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Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2008-02-29.

Permanent Link: http://ufdc.ufl.edu/UFE0021365/00001

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Title: Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2008-02-29.
Physical Description: Book
Language: english
Creator: Lavigne, Eric
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Statement of Responsibility: by Eric Lavigne.
Thesis: Thesis (M.S.)--University of Florida, 2007.
Local: Adviser: Sjoden, Glenn E.
Local: Co-adviser: Baciak, James.
Electronic Access: INACCESSIBLE UNTIL 2008-02-29

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021365:00001

Permanent Link: http://ufdc.ufl.edu/UFE0021365/00001

Material Information

Title: Record for a UF thesis. Title & abstract won't display until thesis is accessible after 2008-02-29.
Physical Description: Book
Language: english
Creator: Lavigne, Eric
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2007

Subjects

Subjects / Keywords: Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Statement of Responsibility: by Eric Lavigne.
Thesis: Thesis (M.S.)--University of Florida, 2007.
Local: Adviser: Sjoden, Glenn E.
Local: Co-adviser: Baciak, James.
Electronic Access: INACCESSIBLE UNTIL 2008-02-29

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2007
System ID: UFE0021365:00001


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Iwishtothankmysupervisorycommitteechair,Dr.GlennSjoden,forhissupportandguidance.Ithankmysupervisorycommitteecochair,Dr.JamesBaciak,forhiseortsinthelabandforsharinghisknowledgeofdetectorsystems.Additionally,IwishtothankDr.ClairSullivan,fromLosAlamosNationalLaboratory,forreviewingthisdocumentandoeringmanyhelpfulsuggestionsforimprovement.Ienjoyedworkingwithallofthem. 3

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page ACKNOWLEDGMENTS ................................. 3 LISTOFTABLES ..................................... 6 LISTOFFIGURES .................................... 7 ABSTRACT ........................................ 11 CHAPTER 1INTRODUCTION .................................. 12 2PREVIOUSWORK ................................. 13 2.1GammaDetectorResponseandAnalysisSoftware(GADRAS) ....... 13 2.2MaximumEntropy ............................... 13 2.3MaximumLikelihood .............................. 14 2.4NewApproach ................................. 14 3ADAPTIVESPECTRALDENOISINGBYCHI-SQUAREDANALYSIS .... 15 3.1Smoothing .................................... 15 3.2Chi-SquaredAnalysis .............................. 17 3.3Chi-ProcessedDenoisingAlgorithm ...................... 18 3.4AdaptiveChi-ProcessedDenoisingAlgorithm ................ 23 3.5MethodforLeast-SquaresFitting ....................... 24 3.6SuitabilityforReal-TimeSpectralAnalysis .................. 30 4GENERATINGSYNTHETICPHOTOPEAKSANDSPECTRAFORAGAMMARAYDETECTOR .................................. 31 4.1MonteCarloN-ParticleTransport(MCNP)Simulations ........... 31 4.2Denoising .................................... 32 4.3Interpolation .................................. 32 4.4ElectronicBroadening ............................. 39 4.5CompleteDetectorSpectra ........................... 41 4.6ApplicationsforSyntheticallyGeneratedDetectorResponseFunctions .. 42 5PEAKSEARCHALGORITHM ........................... 43 5.1InputFiles .................................... 45 5.2Example ..................................... 48 6PEAKSEARCHWITHSIMULATEDSPECTRAANDNONOISE ...... 62 6.1Cesium-137 ................................... 62 6.2Cobalt-60 .................................... 64 4

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................................... 66 7PEAKSEARCHWITHSIMULATEDSPECTRAANDNOISE ......... 69 7.1Cesium-137 ................................... 69 7.2Cobalt-60 .................................... 70 7.3Barium-133 ................................... 70 8PEAKSEARCHWITHMEASUREDDETECTORSPECTRA ......... 80 8.1Cesium-137 ................................... 80 8.2Cobalt-60 .................................... 80 8.3Barium-133 ................................... 81 8.4PlutoniumBerillium(PuBe) .......................... 82 9CONCLUSION .................................... 91 9.1AdaptiveChi-Processed(ACHIP)Denoising ................. 91 9.2DetectorResponseGeneration ......................... 91 9.3DetectorSpectrumDeconvolution ....................... 92 10FUTUREWORK ................................... 93 10.1AdaptiveChi-Processed(ACHIP)Denoising ................. 93 10.2DetectorResponseGeneration ......................... 93 10.3DetectorSpectrumDeconvolution ....................... 94 APPENDIX AGRAPHICALUSERINTERFACE ......................... 95 REFERENCES ....................................... 97 BIOGRAPHICALSKETCH ................................ 98 5

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Table page 4-1Detectorresponsefunctionfeatures. ......................... 35 4-2Detectorresolution(full-widthhalf-max)calibrationdata. ............ 39 8-1Energycalibrationdata ............................... 80 6

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Figure page 3-1MonteCarlogenerateddetectorresponsefunctionfora350keVgammasourceandasodiumiodidescintillationdetector. ..................... 16 3-2WeightedaveragingappliedtoaMonteCarlogenerateddetectorresponsefunc-tion. .......................................... 17 3-3Chi-processeddenoisingalgorithmalgorithmappliedtoaMonteCarlogener-atedresponsefunction. ................................ 20 3-4ExcerptfromaBa-133spectrum,collectedwithasodiumiodidescintillationdetector. ........................................ 21 3-5Chi-processeddenoisingalgorithmappliedtoameasuredBa-133spectrum. ... 21 3-6ExcerptfromameasureddetectorspectrumforBa-133. ............. 22 3-7Adaptivechi-processeddenoisingalgorithmappliedtoaBa-133spectrum. ... 23 3-8Adaptivechi-processeddenoisingalgorithmappliedtoameasuredBa-133de-tectorresponsefunction. ............................... 25 3-9MonteCarlogenerateddetectorresponsefunctionfora350keVgammasourceandasodiumiodidescintillationdetector. ..................... 26 3-10Chi-processeddenoisingalgorithmappliedtoaMonteCarlogenerateddetectorresponsefunction. ................................... 27 3-11Adaptivechi-processeddenoisingalgorithmappliedtoaMonteCarlogenerateddetectorresponsefunction. .............................. 28 3-12MonteCarlogenerateddetectorresponsefunctionfora350keVgammasourceandasodiumiodidescintillatorwithfewerhistories. ............... 29 3-13Adaptivechi-processeddenoisingalgorithmappliedtoaMonteCarlogenerateddetectorresponsefunctionwithfewerhistories. .................. 30 4-1MonteCarlotransportmodelofNaIsystemwithscatteringplate. ........ 32 4-2MonteCarlosimulationofenergydepositedperphotoninaNaI(Tl)scintilla-tiondetectorfroma650keVsource. ........................ 33 4-3ResultofapplyingtheACHIPdenoisingtooltotheMCNPpulseheighttallyinFigure 4-2 ..................................... 34 4-4Interpolatedresponsefunctionforamonoenergetic662keVsourcewitha1.4millioncountphotopeak. ............................... 37 7

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4-4 whencomparedtoadirectMCNPsimulationfora662keVsource. ....... 38 4-6Illustrationoflow-energytailinginsimulatedelectronicbroadening. ....... 40 4-7SimulateddetectorresponseforBa-133,combiningdetectorresponsefunctionsforeightemissionenergies. .............................. 41 4-8MeasureddetectorresponsespectrumforBa-133,forcomparisonwiththesim-ulateddetectorresponseinFigure 4-7 ....................... 42 5-1Advancedsyntheticallyenhanceddetectorresolutionalgorithmowdiagram. .. 44 5-2Advancedsyntheticallyenhanceddetectorresolutionalgorithmsettingsle,whichisalwaysnamed\process.txt." ............................ 46 5-3Detectorresolutioncalibrationle. ......................... 47 5-4Energycalibrationle. ................................ 47 5-5SyntheticallygeneratedBa-133samplespectrum. ................. 49 5-6Remainderspectrumisshowninblueandisidenticaltotheoriginalsamplespectrum.Therstidentiedpeakisshowninred. ................ 50 5-7Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersub-tractingtherstidentiedpeak,isshowninred. ................. 51 5-8Remainderspectrumisshowninblue.Thesecondidentiedpeakisshowninred. 52 5-9Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersub-tractingthersttwoidentiedpeaks,isshowninred. .............. 53 5-10Remainderspectrumisshowninblue.Thethirdidentiedpeakisshowninred. 54 5-11Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersub-tractingtherstthreeidentiedpeaks,isshowninred. .............. 55 5-12Remainderspectrumisshowninblue.Thefourthidentiedpeakisshowninred. 56 5-13Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersub-tractingtherstfouridentiedpeaks,isshowninred. .............. 57 5-14Remainderspectrumisshowninblue.Thefthidentiedpeakisshowninred. 58 5-15Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersub-tractingtherstveidentiedpeaks,isshowninred. ............... 59 5-16Remainderspectrumisshowninblue.Thesixthidentiedpeakisshowninred. 60 8

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.................. 61 6-1InputleforgeneratingasimulatedCs-137detectorresponsefunction. ..... 62 6-2InputsettingsleforsimulatedCs-137. ....................... 63 6-3Detectorresolutioncalibrationdata. ........................ 64 6-4AdvancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedontheoriginalsimulatedCs-137detectorresponsefunction. ........... 65 6-5InputleforgeneratingasimulatedCo-60detectorresponsefunction. ..... 65 6-6Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)re-sultsoverlayedontheoriginalsimulatedCo-60detectorresponsefunction.ASE-DRAfoundbothpeaks:1173keVand1332keV. ................. 66 6-7InputleforgeneratingasimulatedBa-133detectorresponsefunction. ..... 67 6-8Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)re-sultsoverlayedontheoriginalsimulatedBa-133detectorresponsefunction.ASE-DRAfoundallofthephotopeaks,includingtheoverlappingpeaksat276/303keVand356/384keV. ................................... 68 7-1Adaptivedenoisingisturnedonbysettingthechi-squaredthresholdto-1.Allothersettingsareidenticaltothesettingsinthepreviouschapter. ........ 69 7-2Simulated,one-minute,Cs-137detectorresponsefunctionwithPoissonnoise. .. 70 7-3Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)re-sultsoverlayedonthedenoisedversionofthesimulatedCs-137detectorresponsefunctioninFigure 7-2 .ASEDRAfoundtheonlyphotopeakat661keV. ..... 71 7-4Simulated,one-minute,Co-60detectorresponsefunctionwithPoissonnoise. .. 72 7-5Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)re-sultsoverlayedonthedenoisedversionofthesimulatedCo-60detectorresponsefunctioninFigure 7-4 .ASEDRAfoundbothphotopeaksat1176keVand1336keV. 73 7-6Simulated,one-minute,Ba-133detectorresponsefunctionwithPoissonnoise. 74 7-7Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthesimulated,one-minuteBa-133detectorresponsefunctioninFigure 7-6 ................................ 75 7-8Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsforthesimulated,one-minuteBa-133detectorresponsefunctioninFigure 7-6 .Denois-ingwasnotusedfortheseresults. .......................... 76 9

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. 77 7-10AdvancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthesimulatedBa-133detectorresponsefunctioninFigure 7-9 ....................................... 78 7-11Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsforthesimulated,ve-minuteBa-133detectorresponsefunctioninFigure 7-9 .Denois-ingwasnotusedfortheseresults. .......................... 79 8-1Measured,one-minute,Cs-137detectorresponsefunction. ............ 81 8-2Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthemeasured,one-minuteCs-137detectorresponsefunctioninFigure 8-1 ................................ 82 8-3Measured,one-minute,Co-60detectorresponsefunction. ............. 83 8-4Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthemeasured,one-minuteCo-60detectorresponsefunctioninFigure 8-3 ................................ 84 8-5Measured,one-minute,Ba-133detectorresponsefunction. ............ 85 8-6Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthemeasured,one-minuteBa-133detectorresponsefunctioninFigure 8-5 ................................ 86 8-7Measured,one-minute,PuBedetectorresponsefunction. ............. 87 8-8Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthemeasured,one-minutePuBedetectorresponsefunctioninFigure 8-7 ................................ 88 8-9AdvancedsyntheticallyenhanceddetectorresolutionalgorithmresultsfromFig-ure 8-8 comparedwithadenoised,higherresolution(Germanium)spectrumforthesamesample. ................................... 89 8-10Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsforasim-ulatedPuBespectrumwithnostochasticnoise. .................. 90 A-1AgraphicuserinterfaceforASEDRAisavailableasanalternativetoeditingtheprocess.txtle. .................................. 96 10

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1 ].Portalmonitoringisanenormoustask,requiringaccuratenuclideidentication.CostsperportalmonitoringsystemmustbelowenoughtoprovideinspectionsateachentrypointtotheUnitedStates,andanalysisofresultsmustbefastenoughtokeeptracmoving.Thereisagrowingdemandforlowcost,portable(roomtemperature),highresolutiongamma-raydetectorsystems.Sodiumiodide(NaI)scintillatorsmeetmostoftheserequirements,butdonotprovidesucientenergyresolution.Therehavebeenmanyapproachesinvestigatedforpost-processingofNaIscintillatoroutputforsyntheticallyenhancedresolution.IhavedevelopedanovelalgorithmforspectraldeconvolutionofNaIscintillatoroutput.Usingacombinationofpreviouslydevelopedmethodologies,novelprocessingschemes,andradiationsimulationdata,theadvancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)syntheticallyenhancestheresolutionofapoorresolutionspectrumcollectedfromasodiumiodide(NaI)detector-photomultipliersystem.Infact,thealgorithmcansyntheticallyextractenhanceddoubletsfromunresolved,lowresolutionpeaks.Thisnewcomputeralgorithm,implementedasaspectralpost-processingcode,rapidlyprocessesthecollectedspectrumandsyntheticallyrendersphotopeaksbasedonaspecicsetofparametricpeaksearchcriteria.ThephotopeaksearchcapabilityofASEDRAisbuiltonafoundationofmorespecictools,includingtheadaptivechi-processed(ACHIP)denoisingalgorithmandadetectorresponsefunctiongenerator.Idiscussthephotopeaksearchalgorithmanditscapabilities,aswellasideasforfurtherdevelopmentoftheASEDRAalgorithm. 12

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2 3 ]iscurrentlytheindustryleaderfornuclideidentication,andavarietyofothermethods[ 4 5 ]havebeendevelopedforresolutionenhancementinsupportofphotopeakidentication. 6 ]simula-tion,ratherthanonaparameterizedtemplateasinGADRAS.ASEDRAalsoanalyzesdetectorspectra,withoutanyknowledgeofcommonnuclides,toidentifyandcharacterizephotopeaks.OneadvantageofASEDRA'sapproach,whichreliesonlocalanalysisratherthanglobalanalysis,isthatinterferenceinonepartofthespectrumshouldnotpreventASEDRAfromcorrectlyidentifyingphotopeaksinanotherpartofthespectrum.AfterASEDRAidentiesthephotopeaksinadetectorspectrum,anothertoolcanbeusedtocorrelatethosephotopeakswithspecicnuclides. 2{1 ,inwhichSisameasureofentropy,asdenedinEquation 2{2 ,andisthesmoothing/regularizingterm.Thefunctionsfandmrepresenttheenhanced 13

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22(2{1) 5 ]. 2{3 .Iisanestimateoftheincidentradiationspectrum,andmisthemeasuredabsorptionspectrum.Risaresponsefunctionmatrix,whichmapsincidentsourceenergiestomeasuredresponsesinchannels. 5 ]. 14

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7 8 ]thataddressesthisnoisereductionneedwhileminimizingthedegradationofsharpfeaturesofinterestinthespectrum;thealgorithmissummarizedhere.Inthischapter,IdiscusssmoothinganddenoisingtechniquesforMonteCarlosimulated[ 6 ]andactualradiationdetectorspectraldata,focusinginparticularonanewalgorithmbasedonchi-squaredanalysis. 3{1 ,forexample,implementsaformofweightedaveragingwhichiscommonlyusedforgammadetectorspectra[ 9 ].F(x)representsthespectrumaftersmoothing,whilef(x)representstheoriginalmeasuredspectrum. 8f(x)+1 4f(x1)+1 4f(x+1)+1 16f(x2)+1 16f(x+2)(3{1)Theweightedaveragingprocess,however,maybroadenorremoverealfeaturesofinterestfromthespectrum.Figure 3-1 showsanMCNP-generateddetectorresponse 15

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3-2 showsthesamedetectorresponsefunctionafterapplyingtheweightedaveragingtechniqueforsmoothing.Thetwox-rayescapepeaksaround320keVaresobroadenedthattheyarenolongerdistinguishableaftersmoothing.TheK-shelledgearound40keV,whilestillvisible,isalsobroadenedandreducedinprominence. Figure3-1. AMonteCarlogenerateddetectorresponsefunctionfora350keVgammasourceandasodiumiodidescintillatorwith1.2x109histories(plottedascountsvsdeposited-rayenergy).Pulseheighttalliesaresharperthanexperimentalspectrabecauseelectronicbroadeningisnotsimulated. Myapproachistodistinguishnoisyregions,inwhichstochasticuctuationdominatesandsmoothingisessential,fromregionswithsharp,statisticallysignicantfeatures,inwhichsmoothingattemptsmaybedestructive.Thisdeterminationisbasedonacommontechniquefromstatistics:chi-squaredanalysis. 16

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AfterapplyingweightedaveragingtotheMonteCarlogenerateddetectorresponsefunctioninFigure 3-1 ,thestochasticnoiseissignicantlyreduced.Thetwosharpfeaturesaround320keV,however,cannolongerberesolved.TheK-shelldiscontinuityaround40keV,whilestillvisible,isbroadenedandreducedinprominence. 3{2 ,isthesumofnAandnB,thecountsaccumulatedinchannelsAandBrespectively. 17

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3{2 ,correspondstoacertaintyof99.5%[ 10 ],indicatingthatthisdierenceinneighboringchannelsisastatisticallysignicantfeature.Inthecontextofgammadetectorspectra,suchfeaturesshouldbepreserved.ForlowervaluesofX2,thedierenceisattributabletostochasticuctuationandshouldbesmoothedaway.Chi-squaredanalysisistraditionallyparameterizedby,whichistheprobabilitythatthetestincorrectlyindicatesasignicantdierence.Inthiscase,=10:995=0:005. 3{3 3{4 18

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3-1 .TheeectoftheCHIPalgorithmisshowninFigure 3-3 .ComparedwithweightedaveraginginFigure 3-2 ,CHIPprovidessimilarsmoothingqualityinthoseareasthatneedit.TheadvantageofCHIP,however,isthatitdoesnotdegradethespectruminthoseareaswheresmoothingisharmful.Thetwox-rayescapepeaksaround320keV,forexample,areleftuntouched,asistheK-edgediscontinuityaround40keV.Thesecondexample,inFigure 3-4 ,showsanexcerptfromaBa-133spectrum,collectedwithasodiumiodidescintillationdetector.TheCHIPdenoisingalgorithmprovidessignicantreductionofstochasticuctuationforameasuredBa-133spectrum,asshowninFigure 3-5 ,whilestillpreservingsignicantfeatures.Thesmallfull-energyphotopeakat276keV,forexample,remainsvisiblewhilenearbystochasticnoiseisremoved.Unfortunately,denoisingisnotsucienttoresolvetheconvolutedpeakat384keV,whichisroughlyseventimessmallerthanthenearbypeakat356keV.TheseresultsclearlydemonstratethattheCHIPalgorithm,appliedtoradiationdetectordata,cansignicantlyreducestochasticnoiseinagammadetectorspectrum,whilepreservingstatisticallysignicantfeatures. 19

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Chi-processeddenoisingalgorithmappliedtoaMonteCarlogeneratedresponsefunctionwith1.2x109histories.ComparewiththeoriginalmeasuredspectruminFigure 3-1 TheCHIPalgorithmisfarfromperfect,however.Thestochasticnoiseisnotcom-pletelyremovedinanyoftheseexamplesand,asshowninFigures 3-6 and 3-7 ,thealgorithmcanevenintroducedefectsintoaspectrum.TheCHIPalgorithmdeterminesthatstochasticnoiseisanissueinFigure 3-6 ,sothatsmoothingisneeded.Unfortunately,CHIPsmoothingisbasedonlinearttingoveraneighborhoodofvechannels.Thisdoesnotworkwellinregionswithsignicantcurvature,andFigure 3-7 showstheresult.TheproblemisthattheCHIPalgorithmusesanassumptionthatlocallyconstant,overaneighborhoodoftwochannels,implieslocallylinear,overalargerneighborhoodofvechannels.Therefore,smallnoisyregions 20

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ExcerptfromaBa-133spectrum,collectedwithasodiumiodidescintillationdetector. Figure3-5. Thechi-processeddenoisingalgorithmappliedtothemeasuredBa-133spectruminFigure 3-4 21

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ExcerptfromameasureddetectorspectrumforBa-133. ofaspectrumarelinearizedwithoutregardforanycurvatureintheoriginalmeasuredspectrum.Onepossiblesolutiontothisproblemistotparabolas,whichcanbetterrepresentcurvedregions,ratherthanlines.Anotherissueistheamountofnoisereduction.Fittingoveralargernumberofpoints(ratherthanjustvechannels)wouldincreasethedegreeofnoisereduction,butchoosingtoomanypointscouldcauseproblemswhenaparabolaisunabletoadequatelyrepresenttheentireregion.Basedonexperiencewithmyrstdenoisingalgorithm,CHIP,Icreatedtheadaptivechi-processeddenoising(ACHIP)algorithm,whichcombinesparabolicttingwithdynamicrangeselectiontoaddressalloftheseissues. 22

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Resultofapplyingthechi-processeddenoisingalgorithmtotheBa-133spectruminFigure 3-6 .Theincorrectassumptionthatlocallinearityoveraregionofvechannelsisimpliedbylocalconstancyovereachpairofneighboringchannelsleadstoa\chopping"defect. 3.3 ,usesatwo-stepprocess,inwhichitrstdetermineswhethersmoothingisnecessaryinsomeregion,andthenperformsthesmoothingoperation.Theadaptivechi-processeddenoisingalgorithm(ACHIP)followsamoresophisticatedapproach,inwhichthesmoothingprocessisadaptedtoeachsituation.TheACHIPalgorithmusesasmanychannelsaspossible,increasingthepowerofthesmoothingoperation,withintheconstraintthatthettedmodelmustmatchthemeasureddataaccordingtochi-squaredanalysis.ACHIPalsotsparabolicmodels,rather 23

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3.5 ,butamodelisrejectedifchi-squaredanalysisshowswith99.5%certaintythatthemodeldoesnotadequatelyrepresenttheexperimentaldata.Inotherwords,theACHIPalgorithmwilltendtosmoothawayfeaturesunlessthereis99.5%certaintythatthosefeaturesarenottheresultofstochasticnoise.Bychoosingasmanypointsaspossibleforeachparabolictting,theeectsofstochasticnoiseareminimized.Theprocessofaddingadditionalchannelscontinuesuntilitisnolongerpossibletofurtherincreasethesizeoftheneighborhoodwhilestillpassingthechi-squaredtest.Thisnalmodelthenpredictsanappropriatedenoisedvalueforthechannelofinterest,xo. 3{5 24

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Adaptivechi-processeddenoisingalgorithmremovesnoisefromthespectruminFigure 3-6 withoutintroducingdefects.ComparewithFigure 3-7 inwhichchi-processeddenoisingalgorithmactuallymadethisspectrumworse. 3{6 25

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MonteCarlogenerateddetectorresponsefunctionfora350keVgammasourceandasodiumiodidescintillatorwith1.2x108histories(plottedascountsvsdeposited-rayenergy).Pulseheighttalliesappeardierentlyfromexperimentalspectrabecauseelectronicbroadeningisnotsimulated. Thegoalistochoosethesetofconstantsfc0;c1;c2gsothat~uand~mwillbeascloseaspossibleaccordingtotheleast-squaresmetricinEquation 3{7 3{9 because,forx>0,p 26

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Chi-processeddenoisingalgorithmremovessomeofthenoisefromtheMonteCarlogenerateddetectorresponsefunctioninFigure 3-9 3{8 andsaythatthegoalofleast-squaresttingisequivalenttominimizingthelength[ 11 ]ofthedierencebetween~uand~masinEquation 3{9 27

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Adaptivechi-processeddenoisingalgorithmenhancestheMonteCarlogenerateddetectorresponsefunctioninFigure 3-9 .ACHIPproducesamuchcleanerspectrumthanCHIP(comparewithFigure 3-10 )whilestillpreservingrealfeatures. Determiningthevalueof~uthatminimizesEquation 3{9 wouldbecomputationallyeasierif~uwereexpressedasalinearcombinationoforthonormalvectors.Infact,itispossibletochooseasetoforthonormalvectorsf~w0;~w1;~w2gsuchthatthesetofallpossiblelinearcombinationsoff~w0;~w1;~w2gisequivalenttothesetofallpossiblelinearcombinationsoff~v0;~v1;~v2g.Gram-Schmidtorthogonalization[ 12 ]isastandardtechniqueforchoosingasetoforthonormalvectorsf~w0;~w1;~w2gthatmeetthatrequirement,asshowninEquation 3{10 ,inwhichthedotproductandlengtharedenedasinEquations 3{8 and 3{9 .Anarbitraryparabola~ucanthenberepresentedas~u=d0~w0+d1~w1+d2~w2forsomesetofconstantsfd0;d1;d2g. 28

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AMonteCarlogenerateddetectorresponsefunctionfora350keVgammasourceandasodiumiodidescintillatorwith1.2x107histories(plottedascountsvsdeposited-rayenergy).Pulseheighttalliesappeardierentlyfromexperimentalspectrabecauseelectronicbroadeningisnotsimulated. 29

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Adaptivechi-processeddenoisingalgorithmenhancestheMonteCarlogenerateddetectorresponsefunctioninFigure 3-12 .Thisisaparticularlychallengingspectrum,duetothelownumberofcountsinmanyofthechannels.Notethatchi-squaredanalysisdoesnotworkwellwithfewerthan20countsperchannel. Oncetheorthonormalvectorsf~w0;~w1;~w2garecalculated,asdescribedabove,theoptimalvaluesfd0;d1;d2gareeasilycalculatedbydi=<~m;~wi>[ 13 ].Thismethodisfastbecausetheorthonormalsetf~w0;~w1;~w2gdependsonlyonthenumberofchannelsbeingconsidered,andcanthereforebereusedeachtimealeastsquaresttingisperformed. 30

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6 ]radiationsimulationprogram.Figure 4-1 showstheMCNPmodelcorrespondingtoourNaIscintillationdetectorsetup.Thesampleisrepresentedbyapointsource,10.5cmfromthe5cmsquarecylindricalNaI(Tl)detectorcrystal.Iperformedsimulationsatavarietyofsourceenergies,aswellasbothwithandwithouta0.5cmthickironplateplacedbetweenthesourceandthedetector.Figure 4-2 showsahistogramoftheamountofenergydepositedinthedetectorcrystalforeachmonteCarlosimulated650keVphoton.ThisplothasmuchsharperfeaturesthanarealNaIscintillationdetectorspectrumbecauseitdoesnotincludetheeectsofelectronicbroadening.ThesimulationresultsinFigure 4-2 required1.2x109trialsandabout10hoursofcomputertime.Inordertosimulatedetectorresponsesforradioactiveisotopes,suchresultsareneededforawidevarietyofsourceenergiesfrom20keVupto3000keV,leadingtoenormousamountsofcomputertime.Weusedtwotechniquestoreducethe 31

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MonteCarlotransportmodelofNaIsystemwithscatteringplate.Materials:(10)NaIdetectorcrystal-(20,30)Air-(40)Ironplateorair-(999)Void. timerequirementsforradiationsimulation:denoisingandinterpolation.Denoisingreducesthenumberoftrialsrequiredforeachsimulation,andinterpolationreducesthenumberofsimulationsrequired. 4-2 arerandomvariables.Theaccuracyofthesevaluescanbeimprovedbyincreasingthenumberoftrials,butthisstrategyiscomputationallyexpensive.ThedenoisingtooldiscussedinChapter 3 providessimilarresultswithmuchlowercomputationalcost.Figure 4-3 showstheresultofonlyafewadditionalsecondsofprocessingtimewiththeadaptivechi-processed(ACHIP)denoisingalgorithm,comparedtotheoriginaldatainFigure 4-2 whichtooktenhourstogenerate. 32

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MonteCarlosimulationofenergydepositedperphotoninaNaI(Tl)scintillationdetectorfroma650keVsource.Thefullenergyphotopeakat650keVhasaheightof1.45x106counts.Atotalof1.2x109photonsweresimulated,manyofwhichdidnotreachthedetector.Theironplatewasnotincludedinthissimulation. monoenergeticsourcesrangingfrom20keVto3000keV.WithintheASEDRAcode,weneededtheabilitytochoosesourceenergiestowithin1keV.SimulatingsomanysourcesdirectlyinMCNPwouldbeimpracticalduetotimeconstraints.Therefore,wedecidedtochoosesourceenergiesat50keVintervals(afactorof50reductionincomputertime)andestimateresponsefunctionsforintermediateenergiesbyinterpolation.Usinginter-polationtoreducethecomputationalcostofproducingdetectorresponsefunctionsisdiscussedfurtherinsectionII.BofMengandRamsden[ 5 ],whichinturncitesKiziahandLowell[ 14 ]. 33

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ResultofapplyingtheACHIPdenoisingtooltotheMCNPpulseheighttallyinFigure 4-2 Accurateinterpolationbetweenresponsefunctionsrequirestransformingthoseresponsefunctionssothattheirfeatureslineupwithfeaturesintheinterpolatedresponsefunction.Keyfeaturesinthedetectorresponsefunctionsinclude:thephotopeak,singleanddoubleescapepeaks,thek-edgediscontinuity(notconsidered),thebackscatterpeak,andtheComptonedge.Thesefeatureschangepositionasafunctionofsourceenergy,asshowninEquation 4{1 .Itmakessense,then,tostretcheachofthesimulatedresponsefunctionssuchthattheknownpositionsofsuchfeatureslineupwiththeknownpositionsofthesamefeaturesintheinterpolatedresponsefunction. 34

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EsourceECompton=EsourceEbackscatter(4{1)Asanexample,supposethatMCNPsimulationshavebeenperformedforphotonsourcesof300keVand350keV,yieldingdetectorresponsefunctionsf300(E)andf350(E),respectively.Asimulationforasourceof310keVisnotavailable,butanestimateforf310(145keV)isneeded.Therststepforestimatingf310(145keV)istocharacterizeknownfeaturesofthethreeresponsefunctions,asinTable 4-1 Table4-1. Detectorresponsefunctionfeatures. Featuref300f310f350 Onthef310responsefunction,145keVisbetweenthebackscatterpeakat140keVandtheComptonedgeat170keV.Moreprecisely,145keVisone-sixthofthewayfromthebackscatterpeakat140keVtotheComptonedgeat170keV.Similarly,142keVand157keVareone-sixthofthewayfromthebackscatterpeaktotheComptonedgeonthef300andf350responsefunctions,respectively.Therefore,f310(145keV)canbeestimatedbylinearinterpolationbetweenf300(142keV)andf350(157keV)asinEquation 4{2 35

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350keV300keV(310keV300keV)+f300(142keV)(4{2)ASEDRA'sinterpolationmethodisactuallyasimplicationofthemethoddescribedinthepreviousparagraphandinEquation 4{2 .Thissimplicationleadstoareductionininterpolationaccuracy,butismoreeasilyimplementedandprobablyrunsfaster.Insteadofnoting,forthef310responsefunction,thatthat145keVisone-sixthofthewayfromthebackscatterpeakat140keVtotheComptonedgeat170keV,ASEDRAnotesthat145keVis25keVlessthantheComptonedgeat170keV.Similarly,137keVand177keVare25keVlessthanthef300andf350Comptonedges,respectively.Therefore,f310(145keV)canbeestimatedbylinearinterpolationbetweenf300(137keV)andf350(177keV)asinEquation 4{3 350keV300keV(310keV300keV)+f300(137keV)(4{3)Thissimplerinterpolationmethodgivessimilarresultstotheearlier,moreaccurateinterpolationmethodwhenestimatingthevalueforanenergywhichisclosetoahigher-energyfeature.Intheexample,however,thevalueoff310isestimatedat145keV,whichisveryclosetoalower-energyfeature,thebackscatterpeakat140keV.NotethatEquation 4{3 suggeststhatf310(145keV),whichisbetweenthebackscatterpeakandtheComptonedge,issimilartof300(137keV),whichisatalowerenergythanthebackscatterpeak.ASEDRA'sinterpolationmethodworkswellforthe662keVresponsefunctionshowninFigure 4-4 .Figure 4-5 showstheabsoluteerrorbetweenthatinterpolatedresponsefunctionandadirectMCNPsimulationforthesameenergy.Notethatthelargestabsoluteerrorsoccuraroundsharpfeaturesinthespectrum:thephotopeak,thex-ray 36

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Interpolatedresponsefunctionforamonoenergetic662keVsourcewitha1.4millioncountphotopeak. escapepeaks,andtheComptonedge.TheComptonedgeintheinterpolatedspectrumisshiftedby1keVinthehigh-energydirectionbecausetheinterpolationmethoddoesnotguaranteesynchronizationonthehigh-energysideofafeature.ThedetectorhasaFWHMofaround40keVatthisenergy,soalargeerrorinonechannelneartheComptonedgeonlyhasarounda1%eectonanychannelafterelectronicbroadeningisconsidered.Theerrorof2000countsatthephotopeakisnegligiblecomparedtothe1.4millioncountsinthephotopeak.TheComptoncontinuumhasafarmoresignicanterrorofaround3%,whichcanbeattributedtononlinearityintheNaIcrosssections.Whileitmaybepossibletoslightlyreduceinterpolationerrorwithamoresophisti-catedalgorithm,signicantreductionofinterpolationerrorwouldprobablyrequiredirect 37

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AbsoluteinterpolationerrorfortheinterpolatedresponsefunctioninFigure 4-4 whencomparedtoadirectMCNPsimulationfora662keVsource. simulationofmoresourceenergies.Onepossibilityistoperformdirectsimulationof\interesting"sourceenergies,suchasthephotopeakenergiesfornuclidesofinterest,tosupplementtheequallyspacedsourceenergiesthathavealreadybeensimulated.Anotherpossibilityistoperformsimulationsatamuchlargernumberofsourceenergies,butwithfewerhistoriespersimulation,anddealwiththeresultingstochasticnoisebyapplyinga2-Ddenoisingalgorithmtotheentirelibraryofdetectorresponsefunctions.Suchastrategywouldincreaseaccuracybycompletelyeliminatingtheneedforinterpolation. 38

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4{4 .TheGaussiantransformationisdenedinEquation 4{5 andtransformscountsColdasafunctionofenergyinapulseheightallytocountsCnewasafunctionofenergyinarealisticdetectorresponsefunction. 22;where=FWHM=2:35(4{4) 4{5 ,Ineededfull-widthhalf-maxvaluesforthatdetector.Table 4-2 showsestimatedfull-widthhalf-maxvaluesforphotopeaksinseveralexperimentalspectra:Cs-137,Co-60,andBa-133.FWHMvaluesforotherenergiescanbeestimatedbylinearinterpolationbetweenvaluesinTable 4-2 Table4-2. Detectorresolution(full-widthhalf-max)calibrationdata. Energy(keV)Width(keV) 50.0781.09302.928356.032448.042661.7451173.2681332.570 TheGaussiantransformationdescribedinEquation 4{5 worksverywellatenergiesgreaterthanaround200keV.Atlowerenergies,however,photopeaksarenoticeablyskewedinthelow-energydirection.Amorecomplicatedtransformation,describedinEquation 4{6 andillustratedinFigure 4-6 ,compensatesforsuchlow-energytailingwithtwoadditionalparameters,Rtailandtail(=FWHMtail=2:35),whichcontroltheprominanceandlengthofthelow-energytail. 39

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Figure4-6. TherightsideisaGaussianwithstandarddeviation,andtheleftsideisthesumoftwoGaussianswithstandarddeviationsandtail.ThetailingratioRtailinthiscaseis0.25,meaningthattheGaussianwithstandarddeviationtailmakesupone-quarterofthetotalheightatthecenter. Forourdetector,Rtailis0.25andFWHMtailis23keV.Afterapplyingatransforma-tionforelectronicbroadening,thedetectorresponsefunctionscanbeusedindividuallyorcombinedtosimulatecompletedetectorspectraforanyincidentgamma-rayspectrum. 40

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4.4 canbecombinedtosimulatecompletedetectorspectraforanygammasource.Suchspectracouldbecomparedwithexperimentaldetectorspectratovalidateourdetectorresponsefunctiongenerationcapability.Wecouldalsosimulatespectraforisotopesthatarenotavailableinourlab,creatingalibraryoftestcasesforourpeaksearchcapability(discussedinalaterchapter).Figure 4-7 showsasimulateddetectorspectrumforBa-133.Forcomparison,Figure 4-8 showsanrealdetectorspectrumobtainedwitha5cmx5cmsquarecylindricalNaIdetector. Figure4-7. SimulateddetectorresponseforBa-133,combiningdetectorresponsefunctionsforeightemissionenergies. TherearetwosignicantdierencesbetweenthesimulateddetectorresponseinFigure 4-7 andthemeasureddetectorresponseinFigure 4-8 .Themeasureddetector 41

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MeasureddetectorresponsespectrumforBa-133,forcomparisonwiththesimulateddetectorresponseinFigure 4-7 responsehasaverylargepeakat30keV,whilethesimulateddetectorresponsehasamuchsmallerpeakatthesameposition.Themeasureddetectorresponsealsohasasmall,broadpeakat160keV. 42

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5-1 .First,theadaptivechi-processed(ACHIP)denoisingalgorithm,describedinChapter 3 ,isappliedtobothmeasuredspec-tra:thesamplespectrumandthebackgroundspectrum.Then,thebackgroundspectrumissubtractedfromthesamplespectrum.Finally,theproblemofdeconvolvingphoto-peaksfromthesampleissolvedbyarecursivealgorithmthatndsandstripsawayonephotopeakatatime.Backgroundspectrausuallyhavehighercountingtimesthansamplespectra,sothenumberofcountsinabackgroundspectrummustbescaleddownaccordinglybeforebackgroundsubtraction.TherescalingandsubtractionisperformedasdescribedbyEquation 5{1 .Thesignicancefactorshouldordinarilybesetto1.0,butmaybeincreasedtoaccountforuncertaintyinthebackgroundspectrumduetoenvironmentalchanges.Thechannelindexisrepresentedbyi. (Samplenew)i=(Sampleold)i(Background)i(SignificanceFactor)Timesample=Timebackground(5{1)Acopyofthesamplespectrumiscreatedtorepresenttheportionofthesamplespectrumthathasnotyetbeenattributedtoincidentradiation;thatcopyiscalledtheremainder.TheASEDRAalgorithmsearchesforaphotopeak,startingatthehighenergyendoftheremainderspectrum.ASEDRAidenties,asaphotopeak,therstchanneltomeetthe 43

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Advancedsyntheticallyenhanceddetectorresolutionalgorithmowdiagram. 44

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5.1 .Ifnopeakisfound,thentheASEDRAalgorithmterminates.Otherwise,ifapeakisfound,itspositionandheightmustbecharacterized.Thepositionisthechannelwhichmetthetwocriteriadescribedinthepreviousparagraph.Theheightofthephotopeakisthenumberofcountsintheremainderatthatchannel.Afterthephotopeakischaracterized,adetectorresponsefunctionforthatpeakisgenerated,asdescribedinChapter 4 ,andsubtractedfromtheremainderspectrum.Thenthepeaksearchstartsoverwiththenewremainder. 5-2 .Thersttwosettingsin\process.txt"arepathnamesforthesampleandbackgroundspectra.ThesetwolesusetheMaestroleformattorepresentcounttimes,countsasafunctionofchannel,andotherinformationrelatedtomeasureddetectorspectra.Thethirdsettingin\process.txt"isthebackgroundsignicancefactor,aoating-pointscalefactor,whichisusedinEquation 5{1 .Thebackgroundsignicancefactorisordinarilysetto1.0,butcanbeadjustedtocompensateforchangesinbackgroundradiationlevels.Inthiscase,asettingof0.0completelyturnsobackgroundsubtraction.Thefourthsettingin\process.txt"isthepathnamefortheresolutioncalibration,whichinthiscaseissetto\fwhm.txt."Anexampleresolutioncalibrationle,inFigure 5-3 ,hastwocolumnsrepresentingenergyandfull-widthhalf-max.Thisleprovides 45

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Advancedsyntheticallyenhanceddetectorresolutionalgorithmsettingsle,whichisalwaysnamed\process.txt." resolutioninformationatvariousenergies,andASEDRAllsinthegapsbylinearinterpolationbetweenadjacentpoints.Thefthsettingin\process.txt"isapairoftailingparameters,RtailandFWHMtail,thataredescribedinSection 4.4 .Thesixthsettingin\process.txt"isthepathnamefortheenergycalibration,whichinthiscaseissetto\1k.txt."Anexampleenergycalibrationle,inFigure 5-4 ,hastwocolumnsrepresentingchannelandenergy.Thisleindicatestheenergy,inkeV,associatedwithvariouschannels,andASEDRAllsinthegapsbylinearinterpolationbetweenadjacentpoints.Theseventhsettingin\process.txt"controlsdenoising.Apositivevaluebecomesthechi-squaredthresholddescribedinSections 3.2 and 3.3 andturnsontheCHIPdenoisingalgorithm.Avalueof0completelyturnsodenoising,andanegativevalueturnsontheACHIPdenoisingalgorithm,whichisdescribedinSection 3.4 .IftheACHIPalgorithmis 46

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Detectorresolutioncalibrationle. Figure5-4. Energycalibrationle. turnedon,theeighthsettingcontrolsthevalueof,whichistheprobabilityforanygivenchannelthatstochasticnoisewillbetreatedasarealfeature.Smallervaluesofallowmoredenoising,butmayalsoleadtorealfeaturesbeingsmoothedaway.NotethatthecertaintydescribedinSections 3.2 3.3 ,and 3.4 isequalto1.Theninthsettingin\process.txt"indicatesthematerialforashieldplacedbetweenthesampleanddetector.Sofar,ASEDRAonlyunderstandstwomaterialtypes:(0)air 47

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10 asapossibilityforadditionalresearch. 5.1 ,inwhichbothdenoisingandbackgroundsubtractionareturnedo.ActualASEDRAresultsareshowninlaterchapters.TheoriginalmeasuredspectrumisshowninFigure 5-5 andstartsoutequaltotheremainderspectrum.Thereareeightlocalmaximapointsonthespectrum.Ofthoselocalmaxima,thehighestenergyisat356keV.Theheightoftheremainderspectrumatthatpointis1650counts,sotherstidentiedpeakischaracterizedashavingaphotopeakenergyof356keVandapeakheightof1650counts.ThedetectorresponsefunctionfortherstidentiedphotopeakisshowninFigure 5-6 .Notethatthelocalmaximumnear200keVintheoriginalmeasuredspectrumisduetotheComptonedgeofthis356keVphotopeak. 48

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SyntheticallygeneratedBa-133samplespectrum. The356keVphotopeakissubtractedfromtheremainderspectrum,yieldinganewremainderspectrumthatisshowninFigure 5-7 .Thehighest-energylocalmaximumintheremainderisat384keV.Theremainderhas196countsatthatenergy,soasecondpeakisidentiedwithanenergyof384keVandaheightof196counts,asshowninFigure 5-8 .The384keVphotopeakissubtractedfromtheremainderspectrum,yieldinganewremainderspectrumthatisshowninFigure 5-9 .Thehighest-energylocalmaximumintheremainderisat301keV.Theremainderhas681countsatthatenergy,soathirdpeakisidentiedwithanenergyof301keVandaheightof681counts,asshowninFigure 5-10 .The301keVphotopeakissubtractedfromtheremainderspectrum,yieldinganewremainderspectrumthatisshowninFigure 5-11 .Thehighest-energylocalmaximum 49

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Remainderspectrumisshowninblueandisidenticaltotheoriginalsamplespectrum.Therstidentiedpeakisshowninred. intheremainderisat275keV.Thethresholdis46.6counts,tencountsplus10%ofthe366countsat275keVintheoriginalmeasuredspectrum.Theremainderhas301countsat275keV,whichishigherthanthethresholdvalueof46.6counts,soafourthpeakisidentiedwithanenergyof275keVandaheightof301counts,asshowninFigure 5-12 .The275keVphotopeakissubtractedfromtheremainderspectrum,yieldinganewremainderspectrumthatisshowninFigure 5-13 .Thehighest-energylocalmaximumintheremainderisat223keV.Thethresholdis14counts,tencountsplus10%ofthe40countsat223keVintheoriginalmeasuredspectrum.Theremainderhastencountsat223keV,whichislowerthanthethresholdvalueof14counts,sothislocalmaximumisnotidentiedasaphotopeak. 50

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Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersubtractingtherstidentiedpeak,isshowninred. Thenexthighest-energylocalmaximumintheremainderisat161keV.Thethresh-oldis23.6counts,tencountsplus10%ofthe136countsat161keVintheoriginalmeasuredspectrum.Theremainderhastencountsat161keV,whichislowerthanthethresholdvalueof23.6counts,sothislocalmaximumisnotidentiedasaphotopeak.Thenexthighest-energylocalmaximumintheremainderisat81keV.Thethresholdis538counts,tencountsplus10%ofthe5280countsat81keVintheoriginalmeasuredspectrum.Theremainderhas5100countsat81keV,whichishigherthanthethresholdvalueof538counts,soafthpeakisidentiedwithanenergyof81keVandaheightof5100counts,asshowninFigure 5-14 51

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Remainderspectrumisshowninblue.Thesecondidentiedpeakisshowninred. The81keVphotopeakissubtractedfromtheremainderspectrum,yieldinganewremainderspectrumthatisshowninFigure 5-15 .Thehighest-energylocalmaximaintheremainderareat161keVand223keV,atwhichtheremainderheightsoftencountsandtencountsarelowerthanthethresholdvaluesof23.6countsand14counts.Thenexthighest-energylocalmaximumintheremainderisat53keV.Thethresholdis79.9counts,tencountsplus10%ofthe699countsat53keVintheoriginalmeasuredspectrum.Theremainderhas450countsat53keV,whichishigherthanthethresholdvalueof79.9counts,soasixthpeakisidentiedwithanenergyof53keVandaheightof450counts,asshowninFigure 5-16 52

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Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersubtractingthersttwoidentiedpeaks,isshowninred. The53keVphotopeakissubtractedfromtheremainderspectrum,yieldinganewremainderspectrumthatisshowninFigure 5-17 .Therearetwolocalmaximaintheremainderat161keVand223keV,atwhichtheremainderheightsoftencountsandtencountsarelowerthanthethresholdvaluesof23.6countsand14counts.Therefore,theASEDRAalgorithmcannotndanyadditionalphotopeaks.ThischapterdescribeshowtheASEDRAalgorithmworks,bringingtogethercapa-bilitiessuchasdenoisingandresponsefunctiongenerationforthepurposeofspectraldeconvolution.Thefollowingthreechaptersshowhowthatalgorithmperformsonavarietyofexamplespectra. 53

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Remainderspectrumisshowninblue.Thethirdidentiedpeakisshowninred. 54

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Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersubtractingtherstthreeidentiedpeaks,isshowninred. 55

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Remainderspectrumisshowninblue.Thefourthidentiedpeakisshowninred. 56

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Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersubtractingtherstfouridentiedpeaks,isshowninred. 57

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Remainderspectrumisshowninblue.Thefthidentiedpeakisshowninred. 58

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Originalsamplespectrumisshowninblue.Theremainderspectrum,aftersubtractingtherstveidentiedpeaks,isshowninred. 59

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Remainderspectrumisshowninblue.Thesixthidentiedpeakisshowninred. 60

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Theoriginalsamplespectrumisshowninblue.Theremainderspectrum,aftersubtractingallsixidentiedpeaks,isshowninred.Noadditionalpeakscanbeidentiedbecausetheremainingpeaksat161keVand223keVarebelowthethresholdforpeakidentication. 61

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4.5 ,sothatanyerrorisattributablesolelytothepeaksearchalgorithm.LaterchapterswillbringsuchcomplicatingfactorsbackintothepicturesothatASEDRA'soverallperformancecanbejudged,andsothatitwillbeclear,forthesakeofguidingfurtherresearch,whichcomplicatingfactorshavethegreatestimpactonASEDRA'sperformance. 4.5 andthesampledescriptioninFigure 6-1 ,whichindicatesthatthereisasinglepeakat661.7keVwithaheightof650counts. Figure6-1. InputleforgeneratingasimulatedCs-137detectorresponsefunction.Therstcolumnliststheenergies,inkeV,ofthephotopeaks.Thesecondcolumnliststhephotopeakheightsincounts. Theprocess.txtinputle,showninFigure 6-2 ,providesinformationaboutthesampleandthedetector,indicateswhereotherinputlescanbefound,andallowssometuning 62

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5 .Inthiscase,thebackgroundsignicancefactorissetto0sothatthebackgroundlewillbeignored.Thissettingmakessenseforasyntheticallysimulatedspectrum,forwhichthereisnobackground.Inthischapter,thechi-squaredthresholdissetto0,whichturnsodenoising,becausethespectrainthissectionhavenostochasticnoise. Figure6-2. InputsettingsleforsimulatedCs-137. Resolutionforaparticulardetectorvariesasafunctionofenergy.Thefull-widthhalf-maxcalibrationfunction,measuredinkeVandprovidedasafunctionofenergy(keV),isdenedinthelefwhm.txt,asindicatedbyprocess.txt.TheFWHMcalibrationleisshowninFigure 6-3 .ThespectraldeconvolutionprocessforthesimulatedCs-137spectruminFigure 6-4 hasonlyafewsimplesteps.First,ASEDRAscansthespectrum,startingatthehighenergyend,searchingforachannelwhichmeetsthefollowingconditions:morecountsthananyotherchannelwithinoneFWHM,morecountsthantherejectionthreshold,andmorecountsthantherelativechannelthresholdtimesthenumberofcountsintheoriginalspectrumatthatchanneldividedbyonehundred.Therstchanneltomeetallthreeof 63

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Detectorresolutioncalibrationdata. theseconditionsisat662keV,andASEDRAreportsaphotopeakatthatlocationwithaheightequaltothecountsperchannelatthephotopeak'scentroid.Next,ASEDRAcreatesamatching662keVdetectorresponsefunctionasinChapter 4 andsubtractsthatdetectorresponsefunctionfromthespectrum.Peaksearchisrepeatedontheremainder,butthistimenochannelsmatchtheconditionsforndingaphotopeak.Thepeaksearchiscomplete.SpectraldeconvolutionisverysimpleforCs-137becausethereisonlyonephotopeak.Next,IdemonstratespectraldeconvolutionfortheslightlymorecomplicatedcaseofCo-60,whichhastwophotopeaks. 6-5 .Aftertherstpeakat1332keVisfoundandsubtractedfromthespectrum(ASEDRAstartsatthehighenergyend),thepeaksearchcontinuesontheremainder.Next,ASEDRAndsthe1173keVphotopeakandsubtractsitaswell.Finally,theremaindercontainsnochannelswhichmeettheconditionsforidentifyingaphotopeak,andthedeconvolutionprocessiscomplete.TheresultsareshowninFigure 6-6 64

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsoverlayedontheoriginalsimulatedCs-137detectorresponsefunction.Thesimulatedresponsefunctionisshowninred.ASEDRAfoundonlyonepeak,at661keV,whichisshownasaredlinewhoseheightindicatestheheightoftheidentiedphotopeak. Figure6-5. InputleforgeneratingasimulatedCo-60detectorresponsefunction.Therstcolumnliststheenergies,inkeV,ofthephotopeaks.Thesecondcolumnliststhephotopeakheightsincounts. 65

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsoverlayedontheoriginalsimulatedCo-60detectorresponsefunction.ASEDRAfoundbothpeaks:1173keVand1332keV. 6-8 thatthesetwopeaksareoverlapping.Althoughthehighestenergyphotopeakisat384keV,thephotopeakat356keVisfoundrst.Afterthe356keVpeakisfoundandstrippedaway,the384keVpeakisexposedandcanbefoundnext.Thesecasestudiesshowthat,givenidealconditions,theASEDRAalgorithmper-formsverywell.Complicationsareaddedgraduallyinthefollowingtwochapters,demon-stratinghowASEDRAcopeswitheachchallenge. 66

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InputleforgeneratingasimulatedBa-133detectorresponsefunction.Therstcolumnliststheenergies,inkeV,ofthephotopeaks.Thesecondcolumnliststhephotopeakheightsincounts. 67

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsoverlayedontheoriginalsimulatedBa-133detectorresponsefunction.ASEDRAfoundallofthephotopeaks,includingtheoverlappingpeaksat276/303keVand356/384keV. 68

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6 .Next,IexploreASEDRA'sre-sponsetonoisebyaddingstochasticnoisetotheexamplespectra.Theprocess.txtleinFigure 7-1 ischangedonlyslightlyfromthepreviouschapter.Adaptivechi-processed(ACHIP)denoisingisturnedonbysettingthechi-squaredthresholdto-1.Thealpha()parameterindicatestherelativeimportanceofremovingnoiseandpreservingrealfeatures.FurtherdiscussionofcanbefoundinChapter 3 Figure7-1. Adaptivedenoisingisturnedonbysettingthechi-squaredthresholdto-1.Allothersettingsareidenticaltothesettingsinthepreviouschapter. Countsineachchanneloftheexamplespectrafromthepreviouschapterareran-domlyshiftedaccordingtoaPoissonprobabilitydistribution.Ideally,theACHIPdenois-ingalgorithmshouldcompletelyremovetheeectsofthatnoise.TheACHIPalgorithmisfarfromperfect,however,andASEDRAmustcopewiththedierence. 7-2 .Theresultsofdenoising,followedbyspectraldeconvolution,areshowninFigure 7-3 .ACHIP 69

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Figure7-2. Simulated,one-minute,Cs-137detectorresponsefunctionwithPoissonnoise. 7-4 .Theresultsofdenoising,followedbyspectraldeconvolution,areshowninFigure 7-5 .ACHIPdenoisingremovedmostofthestochasticnoise,andASEDRAcorrectlyidentiedbothofthephotopeaks. 7-6 showsthenoisyBa-133spectrum,andthestochasticnoisy 70

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsoverlayedonthedenoisedversionofthesimulatedCs-137detectorresponsefunctioninFigure 7-2 .ASEDRAfoundtheonlyphotopeakat661keV. makestheoverlappingpeaksevenlessdistinguishable.Figure 7-7 showsthatthersttwophotopeaksat356keVand384keVarecorrectlyidentied.Thenextphotopeaktobeidentiedisat303keV,butitspositionisincorrectlycharacterizedas299keV,leadingtoaslightlyincorrectsubtractionofthe303keVresponsefunction.Thatdierenceleavessomecountsintheremainderat316keV,whichareincorrectlyidentiedasaphotopeak.TheresultsaresimilarinFigure 7-8 ,forwhichdenoisingwasnotused.ASEDRAmakesmistakeswhenanalyzingaone-minuteBa-133spectrum,soIalsoshowASEDRA'sperformancewiththeve-minutespectruminFigure 7-9 ,whichhaslessstochasticnoise. 71

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Simulated,one-minute,Co-60detectorresponsefunctionwithPoissonnoise. TheASEDRAresultsonave-minuteBa-133spectrumaresimilartotheresultsforaone-minutespectrum,asshowninFigure 7-10 .TheresultsforanalyzingthesamespectrumwithoutdenoisingareshowninFigure 7-11 .Withoutdenoising,the303keVphotopeakiscorrectlycharacterized,andnofalsephotopeakisidentiedat316keV.Inthiscase,denoisingactuallymakesthesituationworse.Oneexplanationisthatthephotopeaksat276keVand303keVformashapewhichisnotwellmodelledbyasetofparabolas.Perhapsadenoisingtoolthatuseshigherorderpolynomialswoulddoabetterjobonthisproblem.SeveralcasestudiesinthisChapterdemonstrateASEDRA'sperformanceunderconditionsthatareidealexceptforsynthesizedstochasticnoise.Avarietyofother 72

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsoverlayedonthedenoisedversionofthesimulatedCo-60detectorresponsefunctioninFigure 7-4 .ASEDRAfoundbothphotopeaksat1176keVand1336keV. factorscancomplicatespectraldeconvolution:changesinthebackgroundradiation,scatteredradiationfromnearbyobjectsinthelab,anduncertaintyintheenergyandFWHMcalibrationcurves.ThenextchapterincludesallofthesecomplicatingfactorsbyusinglaboratorymeasurementswitharealNaIscintillationdetector.Additionally,aplutoniumberylliumsourceisintroducedasanexampleofaparticularlyconvoluteddetectorspectrum. 73

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Simulated,one-minute,Ba-133detectorresponsefunctionwithPoissonnoise. 74

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Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthesimulated,one-minuteBa-133detectorresponsefunctioninFigure 7-6 75

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Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsforthesimulated,one-minuteBa-133detectorresponsefunctioninFigure 7-6 .Denoisingwasnotusedfortheseresults. 76

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Simulated,ve-minute,Ba-133detectorresponsefunctionwithPoissonnoise. 77

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AdvancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthesimulatedBa-133detectorresponsefunctioninFigure 7-9 78

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Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsforthesimulated,ve-minuteBa-133detectorresponsefunctioninFigure 7-9 .Denoisingwasnotusedfortheseresults. 79

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8-1 showstheenergycalibrationdatafortheexamplesinthischapter. Table8-1. Energycalibrationdata ChannelEnergy(keV) 6253.29781.0334302.9387356.0705661.712391173.214021332.5 8-1 ,andthecorrespondingASEDRAresultsareshowninFigure 8-2 .ASEDRAndsthe662keVphotopeak,asbefore,butitalsondsanadditionalfeaturesat292keV.Theadditionalfeatureat292keVhasaheightofonly12counts,onlytwocountsabovethethresholdforrejection. 8-3 .Unlikethesimulatedspectrainthepreviouschapters,themeasuredCo-60spectrumhasabroadpeakbetween200keV 80

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Measured,one-minute,Cs-137detectorresponsefunction. and350keV.TheASEDRAresultsinFigure 8-4 showthreefeaturesinthisregion:208keV,233keV,and272keV.ThesefeaturesmaybetheresultofscatteringfromobjectsthatwerenotincludedintheMCNPsimulations.Eachofthesethreefeatureshasaheightoflessthan15counts. 8-5 ,andthecorrespondingASEDRAresultsareshowninFigure 8-6 .ASEDRAincorrectlycharacterizesthe303keVphotopeakashavingapositionof299keV,asinthepreviouschapter,and,consequently,identiesanadditionalfalsephotopeakat316keV.ASEDRAalsoidentiessixverysmallfeaturesbetween100keVand250keV.Thesourceoftheseadditionalfeaturesisnotknown. 81

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsoverlayedonthedenoisedversionofthemeasured,one-minuteCs-137detectorresponsefunctioninFigure 8-1 .ASEDRAfoundtheonlyphotopeakat661keV.Theadditionalpeakat290keVisonlytwocountsabovetherejectionthresholdandisnotreal. 8-7 ,andthecorrespondingASEDRAresultsareshowninFigure 8-8 .TheexactcompositionofthePlutoniumBerillium(PuBe)sourceanditsradiationspectrumaretopicsofcurrentinvestigation,soASEDRA'sresultsarecomparedwithahigh-purityGermaniumspectrumforthesamesampleinFigure 8-9 82

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Measured,one-minute,Co-60detectorresponsefunction. WithoutproperenergycalibrationfortheGermaniumdetector,itisdiculttodeterminehowcloselytheASEDRAresultsmatchtheGermaniumresults.However,whilesomeskepticismiswarranted,thesimilaritiesshowninFigure 8-9 areveryencouraging.ItriedsimulatingaplutoniumberylliumspectrumthatincludesonlythelabelledphotopeaksinFigure 8-9 ,whichmatchphotopeaksintheHPGedetectorspectrum.ThesimulatedplutoniumberylliumspectrumandassociatedASEDRAresultsareshowninFigure 8-10 ,fromwhichtwoveryinterestingconclusionscanbedrawn.First,thesimulatedplutoniumberylliumspectruminFigure 8-10 hasnoticeablegapscomparedtothemeasuredspectruminFigures 8-8 and 8-9 .Thisshowsthatthereareadditionalphotopeaks,notvisibleintheHPGespectrum,whichhaveasignicanteect 83

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsoverlayedonthedenoisedversionofthemeasured,one-minuteCo-60detectorresponsefunctioninFigure 8-3 .ASEDRAfoundbothprimaryphotopeaksat1176keVand1336keV.Theadditionalthreephotopeaksbetween200keVand300keVareunidentied,butthisspectrumclearlycontainsmorefeaturesthancanbeexplainedbyCo-60alone. ontheNaIspectrum.AtleastsomeoftheextrapeaksinFigure 8-10 ,whichdonotmatchHPGepeaks,mustberealphotopeaksthatwereidentiedbyASEDRA.ThismeansthatASEDRAcandeconvolvephotopeaksfromalow-resolutionNaIdetectorthatarenotvisibleonahigh-resolutionHPGedetector.Second,ASEDRAresultsshowveryhighreliability.Inahighlyconvoluteddetec-torspectrumwithtwenty-twophotopeaks,ASEDRAcorrectlyidentiedallbutthreephotopeakswithnofalsepositives. 84

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Measured,one-minute,Ba-133detectorresponsefunction. ThischapterdemonstratedASEDRA'scapabilitiesonreallaboratorydata,collectedwithaNaIscintillationdetector,aswellasonahighlyconvolutedsimulationspectrum.Thereremainsroomforimprovement,buttheseresultsdemonstrateasignicantcapabil-ityforenergyresolutionenhancement.Inparticular,ASEDRAisdesignedtoworkreliablywithintimeandcostconstraints:rapidexecution,toleranceofshortcountingtimes,andresolutionenhancementforrelativelyinexpensivedetectors. 85

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsoverlayedonthedenoisedversionofthemeasured,one-minuteBa-133detectorresponsefunctioninFigure 8-5 .ASEDRAcorrectlyextractedtheoverlappingphotopeaksat356keVand384keV.ASEDRAincorrectlyindicatedthatthe303keVphotopeakwasat298keV.Incorrectsubtractionofthe303keVphotopeakledtoafalsepositiveat316keV,butthe276keVphotopeakwasstillcorrectlyidentied. 86

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Measured,one-minute,PuBedetectorresponsefunction. 87

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Advancedsyntheticallyenhanceddetectorresolutionalgorithmresultsoverlayedonthedenoisedversionofthemeasured,one-minutePuBedetectorresponsefunctioninFigure 8-7 88

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AdvancedsyntheticallyenhanceddetectorresolutionalgorithmresultsfromFigure 8-8 comparedwithadenoised,higherresolution(Germanium),butuncalibratedspectrumforthesamesample.Labelsareprovidedtoindicatepeaksthatappeartomatchbetweenthetwospectra. 89

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Advancedsyntheticallyenhanceddetectorresolutionalgorithm(ASEDRA)resultsforasimulatedPuBespectrumwithnostochasticnoise.ASEDRAmadeonlythreemistakes.Asmallphotopeakaround150keVthatshouldhavebeenbetweenQandSwasmisplaced.Twoothersmallphotopeaks,GandI,werenotidentied.LabelsinthisgurematchthelabelsinFigure 8-9 90

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15 16 ].Additionally,ACHIP'sdenoisingstrategycouldbeappliedtoawidervarietyofproblemsifthealgorithmweregeneralizedtosupport2Dand3Ddata. 93

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AgraphicuserinterfaceforASEDRAisavailableasanalternativetoeditingtheprocess.txtle. 96

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[1] U.S.Dept.ofHomelandSecurity.Successofradiationportalmonitorprogramremainsundiminished.U.S.CustomsandBorderProtectionToday.4-5(2006) [2] D.J.Mitchell.SodiumIodideDetectorAnalysisSoftware(SIDAS).SandiaNationalLaboratory(1986) [3] Abelquistetal.RadiologicalSurveysforControllingReleaseofSolidMaterials.U.S.Nucl.Reg.Comm.(2002) [4] LikarandVidmar.JournalofPhysicsD:AppliedPhysics.36,1903-1909(2003) [5] L.J.MengandD.Ramsden.IEEETransactionsonNuclearScience.47-4(2000) [6] [7] E.Lavigneetal.Chi-squarebasedselectivedatasmoothingfordetectorspectra.ProceedingsRPSD2006:ANSTopicalMeetinginRadiationProtectionandShielding(2006) [8] E.Lavigneetal.Amethodforstochasticnoisereductionbychi-squaredanalysis.TransactionsoftheAmericanNuclearSociety2006WinterMeetingandTechnologyExpo.BestofRPSD(2006) [9] [10] Wackerlyetal.MathematicalStatisticswithApplications,5thed.WadsworthPublishingCompany.732-733(1996) [11] Friedbergetal.DenitionsofLengthandEuclideanLength.LinearAlgebra,3rded.PrenticeHall(1997) [12] Friedbergetal.Theorem6.4.LinearAlgebra,3rded.PrenticeHall(1997) [13] Friedbergetal.Proposition6.6andCorollary.LinearAlgebra,3rded.PrenticeHall(1997) [14] R.R.KiziahandJ.R.Lowell.Nucl.Instrum.Meth.305-1,92(1991) [15] W.Cochran.10,417-451(1954) [16] A.Agresti.CategoricalDataAnalysis.Wiley(1990) 97

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EricLavigneearnedaB.S.inmathematicswithaminorinphysicsfromtheUniver-sityofFloridainMay2003.Later,EricreturnedtotheUniversityofFloridatoearnanM.S.innuclearengineeringscienceswhilestudyingcomputerprogrammingontheside.EricLavigneandNongOwensmarriedonValentine'sDayin2007.UponcompletionofhisM.S.program,EricwillworkasaprogrammerfortheUniversityofFlorida'sBureauofEconomicandBusinessResearch. 98