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1、MAGNETICRESONANCEINMEDICINE1,44-65(1984)MagnetFieldProfiling:AnalysisandCorrectingCoilDesignFRANCOISEROMkO*ANDD.I.HOULT~BiomedicalEngineeringandInstrumentationBranch,DivisionofResearchServices,Building13.Room3W13,NationalInstitutesofHealth,Befhesda.Maryland20205ReceivedApril1982Afullmathematicalfram
2、eworkfortheanalysisandproductionoflocalizedmagneticfieldprofilesispresented.Ofprimaryuseintheproducitionofhighlyhomogeneousfieldsfornuclearmagneticresonancestudies,thepaperdetailstheanalysisoffieldsintermsofsphericalharmonics,describeshowfieldplottingintheappropriatemannermaybeusedtoobtainadirectmea
3、sureofwhichharmonicsarepresent,andshowshowtocombinebasic“buildingblocks”toproducethevariouslower-orderzonalandtesseralharmonics.“Buildingblocks”describedincludecoils,arcs,andsinusoidsofcurrentaswellasringsandarcsofsteel.Theuseofshapedmagnetsisalsobrieflymentioned.Attentionisdrawntothepresence,inhigh
4、-orderdesigns,ofpossiblydominantlowerordersofharmonicscreatedbyerrorsinfabrication.Thegoalofthepaperistopresentadesignphilosophy,backedbytheappropriatemathematics,whichisapplicabletothevarietyofsituationsencounteredinmagnetdesign.Practicalexamplesofcorrectingcoilsand‘‘shims’’arealsogiven.INTRODUCTIO
5、NTheproductionofmagneticfieldshavingaspecificspatialvariationoveralocalizedregionisaproblemwhicharisesinseveralareasofresearch,butnotablyintheapplicationofnuclearmagneticresonance.Afieldhomogeneoustotheorderofonepartinlo9overavolumeofseveralmillilitersmaybeneededincertainhigh-resolutionexperiments,w
6、hileclinicalNMRimagingmaydeimandahomogeneityoftheorderof1ppmoverseveralliters.Publicationsonthetheoryanddesignofsystemscapableofattainingsuchperformancesareincompleteandscattered(1-23),andtheaimofthepresentworkisthereforetopresentacohesivemathematicalframework,buildingonthefoundationslaidbyGolay(2,5
7、,6),inorderthattheprospectivefieldprofilerrnayhavetohandthemethodsandequationswhdchareaprerequisitetoeffectivedesign.Whileexamplesoftheproductionofspecificfieldprofilesaregiven,noworkofthepresentnatur