Beamforming for novel matrix arrays PDF
Preview Beamforming for novel matrix arrays
Beamforming for novel matrix arrays Fresnel Zone Beamforming and Stolt Migration Fabian Fool y g o ol n h c e T f o y t si r e v ni U t f el D B EAMFORMING FOR NOVEL MATRIX ARRAYS FRESNEL ZONE BEAMFORMING AND STOLT MIGRATION by FabianFool inpartialfulfillmentoftherequirementsforthedegreeof MasterofScience inAppliedPhysics attheDelftUniversityofTechnology, tobedefendedpubliclyonThursdayMarch23,2017at13:30PM. Supervisor: Dr.ir.MartinVerweij TUDelft/ErasmusMC Thesiscommittee: Prof.dr.ir.NicodeJong TUDelft/ErasmusMC Dr.ir.MichielPertijs TUDelft Dr.ir.RikVos ErasmusMC/TUDelft Anelectronicversionofthisthesisisavailableathttp://repository.tudelft.nl/. iii A BSTRACT Healthcareisamajorsocietalexpenseandthecostsriseeachyear. Furtherdevelopmentofultra- soundcouldhelpreducethecosts.Currentlyalotofeffortisputintodevelopingmatrixarrayswhich allowforvolumetricimagingandnewapplications.Therearehowevermultipleproblems.Compared toarrayscurrentlyinusewhichhaveintheorderof128elements,matrixarrayscaneasilycontain 1000to10000elements.Ifallelementswouldbeconnectedindependently,thecablewouldbecome verythick.Therefore,beamformingmethodsarerequiredthatcanoperatewithfewertransmitand receivechannels. Furthermore, theroomforelectronicsonthechipislimited. So, therequired electronicsforthebeamformingmethodsshouldbekeptsimple. Currently,tofocusintransmitallelementshavetobewiredout.Transmittinganunfocusedbeam wouldbeanoptiontoreducethechannelcount,butthisseverelylimitedpenetration. So,anew methodisrequiredtofocusintransmitthatrequiresasfewaspossiblechannels. Theamountof receive channels also has to be reduced. This might be done by combining the data from each elementinsomeway.However,thisresultsinproblemswithimageformationasthecurrentgolden standard,DynamicReceiveFocusing(DRF),usesthedatafromallindividualelements. Thus,we needanewimagingalgorithmwhichcanworkwithfewerchannels,butontheotherhandhavea similarorbetterimagequality. Inthisthesiswewillproposesolutionstotheabovementionedproblemswithmatrixarrays.Thiswill bedoneseparatelyforthetransmitandreceivepart,buttheydoinnowayexcludeeachother.Tobe abletofocuspulsedwavesintransmitweproposeamethodbasedonFresnelzoneplateswhichare usedinopticstofocuscontinuouswavelight.Ourmethodonlyrequiresasinglecontinuous-wave excitationsignaltobepresent,whichisconnectedanddisconnectedondemandtoeachelement.We haveevaluatedourmethodwithmeasurementsandsimulations.Ascomparedtotheconventional focusingmethod,thespatialresolutionisnotaffectedbyourmethod,buttheContrast-to-Noise ratiois5%lowerforshallowdepthsandupto20%lowerdeeperintothemedium.Overallthough, thedifferenceswererelativelysmallandsoitisclearthatournewfocusingmethodworksverywell. Ifneeded,betterresultscanbeobtainedbytradinginframerate.Inthiscasetheresultsarealmost indistinguishablefromtheconventionalfocusingmethod. To solve the problem with image formation, we have developed a frequency domain two stage beamforming method for use with matrix arrays, which does not require all element data to be present. Thishasbeendonefortwomatrixtypes. Forthefirstmethodwehaveconfirmedwith simulationsthatitperformssimilartotherespectiveresultsobtainedwithtwo2Dfrequencydomain twostagebeamformingmethodthathavealreadybeenexperimentallyverified. Forthesecond methodwehaveevaluatedtheperformancewithsimulationsandmeasurements.Ourmethodwas abletoobtaina25%betterspatialresolutionascomparedtoDRF,withoutadditionalartefacts.Asan alternativetothelastmethod,wehavealsodevelopedafrequencydomainbeamformingmethod thatdoesrequireallelementdata,butonlyrequiresasingleinsonificationbyasphericalwave.This methoddidperformworsethanthemethoddiscussedbeforeinbothsimulationsandmeasurements, butitdoesoutperformDRFappliedtosphericalwavedata. CONTENTS v C ONTENTS Page 1 Introduction 1 2 Backgroundknowledge 3 2.1 Wavepropagationandextrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Ultrasoundimaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Virtualpointssourcesandreceivers . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 SyntheticApertureSequentialBeamforming . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Stoltmigration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Imagingperformance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.7 FastHankelTransform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.8 SphericalHarmonicTransform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 I FresnelZoneBeamforming 17 I.1 Theory 19 I.1.1 Fresnelzoneplatesandlenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 I.1.2 Fresnelzoneplatesinacoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 I.1.3 ImprovedFresnelzonefocusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 I.2 SimulationandexperimentalSetup 25 I.2.1 Beamprofile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 I.2.2 Imagequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 I.3 Results 29 I.3.1 Beamprofile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 I.3.2 Imagequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 I.4 Discussionandconclusions 45 I.4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 I.4.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 II CylindricalStoltMigration 49 II.1 Methoddevelopment 51 II.1.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 II.1.2 ComparisontopolarandlinearStoltMigration. . . . . . . . . . . . . . . . . . . . . 53 II.1.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 II.2 Simulationsetup 55 II.3 Results 57 II.4 Conclusions 61 vi CONTENTS III SphericalStoltMigration 63 III.1 Methoddevelopment 65 III.1.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 III.1.2 ComparisontopolarStoltmigration . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 III.1.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 III.1.4 Computationtime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 III.1.5 Extensiontosphericalwaves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 III.2 Simulationandexperimentalsetup 71 III.2.1 Setup1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 III.2.2 Setup2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 III.3 Results 75 III.3.1 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 III.3.2 Leastsquarestransformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 III.3.3 Computationtime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 III.3.4 SphericalWaveStoltMigration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 III.3.5 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 III.3.6 PSASBvsStolt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 III.4 Discussionandconclusions 89 III.4.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 III.4.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Acknowledgments 93 Bibliography 95 A Hankelfunctionapproximation 99 A.1 Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 A.2 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 A.3 Effectonresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 A.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 1 1 I NTRODUCTION Healthcare is a major societal expense and the costs rise each year. Since 2000 the costs in the Netherlandshavemorethandoubledto95.5billionEuroin2015,orabout5.628Europerperson.[1] Becauseofthesehighcostsitisimportanttofindnewwaystoprevent,diagnoseandcurediseases thatwillhaveapositiveimpactonthecosts,butalsoofcourseonqualityoflife. Oneoftheimagingmodalitiesusedinhealthcareisultrasound,whichusesacousticalwaveswith ahighfrequency. AnultrasoundsystemisportableandmuchcheaperthanbothanMRIandCT scanner.[2] Also, there is no radiation burden. However, it is not applicable everywhere. Bones reflectmostoftheultrasound,whichmakesimagingtheorgansbehindtheribsdifficult.Also,the penetrationdepthislimited,whichbecomesespeciallyproblematicifthereisathickfatlayer,and theresolutionisnotalwayssufficient. Further development of ultrasound could help reduce the costs. Currently a lot of effort is put into developing matrix arrays which allow for volumetric imaging and new applications. There arehowevermultipleproblems. Comparedtoarrayscurrentlyinusewhichhaveintheorderof 128elements,matrixarrayscaneasilycontain1000to10000elements. Ifallelementswouldbe connected independently, the cable would become very thick. This is for example especially a problemforamatrixarraytobeusedintransesophagealechocardiography,whereaprobeisput intotheoesophagusthroughthethroattoimagetheheart. Asimplewayofreducingtherequiredamountofchannelsthathavetobeusedintransmitistoexcite allelementsatthesametime.Inotherwords,useunfocusedbeamsinsteadoffocusedones.This howeverseverelylimitspenetrationdepthinhighlyattenuatingmedia,especiallyifhighfrequencies havetobeusedtoallowforahigherresolution.Thisisforexamplethecaseinthebrainofpre-term babies,whereonewouldliketoimagethebrainandmeasuretheperfusion.Alackofperfusionisa commonhealthproblemwhichcanleadtocognitivedeficits,motordisabilitiesorevendeath.Sowe needawaytofocusabeamintransmitwithasfewaspossiblechannels.Thereishoweveranother restriction.Forsmallprobes,aswellasarraysusinghighfrequencies,theelectronicsshouldbekept simple. ThismakesitforexampleimpossibletointegrateindividualpulsersontheASICforeach element. The amount of receive channels also has to be reduced. This might be done by combining the datafromeachelementinsomeway. However,thisresultsinproblemswithimageformationas thecurrentgoldenstandard,DynamicReceiveFocusing(DRF),usesthedatafromallindividual elements.Thus,weneedanewimagingalgorithmwhichcanworkwithfewerchannels,butonthe otherhandhaveasimilarorbetterimagequality. 2 1.INTRODUCTION Inthisthesiswewillproposesolutionstotheabovementionedproblemswithmatrixarrays.Thiswill bedoneseparatelyforthetransmitandreceivepart,buttheydoinnowayexcludeeachother.Tobe abletofocuspulsedwavesintransmitweproposeamethodbasedonFresnelzoneplateswhichare usedinopticstofocuscontinuouswavelight.Ourmethodonlyrequiresasinglecontinuous-wave excitationsignaltobepresent,whichisconnectedanddisconnectedondemandtoeachelement. Tosolvetheproblemwithimageformation,wewilldevelopafrequencydomaintwostagebeam- formingmethodforusewithmatrixarrays,whichdoesnotrequireallelementdatatobepresent. Inliterature, twostagebeamformingmethodsinbothtimeandfrequencydomainhavealready beendevelopedforlinear[3][4]andphasedarrays[5][6].Allmethodshavetoshowntooutperform DRF.Furthermore,oneofthesemethodshasalreadybeenextendedforusewithonekindofmatrix arrays[7].Thismethodishowevernotapplicabletotwootherkindsofmatrixarrays,forwhichwewill developthemethodshere.Asanalternative,wewillalsomodifyoneofthedevelopedbeamforming methodstoworkwithsphericalwaves.Thisdoesrequireallelementdata,buttheframeratecanalso bemuchhigher. THESISOUTLINE Wewillfirstintroducebackgroundknowledgeinthenextchapterthatwillbehelpfulinunderstanding therestofthethesis.Thiswillincludewavepropagation,wavefieldextrapolationandthebasicsof ultrasoundimaging.Furthermore,twotwo-stagebeamformingmethodsthatarealreadydeveloped inliterature,SequentialApertureSequentialBeamformingandStoltMigration,willbeintroduced. Afterthis,thethesisbranchesintothreeparts. Thesepartscanbereadindependentlyfromeach other.ThefirstpartisaboutFresnelZoneBeamformingthatonlyrequiresasinglehigh-voltagesignal forfocusing. InchapterI.1ofthispartthetheorybehindFresnelzonefocusingandourmethod areintroduced. Thiswillbefollowedupbythesimulationandexperimentalsetupusedforthe investigationofthenewmethod.ChapterI.3containsthesimulationandexperimentalresultsand inthenextchaptersomeopenendsarediscussedandtheconclusionsarepresented. PartIIisallaboutthedevelopmentofamigrationmethodincylindricalcoordinates. Inthefirst chapter of this part the mathematical derivation is given. Also, a comparison with Linear and PolarStoltismadeandanimplementationschemeisgiven.InchapterII.2thesimulationsetupis describedandtheresultsobtainedwiththissetupareshowninthenextchapter.Thefinalchapterof thispartcontainstheconclusions. InthefinalpartStoltMigrationinasphericalcoordinatesystemisdevelopedandextendedtoallow forinsonificationwithsphericalwaves.Likethepreviouspart,thefirstchaptercontainsthemathe- maticalderivationandacomparisonwithPolarStolt.Also,wederiveaquasifastHankeltransform likealgorithmforapossiblefastermigrationandgivetheimplementationscheme.Attheendofthis chapter,wemodifythealgorithmtoworkwithsphericalwaves.ChapterIII.2containsthesimulation andexperimentalsetupthatisusedtoevaluatetheperformanceofthenewlydevelopedmethods incomparisonwiththecurrentgoldenstandard.Inthenextchaptertheresultsarepresentedand discussed.Finally,inchapterIII.4afewopenendsarediscussedandtheconclusionsaregiven. TheappendixcontainsaninvestigationintheapproximationthatweusefortheHankelfunction in this thesis. We will show how good this approximation is and how it might have affected the results. Furthermore, weintroducetwoalternativeapproximationsandcomparethemwiththe approximationthatwehaveused.
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