 42 2.2.6 Otherimportantproperties................... 42 2.3Non-proportionalityandtheFanofactor................ 42 CHAPTER 3 Estimation of Fano Factor in Inorganic Scintillators ...... 47 3.1Introduction................................ 47 3.2Theory................................... 49 3.2.1 Fanofactorofopticalphotonsandphotoelectrons....... 49 3.2.2 Modelingatwo-detectorexperiment............... 51 3.2.3 Signal processing and PMT gain variance ............ 55 3.3Experimentalsetup............................ 56 3.4DataanalysisandestimationofFanofactor.............. 59 3.4.1 Dataanalysis........................... 59 3.4.2 EstimationofFanofactor.................... 59 3.5Results................................... 60 3.5.1 SrI2:Eu............................... 60 3.5.2 YAP:Ce.............................. 61 3.5.3 CsI:Na............................... 62 3.5.4 Fanofactorestimates....................... 63 3.6Conclusion................................. 68 CHAPTER 4 Time Statistics in Scintillation Crystals ............. 69 4.1Introduction................................ 69 4.2Theory................................... 70 4.2.1 Pointprocess........................... 70 4.2.2 Renewal process .......................... 71 4.2.3 Classification of point processes ................. 71 4.2.4 Inter-event time for a Poisson point process .......... 71 4.2.5 Modeling the inter-event time as a gamma distribution .... 73 4.2.6 Relationship between shape factor and Fano factor for a sta- tionary point process ....................... 74 4.2.7 Relationship between shape factor and Fano factor for a non- stationary point process ..................... 76 4.2.8 Correlation,covarianceandcoherence.............. 76 4.3 Implementation .............................. 80 4.3.1 Simulation............................. 80 4.3.2 Experiment............................ 89 4.4Results................................... 94 4.4.1 Simulationresults......................... 94 8 TABLE OF CONTENTS –Continued 4.4.2 Experimentalresults....................... 97 4.4.3 Cross-covariance for different values of relative time shift . 99 4.4.4 EstimateoftheFanofactor...................100 4.5 Comparison of Fano factor estimates from temporal and integral cor- relations..................................100 CHAPTER 5 Impact of Fano Factor on Position and Energy Estimation in Scintillation Cameras ..............................103 5.1Introduction................................103 5.2Theory...................................105 5.2.1 Likelihood function ........................105 5.2.2 Score, Fisher information matrix and Cram´er-Rao bound . 105 5.2.3 Varianceofmaximumlikelihoodestimator...........107 5.3Model...................................107 5.3.1 Modeling the scintillation process ................107 5.3.2 Modeling the optical photon transport .............109 5.4 Implementation ..............................110 5.4.1 Assumptions for maximizing the impact of Fano factor ....110 5.4.2 Computation limitations for calculating the Cram´er-Rao bound111 5.4.3 Geometry of 3 × 1detector...................112 5.4.4 Geometry of 3 × 3detector...................113 5.4.5 Analyticalsolution........................115 5.4.6 Calculation of the Fisher information matrix and the Cram´er- Raobound.............................118 5.4.7 Estimating the variance of the maximum likelihood estimator 120 5.5Results...................................121 5.5.1 Resolutionandvarianceoftheestimator............121 5.5.2 Results for the 3 × 1detectorgeometry............122 5.5.3 Results for the 3 × 3detectorgeometry............131 5.6Analysisofresultsandconclusion....................137 5.6.1 SpatialresolutionandFanofactor................137 5.6.2 EnergyresolutionandFanofactor................137 CHAPTER 6 Conclusion and Future Work ..................139 6.1Conclusion.................................139 6.2FutureWork................................139 6.2.1
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