Beamforming for novel matrix arrays

113 Pages·2017·12.04 MB·English

by  Fabian Fool

Beamforming for novel matrix arrays
Fresnel Zone Beamforming and Stolt Migration
Fabian Fool
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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.