Progress in AberrationCorrected HighResolution Transmission Electron Microscopy Using - PDF document

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particularM.Haider,Heidelberg,H.Rose,Darmstadt,andK.Urban,JŸlich,forthemanydiscussionsonelectronopticsandaberrationcorrection,theopportunitytoworkinthisexcitingfield,supportduringthepastyears,andencouragementincompilingthiswork.M.L.thanksfurtherC.L.Jia,A.Thust,B.Kabius,E.Schwan,K.Tillmann,andB.Jahnenforcollaborationonmethodsandmaterialsscienceapplicationsofaberrationcorrectionandextensivesupportwiththeaberration-correctedprototype.TheprojectonaberrationcorrectionwasfundedbytheVolkswagenStiftung.EFERENCES 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iment,eliminatesanyresidualdelocalization,inparticulardelocalizationduetotheScherzerphaseplateneededforoptimumimaging. Inrecentyears,themajormanufacturersoftransmissionelectronmicroscopeshavestartedtointegrateaberrationcorrectors,allofthedouble-hexapoletype,intotheirinstru-ments.Theobjectiveisnotonlytomakeaberrationcorrec-tionandaberrationcontrolavailableformaterialsscience,butalsotoimprovetheinformationlimitofmedium-voltageinstrumentssubstantially,intotheregionofsub-ngstršmresolution.Meanwhile,newinstrumentswithanaberration-correctedobjectivelenshavebeeninstalled,oneatOxfordUniversityandanotherattheUniversityofNagoya.TheinstrumentatOxfordhasbeenusedforhigh-resolutioninvestigationsofaniobiumoxidecrystal,CdSenanoparti-cles,Si,andtheoxy-fluoride6NbFeFHutchi-sonetal.,2002;Kirklandetal.,2004;theinstrumentatNagoyahasbeenusedforhigh-resolutioninvestigationsofSiOinterfacesandInGaAsdotsembeddedinGaPHosokawaetal.,2003;Tanakaetal.,2003,2004.Twomoreaberration-correctedinstrumentshavebeeninstalledatCEMES,Toulouse,andattheTriebenbergLaboratory,Dres-den,withfirstresultsofthelatterinstrumentobtainedwithhigh-resolutionelectronholographyofaGaAscrystalLeh-mannetal.,2005Calculations,datingbacktoScherzerÕsarticleof1949,showthatoptimumphasecontrastimagingforsub-ngstršmresolutionwillbelimitedbythefifth-orderspher-icalaberrationScherzer,1970.Itscoefficientispositive,andoptimumimagingwillthusrequirethecombinationofpositivefifth-orderaberrationwithnegativethird-ordersphericalaberrationandoverfocus.Manymoreaberrationcoefficientswillhavetobemea-suredinthefuture,whichwillbepossiblewithimprovedmeasurementroutines.Theprecisetuningofaproperde-focusmay,however,bedifficult,becauseofunevenspeci-mensurfacesandotherexperimentalinsufficienciesthatrequiretherecordingofthrough-focusseriesformaterialsscienceinvestigations.Inourview,thecombinationofhardwareaberrationcorrection,givingadirectviewatthestructureunderinvestigationthroughoptimumphasecon-trastimaging,andnumericalaberrationcorrectionthroughexit-wavereconstructiontechniqueswillpavethewaytomaterialsscienceinvestigationsthatexploittheveryinstru-mentallimits. Morethan60yearsaftertheinventionoftheelectronmicroscope,thedesignandconstructionofthedouble-hexapoleaberrationcorrectorhasmadeitpossibletocon-structtheprototypeofaspherical-aberrationcorrectedtransmissionelectronmicroscopededicatedtohigh-resolutionimagingontheatomicscale.Thekeyfeatureofthecorrectedinstrument,aPhilipsCM200FEGST,isaninformationlimitofbetterthan0.13nmandthepossibilitytovarythesphericalaberrationwithinwidelimits,eventonegativevalues.Theaberrationmeasurementandthecor-rectorcontrolprovideinstrumentalignmentsthatturnedouttobestableenoughformaterialsscienceinvestigations.Analysisofthecontrasttransferwiththenewpossibil-ityofatunablesphericalaberrationhasrevealednewimag-ingmodes:high-resolutionamplitudecontrast,extensionofthepointresolutiontotheinformationlimit,andenhancedimageintensitymodulationfornegativephasecontrast.Inparticular,thelattermodeprovidesthroughthecombina-tionofasmallnegativesphericalaberrationandasmalloverfocusthehigh-resolutionimagingofweaklyscatteringatomcolumns,suchasoxygen,inthevicinityofstronglyscatteringatomcolumns. Theauthorthanksallcoworkersintheprojectonaberra-tioncorrectionofatransmissionelectronmicroscope,in Figure9.High-resolutionimageoftheatomicstructureofaBaTiOthinfilmcontainingtwinlamellae,recordedundernegativephasecontrastconditionsduetoasmallnegativespheri-calaberrationcombinedwithasmalloverfocus.Allatomcol-umns,Ba,Ti-O,andO,appearbrightwithrespecttothemeanintensityfromtheworkpresentedinJia&Urban,2004ProgressinAberration-CorrectedHRTEM andtoallowtheotherplanetobeincontrastthroughthedefocusaberrationequivalenttothedistancebetweenplanes.Forexample,theatomicstructureofsmallcrystallineparti-clesonathinamorphoussupportfilmcanbestudiedwithoutdisturbingcontrastduetothefilmifzerodefocusisappliedforthefilmplane.Thentheparticleyieldsphasecontrastthroughtheamountofdefocusrelatedtoitsthick-seeFig.8 Theaberration-correctedPhilipsCM200FEG,equippedwiththeRoseÐHaiderdoublehexapolecorrector,wastrans-ferredfromtheEMBLHeidelbergtotheResearchCentreJŸlichin1997.AseriesofarticlesdocumentthestateoftheprojectatthebeginningofthematerialsscienceapplicationoftheinstrumentHaideretal.,1998,1998,1998;Uhle-mann&Haider,1998;Urbanetal.,1999.Thekeyresultatthisstagewasthedemonstrationofspherical-aberrationcorrectionwithaninformationlimitof0.12nminthedirectionofthelongaxisofasingle-tiltholderand0.14intheperpendiculardirection.Atthesametime,twomaterialsscienceinvestigationsdemonstratedtheuseofthecorrectedinstrumentforhigh-resolutionstructureinvestigations:thestructureimageofaGaAscrystalviewedalongthezoneaxisandthestructureimageofaSiCoSiinterfacewithandwithoutaberrationscorrectedHaideretal.,1998.Thelatterexampleshowedtheverysmalldelocal-izationofaberration-correctedimagingcomparedwiththelargedelocalizationattheoriginalvalueofthesphericalaberrationof1.23mm.AfteranumberofimprovementsoftheinstallationatResearchCentreJŸlich,aninformationlimitofbetterthan0.13nmwasreachedLentzenetal.,2002.High-resolutioninvestigationswerecarriedoutinseveralmaterialssystems:thinlayersofAlSbembeddedinGaSb,aGaAsAlAsGaAshetero-structure,atiltgrainboundaryinaBaTiOthinfilm,andgrainsandgrainboundariesinaBaTiOthinfilmLentzenetal.,2002.ThelattermaterialwaschosentoimagealltypesofatomiccolumnsintheprojectionofBaTiO,includingtheweaklyscatteringoxygencolumnsclosetoTiÐOcolumns.FurtherworkwasdedicatedtotheinvestigationofoptimumimagingofweaklyscatteringatomcolumnsinthevicinityofstronglyscatteringcolumnsJiaetal.,2003,2004;Jia&Urban,2004.Asdescribedaboveinthesectiononcontrasttransferandnewimagingmodes,imagingwithapositiveaberrationfunction,thatis,negativephasecon-trastwithnegativesphericalaberrationandoverfocus,iswellsuitedtoenhancetheimagecontrastofverythinspecimens.InathinspecimenofSrTiOallatomiccolumnscouldberesolved,inparticulartheweaklyscatteringoxygencolumns.Bycomparisonwithimagesimulations,itwasconfirmedthattheimageintensityattheoxygencolumnsvariesalmostlinearlywiththeoxygenoccupancy,andthiscalibrationwasthenusedtomeasureoxygencontentatindividualsites.Usingtheoxygensublatticeasafingerprint,detailsofthecorestructureoftwodifferenttypesofedgedislocationsinSrTiOwereinvestigated.Negativephasecontrastwasfurtherusedtoimageastackingfaultinwiththinfilmsviewedalongtheandthedirections.Inbothdirections,alltypesofatomcol-umnswereresolved,andatranslationofthetwocrystalsbetweenthedoublecopper-oxidechainplanesbyone-halfofthelatticeparametercouldbeobserved.Thestruc-turalinformationcouldbeusedtoidentifythestackingfaultasa124type.Acloselookattheintensityrelatedtotheoxygencolumnpositionsinthetwoprojectionsrevealedstrongoxygenorderinginthecopper-oxidedoubleplane.AnotherapplicationofnegativephasecontrasthasbeenthemeasurementoftheoxygenoccupancyatthetwinboundariesofaBaTiOthinfilmJia&Urban,2004Figure9displaysahigh-resolutionimageofthethinfilmrecordedundernegativephasecontrastconditions.Theobservedaverageoxygendeficiencyof32%atthetwinboundarysiteswasexplainedbythereductionofthegrainboundaryenergythroughamodifiedTigroup,provid-ingawaytoaccommodateoxygenvacanciesinthisoxygen-deficientmaterialbytheformationofananotwinlamellaestructure.WorkondefectsinGaAsconcentratedonthemeasure-mentoflatticedistortionsarounddislocationsandoninves-tigationofthedislocationcorestructureTillmannetal.,.Ahigh-resolutionimageunderoptimumnegativephase-contrastconditionswascomparedtothephaseoftheexit-wavefunctionreconstructedfromadefocusseriesofimages.Thenegativephasecontrastimageofamultiplestackingfaultterminatedbypartialdislocationsrevealedahigh-resolutionviewoftheatomiccolumns,butwasdis-turbedbyghostintensityatthetunnelpositionsofGaAs.Thephaseofthereconstructedexit-wavefunctionprovidedaclearerview,chieflyforthreereasons:First,theinformationfromtheimageseriesislessaffectedbynoiseduetoamorphouslayers,becausethereconstructionalgo-rithmextractsanaverage.Second,theimagedirectlyresem-blesthestructure,becausetheghostintensityatthetunnelpositionsisabsent.Third,thefine-tuningofresidualaber-rations,bynumericalaberrationcorrectionaftertheexper- Figure8.Simultaneoususeoftwoimagingmodesforaparticleonathinsupportfilm.Forzerosphericalaberrationandzerodefocuswithrespecttothesupportfilmthephasecontrastfromtheparticleisnotdisturbedbycontrastfromthesupport.MarkusLentzen blurinreciprocalspace.Thinstripesofamorphousmate-rial,forexample,producecharacteristicstreaksinreciprocalspace,whichmaybiasthesearchfortheappropriatede-focusandastigmatismwhenevaluatingadiffractogram.Alltheseconditionscanbemetbyusingspecialtestsamples,suchasaverythinamorphoustungstenfilmevaporatedonaverythincarbonfilm.Inmanymaterialsscienceinvestigations,however,onehastoworkwiththethinamorphousmaterialleftbysamplepreparation,whichmaysometimesbetoothickorexhibitonlythinstripes.Usinganaberrationcorrectorforhigh-resolutionimag-ingpermitstheuseofalargerconvergenceangleoftheilluminationthanisusedinanuncorrectedinstrumentHaideretal.,1998.Asmallamountofresiduallensaberrationsislinkedtoverysmallgradientsoftheaberra-tionfunction.Theconvergenceandthegradientoftheaberrationfunctionenterthespatialcoherenceenvelopeasaproduct,andthereforetwoaspectsfollowforhigh-resolutionimaging.First,alargeramountofelectronscanbecollectedfromthesourcebyusinglargerconvergencewithoutaffectingspatialcoherence.Thespecimencanbeilluminatedwithahigherintensity,andshorterexposuretimescanbeused.Inmodernhigh-resolutioninstrumentsequippedwithfield-emissionguns,however,exposuretimesarealreadyshort,ontheorderofasecondorbelow.Second,thenewfreedomofhigherconvergencecanbeusedinsteadtomovetheilluminationcrossoverawayfromthespecimenplaneandtoreturntotraditionalexposuretimesontheorderofonesecond.Becausethecrossoverhasbeenmoved,theouterpartsofthefieldofviewarelessaffectedbyilluminationtilt,whichmayaffectstronglythedirectinter-pretationofstructuredetailsincrystallinesamples.Ifaberrationsarecorrectedperfectly,thenilluminationtiltwillnotinducefurtheraberrations,likeinducedaberra-tionsduetothestrongsphericalaberrationinanuncor-rectedinstrumentHaideretal.,1998.Illuminationtiltcannowbeusedtocompensateglobalspecimentilt,whichisparticularlyusefulforworkwithcrystallinesamples,whichrequireexactorientationofatomcolumnsparalleltotheelectronbeam.Inalmosteverycase,however,aberra-tionscannotbecompensatedperfectly,asfollowsalreadyfromthelimitedaccuracyofaberrationmeasurements.Themeasurementroutinespermitaberrationstojustfulfillthe4criterion,thatis,theareainreciprocalspacegivenbytheinformationlimitoftheinstrumentisjustcorrected,buttheareabeyondtheinformationlimitisnot.Introduc-ingilluminationtiltisequivalenttoashiftinreciprocalspace:Onepartofthewell-correctedareamovesoutside,anotherpartoftheuncorrectedareamovesinsidetheareausedforimaging.Fromthisconsiderationitisclearthatthespecimentiltcompensationcanonlybeusedforlow-resolutionwork,wherethelowresolutionplustheilluminationtiltuseddonotexceedtheradiusoftheaberration-correctedarea.Calculationsforcontrasttransferandcertainimagingmodesalwaysassumeaflatspecimen;thatis,onlyoneobjectplane,usuallytheexitplane,isofinterestforvariouskindsofidealimaging.Realobjectsoftenhaveshapesdeviatingconsiderablyfromthiscondition.Twoimportantexamplesaretheinclinedbottomfaceofawedge-shapedspecimenandtheunevenexitfaceofaparticleonathinsupportseeFig.7.Thesitesforanyoptimumdefocusaregivenbytheintersectionofthespecimenshapeandtherespectiveplaneusedforoptimumimaging.Itisimmedi-atelyclearthattheneedforoptimumimagingofallsitesofanunevenexitfacecompelstherecordingofathrough-focalseriesofimagesLentzenetal.,2002.Suchaseriescanbeexploitedintwoways:First,anoptimumimageofaspecialspecimenlocationofinterestcanbeselectedaftertheexperimentwithouttheneedforexactfocusingduringthemicroscopesession.Second,adefocusseriesofimagescanbeusedtoreconstructtheexit-wavefunctionoverthewholefieldofviewSchiske,1968;Saxton,1988;Coeneetal.,1992,1996;Thustetal.,1996.Valuablestructuralinformationcanbegainedbyimprovingtheaberrationsettingofthemicroscopeaftertheexperimentthroughnumericalaberrationcorrectionoftheexit-wavefunctionThustetal.,1996;Lehmann,2000;Saxton,2000.Anotherbenefitisthefreedomtochangethewavefunctionnumeri-callybydefocusphaseplates.Thesegiveaccesstofocusplanesthatwerenotsampledbytheimageseries,andthusveryaccurateoptimumdefocussettingscanbemadeaftertheexperiment.Incertaincases,aberrationcorrectioncanbeusedtoapplytwodifferentimagingmodessimultaneously.Ifthespecimencontainstwoplanesofinterestperpendiculartotheelectronbeam,thenperfectaberrationcorrection,thatis,zerosphericalaberrationandzerodefocus,canbeusedtomaketheweakcontrastduetoatomsinoneplanevanish Figure7.Defocusseriesforobjectswithunevenbottomsurfaces.Wedge-shapedspecimen.Particleonasupportfilm.ProgressinAberration-CorrectedHRTEM withthespecimenthicknessandthemeanprojectedcrystalpotentialLentzen&Urban,2000Thestrikingpropertyoftheelectronwaveatlargerspecimenthicknessisthatthemodulationofthescatteredwaveisstillproportionaltotheprojectedcrystalpotential,butitsphaserelativetothedirectwavedeviatesfromDependingonthestrengthofthescattering,thatis,depend-ingontheprojectedatomicchargeperunitlengthalongthecrystalcolumn,therelativephasestartsat2andincreasessteadily,iflj,1.Itstartsat2anddecreasessteadily,lj.InlightoftheabovecalculationsontheoptimumZernikephaseplateforbright-atomimaging,enhancingtheintensitymodulationattheatomiccolumnsites,itisclearthattheoptimumcompensatingphase,,oftheZernikephaseplateforthickersamplesisdependentonthepropertiesofelectronchanneling,namely,thespecimen,theextinctiondistance,andthemeanpro-jectedcrystalpotential.AdetailedcalculationLentzen,yieldstwoimportantequations:j!!Thefirsthastobesolvedforthecompensatingaberration,andtheseconddetermineswhichofthesolutionsintheintervalisthenselectedtodeterminetheoptimumsettingfordefocus,optandsphericalaberration,30,optThephaseplateapproximatesanoptimumZernikephaseplateforbright-atomcontrastfromathickersample;itsdelocalizationisoptandtheimageintensityofasingleatomcolumnbecomescosj!!!ljunderthesimplifiedassumptionofcoherentillumination.TheoptimumaberrationsettingsforathickercrystalwereconfirmedthroughanumericalstudyincludingtheeffectsofpartiallycoherentilluminationbyusingimagesimulationsofGeLentzen,2004.Thestudyshowedthattheintensitymodulationattheatomcolumnsitesisenhanced,asexpected,butalsothatproblemsmayariseifthescatteredwavealreadyhasstrongmodulation,forexam-ple,atspecimenthicknessesclosetohalftheextinctiondistance.ThenÒghostintensityÓmayappearatthetunnelpositionbetweentheGecolumns,whichisunrelatedtotheprojectedstructure.Theequationsforoptimumdefocusandsphericalab-errationsshowthatneitherpositivenornegativesphericalaberrationisaloneimportantforimaginginrealmaterialsscienceinvestigations,butanintervalfrom100to100mat200kVispreferred.Thethicknessvariationofthesamplerequiresanadaptationoftheaberrationfunctionfrompositivetonegativevalues. Theabovesectionshaveshownhowanaberrationcorrectorcanbeusedinseveralwaysintransmissionelectronmicros-copytooptimizethehigh-resolutionimagingofobjectsinmaterialsscienceinvestigations.Anoverviewoftheprinci-pleofaberrationmeasurement,aberrationcorrection,andthebeneficialuseofcertaindefocusandsphericalaberra-tionsettingshavebeendescribed.Ithasbeenassumedthatmeasurementsandcorrectionsworkperfectly,andthattheoperatordesireforaspecificaberrationsettingcanbeexecutedprecisely.Thisfinalsectionisdedicatedtopracti-calaspects.TheprerequisiteofpreciseaberrationmeasurementviatheevaluationofaZemlintableauisanaccuratedetermina-tionofdefocusandtwofoldastigmatismfromsinglediffrac-tograms.Thethinamorphousspecimenareasusedtorecorddiffractogramsmustexhibitaconstantdefocusoverthefieldofview,thatis,aflatexitface.Otherwise,thedefocuschangeinduced,forexample,byaninclinedorunevenspecimenwouldintroducearespectivedefocusspreadatten-uatingtheThonringpatternanddeterioratethehigh-frequencyinformationneededforprecisemeasurement.Asimilarconditionappliesforthethicknessoftheamor-phousthinfilm:Scatteringfromatomsatthetopfaceisrelatedtoadifferentfocusplanethanscatteringfromatomsatthebottomface.Thedefocusspreadintroducedbycon-tributionsfrombothfacesandplanesinsidethesamplecanbedeterminedfromthefall-offofthekinematicalenvelope,withsee,e.g.,Hirschetal.,1967toavalueof2,intheframeworkofsinglescattering.Theupperlimittothethicknessoftheamorphousfilm,,isthenequaltothespread:AthirdconditionforprecisemeasurementisalargeenoughextensionoftheamorphousmaterialinrealspacetoavoidaMarkusLentzen ducewithinlinearimagingtheoryanatomcontrastbeingsymmetricalwithrespecttothemeanintensityLentzenetal.,2002.Ifnonlinearcontrastcontributionsareconsid-ered,however,thenastrikingasymmetryoccurs.Thenewimagingmodeproducesstrongercontrastmodulationatatomcolumnsitesthanthetraditionalimagingmode.ThisasymmetryhasbeeninvestigatedbyimagesimulationsforanumberofcrystalstructuresJiaetal.,2004,becauseananalyticaltreatmentinvokingthefullimagingformalismusingthetransmissioncross-coefficientsforpartiallycoher-entilluminationisverycomplicatedandgivesnosimplepictureoftheunderlyingcontrastmechanism.Asimplepicturecanbegained,however,ifanidealZernikephaseplateisassumedforbothimagingmodesJiaetal.,2004,thatis,transmissionofthedirect,unscatteredwavewithacoefficientof1andtransmissionofthescatteredwavewithacoefficientofforpositivephasecontrastandfornegativephasecon-trast.Heredenotestheprojectedcrystalpotentialandthespecimenthickness.Theexitwaveintheobjectplane,isalteredbythephaseplatetotheexitwaveintheimaging7plandtheresultingimageintensitytosecondorderin~plTheuppersignholdsforpositivephasecontrast,thelowersignfornegativephasecontrast,andacommonphaseofhasbeenchosentosettoarealvalue.Figure6displaystheintensitytracesacrossanatomcolumnsite.Thecomparisonofbothcasesshowsthatthelinearcontributionandthequadraticcontributionhaveadiffer-entsignforpositivephasecontrast.Thelocalintensitymodulationatanatomcolumsiteisweak,becausethelinearmodulationispartiallycancelledbythenonlinearmodulation.Thelinearcontributionandthequadraticcon-tributionhavethesamesignfornegativephasecontrast.Thelocalintensitymodulationatanatomcolumnsiteisstrong,becauselinearmodulationandnonlinearmodula-tionreinforceeachother.Inotherwords,usingnegativesphericalaberrationcombinedwithoverfocusenhancestheatomiccontrastfromthinspecimenscomparedtoasettingwithpositivesphericalaberrationandunderfocus.Theaboveconsiderationshavetreatedthecaseofthinsamples,wherethescatteredwavehasonlyasmallmodula-tionrelativetothedirect,transmittedwave,andwheresinglescatteringbytheprojectedcrystalpotentialwithinthefirstBornapproximationleadstoaphaseofthescat-teredwaveof2relativetothedirectwave.Thisrestricts,ingeneral,thecalculationofanoptimumcontrasttransferoftheelectronmicroscopetounrealisticallythinsamples,thatis,theprojectedcrystalcolumnscontainoneheavyatom,atmost,withlargeatomicnumber,oronlyafewlightatomswithsmallatomicnumber.Inmaterialsscienceinves-tigations,however,standardsamplepreparationtechniquesprovidemuchthickersamples,withthicknessesontheorderofafewnanometersandcolumnscontainingmorethanoneheavyatomoralargernumberoflightatoms.Forthickercrystallinesamplesviewedalongalow-indexorientation,thescatteredelectronwavestillhasalocalmodulationresemblingtheprojectedcolumnposi-tions.Atelectronenergiesof200Ð300keVandforatomswithsmallormediumatomicnumbers,thelocalmodula-tionofthescatteredelectronwavecanbedescribedbythesuperpositionoftwoeigenstatesofelectronchanneling,whichleadstocharacteristicbeatingwithathicknessperiodequaltotheextinctiondistanceKambeetal.,1974;Fujimoto,1978.Thedirectelectronwavecanbedescribedcosj!~andthescatteredwaveby!lj Figure6.Intensitydistributionatasingleatomcolumnwithbright-atomanddark-atomcontrast.Imagingwithsmallnega-tivesphericalaberration,,combinedwithasmalloverfocus,providesnegativephasecontrast.Imagingwithasmallpositivesphericalaberration,,combinedwithasmallunderfocus,providespositivephasecontrast.ProgressinAberration-CorrectedHRTEM displacementsvanishaswell,leavingacontrastdelocaliza-tionofzero.Inthisimagingmode,thepointspreadintheimagingplaneisgivenbytheinformationlimitalone.Theimageintensityisgivenbywhereistheexitwavefunctionandisthepoint-spreadfunctionoftheobjectiveapertureorthevirtualapertureoriginatingfromthepartialcoherenceoftheillu-minatingelectronwave.Theresultingamplitudecontrastisnotperceptibleforverythinspecimens,butifthespecimenthicknessincreases,thenmodulationsoftheelectroninten-sitybecomevisible.Theintensitymodulationisparticularlystrongforacrystallineobjectviewedalongalow-indexcrystalaxis,wheretheintercolumndistancesarewellre-solvedandtheintensitymaximaresembletheatomiccol-umnpositions.Insimplecrystalstructures,suchasGe,theexcitationofscatteredwavesislargeatoddmultiplesoftheextinctiondistances,andtheatomicampli-tudecontrastalsotakesamaximumLentzenetal.,2002Hence,perfectaberrationcorrectioncomprisesthreeprop-erties:vanishingcontrastfromaweak-phaseobject,vanish-ingdelocalization,andstrongamplitudecontrast.Ifthecorrectedmicroscopeisalignedforasphericalaberrationofzero,positivephasecontrastofaweak-phaseobjectcanstillbeobtainedbythedefocusaberrationalone:providesapassbanduptotheinformationlimit,atadelocalizationofPositivephasecontrastfromaweak-phaseobjectcanbeoptimizedwiththeaberrationcorrectorbyextendingScherzerÕspointresolutiontotheinformationlimit.UsingSchandsolvingforthesphericalaberrationyieldsLentzenetal.,200230,SchwiththecorrespondingdefocusSchTheresultingdelocalisationisSch,andtheatomicobjectstructureisvisibleasdarkcontrastrelativetothebackground.SimilarexpressionswerederivedbyOÕKeefestartingwiththedefocusconditioninsteadof,andanoldcalculationbyScherzerincludesfurthertheresolutionlimitpossiblyimposedbythefifth-ordersphericalaberration.Itisimmediatelyclearthatsettinghasanunfavorablerelationofblurduetotheinformationlimitandblurduetothedelocalization.Thelatterisalmostthreetimesaslargeastheinformationlimit!Therefore,abetteraberrationsettinghastobefoundthatmaintainsstrongpositivephasecontrastandreducesdelocalization.Thiscompromisecanbeachievedbyequat-ingScherzerÕsdefocusandLichteÕsdefocusofleastconfu-Sch,andsolvingforthesphericalaberrationLentzenetal.,200230,optwiththecorrespondingdefocusoptTheamountofdelocalizationisopt,whichis2timessmallerthanfortheScherzerpassbandextendedtotheinformationlimit.Numericalanalysisshowsthatthephasecontrastisreducedbyonly10%withthisoptimumsettingforthecorrectedPhilipsCM200Lentzenetal.,.Figure1DÐEdisplaysthephasecontrasttransferfunctionsfortheextendedphasecontrastandtheextendedphasecontrastwithreduceddelocalization.Table1givesthecorrespondingsettingsfordefocusandsphericalaberration,aswellastheresultingvaluesfordelocalizationintheimageTheaboveconsiderationshaveshownhowthenewfreedomofvariablesphericalaberrationcanbeexploitedtooptimizetheimagingmodeusedintraditionalhigh-resolutioninvestigations,namelytheimportantpass-bandimagingofverythinweak-phaseobjects.Thelargefixedsphericalaberrationisalwayspositivefortraditionaltransmissionelectronmicroscopes.Thus,theonlywaytoproducephasecontrastfromathinobjectistouseanunderfocussetting.TheresultingaberrationfunctionisnegativeforScherzerpass-bandimaging,andthephasechangeispositive.Thepositivephasecontrastfromaweak-phaseobjectisthereforedarkrelativetothemeanintensity,andcrystallineregionsofathinobjectshowdark-atomcontrast.Thevariablesphericalaberrationoffers,besidesoptimiz-ingpositivephasecontrast,accesstonegativephasecontrastaswell.Thisisachievedbyreversingallaberrations,thatis,tousenegativesphericalaberrationcombinedwithoverfo-Lentzenetal.,2002.Thevaluesarethenthesameasbefore,fortheextendedScherzerpassbandandtheopti-mizedpassbandwithreduceddelocalization,butwithallsignsreversed.Theresultingaberrationfunctionisthenpositiveforthepassbandimaging,andthephasechangeisnegative.Forverythinweak-phaseobjects,thenegativephasecontrastisthereforebrightrelativetothemeanintensity;crystallineregionsofathinobjectshowbright-atomcontrast.Figure1E,Fdisplaysthephasecontrasttrans-ferfunctionsforpositiveandnegativesphericalaberration.Thetraditionalimagingmodewithpositivesphericalaberrationcombinedwithunderfocusandthenewimagingmodewithnegativesphericalaberrationandoverfocuspro-MarkusLentzen usinganelectronenergy-lossspectrometer,duetoreduc-tionofthetemperatureofthefieldemissiontipby100K.Figure5illustratestheintegrationofthedouble-hexapolecorrector,itstransferlenses,andtheadapterlensbetweentheobjectivelensandtheprojectorsystemofthemicroscope.EASUREMENTANDORRECTOR Thedouble-hexapoleaberrationcorrectorprovidesanum-berofwaystocompensatefortheaberrationsofthewholeimagingsystemofthemicroscope,inparticulartheobjec-tivelens,throughtheexcitationofdeflectors,lenses,andthevariouscoilsofthe12-poles.Thecorrespondingcurrentscanbeadjustedwithinwidelimits,andtheactualcurrentsettingsaredependentonpreciseaberrationmeasurementUhlemann&Haider,1998ThemeasurementiscarriedoutbyrecordingaZemlintableauofdiffractogramsZemlinetal.,1978;Typke&Dierksen,1995fromanamorphousspecimenarea.Throughaseriesofdiffractogramswithintentionalilluminationtilts,informationonthetrueaberrationsoftheimagingsystemiscollectedbymeasuringtheindividualinducedfirst-orderaberrationsofdefocusandtwofoldastigmatism.Thelensdefocusissettoacertainunderfocuspriortothemeasure-menttogenerateThonrings,whicharethencompared,diffractogrambydiffractogram,withadatabaseofThonringpatternsforawiderangeofdefocusandtwofoldastigmatismUhlemann&Haider,1998.Themeasuredsetofinduceddefocusandtwofoldastigmatismenters,to-getherwiththeknownilluminationtilts,asetoflinearequationsforthedesiredtruelensaberrations.Finally,thesolutionforthetruelensaberrationsistranslatedviaacalibrationtabletolenscurrentvaluesfortheindividualcorrectorelementsUhlemann&Haider,1998.Thewholemeasurementprocedurerunsonaseparatecomputerdriv-ingthecameraandtheilluminationsystemofthemicro-scopeviaremotecontrol.Themicroscopeoperatorfinallydecidesonthebasisofthedisplayedaberrationanalysistocorrecttheindividualaberrationsviapushbuttons.Anadditionalfeatureofthecontrolsoftwareisapushbuttonforsmallintentionalchangesofthethird-ordersphericalaberration.Theguidefortheoperatoraboutwhichaberrationsmustbecorrectedandwhichaberrationsareunimportantisthe4criterion:Tokeepthewaveaberration,thatis,thedeviationfromawantedreference,withinbounds,themagnitudeofeachsinglelensaberrationshouldnotcauseaphasechangeoflargerthan4attheinformationlimitoftheinstrumentsee,e.g.,thetableinUhlemann&Haider,.Itisappreciatedthatthisruleisonlyapproximateandmaynotreflectthestateofthewholeaberrationfunc-tion,whichisthesumofallindividualaberrationcontribu-tions:Ontheonehand,singleaberrationsofthesamesymmetryviolatingthe4criterionmaycancelfavorablyiftheyhavedifferentsign,suchasasmallpositivethird-ordersphericalaberrationandasmallunderfocus,orasmallpositivetwofoldastigmatismandasmallnegativethird-orderstaraberrationwiththesameazimuth.Ontheotherhand,suchaberrationsmightwelladduptoexceedjointlythe4phasechangeattheinformationlimit.Toaidtheoperatorandtogiveanoverviewofthestateofthewholeaberrationfunction,thecorrespondingphaseplateisdisplayedbythecontrolsoftwareasacontourmaptogetherwiththe4contour.RANSFERAND Intraditionalhigh-resolutionelectronmicroscopy,thefixedlargevalueofthethird-ordersphericalaberrationimposeslimitstothecontrasttransferofthinobjects.Formodernmidvoltagemicroscopes,theScherzerpointresolutionislowerthantheinformationlimit,whichisdeterminedbythetemporalcoherenceoftheelectronsource.AtLichteÕsdefocusofleastconfusion,contrastreversalsstilloccur,makinghigh-resolutionstructureinterpretationdifficult,andattheminimumphase-contrastsetting,thedefocusaberrationandthesphericalaberrationdonotcancelprop-erlyathigherspatialfrequencies.Withtheaddedfreedomofvariablesphericalaberra-tion,theabovethreeimportantimagingmodescanbeoptimizedLentzenetal.,2002.Forperfectaberrationcorrection,zerodefocus,andzerosphericalaberration,thephasecontrastofathinobjectvanishes.Becausetheaberra-tionfunctioniszero,itsgradientandthereforeallray Figure5.Integrationofadouble-hexapolecorrectorintoatrans-missionelectronmicroscope.Thedevice,comprisingthehexapoleelementsH1,H2andthedoubletofroundlenses,T2,isinsertedbetweentheobjectivelensOandtheprojectorsystemPofthemicroscope.Adoubletofroundlenses,T1,isusedtoimagethecoma-freepointoftheobjectivelensintothefirsthexapoleplane.AnadditionallensAisusedtoadaptthewholeraypathtotheprojectorsystem.Theilluminationsystem,I,ofthemicroscopeisunchanged.ProgressinAberration-CorrectedHRTEM matchallopticaxesofthesingleelements,the12-poleelements,andtheroundlenses.Inthefirstfeasibilitystageoftheproject,theaberrationcorrectorwasinstalledonatestbenchtodemonstratesphericalaberrationcorrectionHaideretal.,1995.Thetestsetupconsistedofamodifiedscanningelectronmicro-scopewiththewholecorrectorincorporatedintothespeci-menchamberandaCCDcameracoupledtoascintillatoronaviewingportbeneaththespecimenchamber.Asmallelectronprobewasfocusedonthescintillator,andthroughscanningtheelectronbeamoncircleswithvaryingdiam-eter,theraydisplacementsinducedbytheaberrationcorrec-torcouldbeobserved.Withthisprocedure,thesinglecorrectorelementsweretrimmedandagoodagreementoftheelectronopticpropertieswiththeorywasshown.Inthesecondstageoftheproject,theaberrationcorrec-torwasadaptedtoacommercialPhilipsCM200FEGSTHaideretal.,1995,1998.Thelowerpolepieceoftheobjectivelenswasmodifiedtogainspaceforthefirsttransferlensofthecorrector,andthevacuumsystemofthemicroscopewasadaptedtomaintainhighvacuuminthespecimenarea.Computer-controlledpowersuppliesdrivingthecurrentsthroughthevariouscorrectorelementsweresetuptoprovidearelativestabilityofaround10.Inaddition,aso-calledadapterlenswasaddedbetweentheaberrationcorrectorandprojectorlensesofthemicroscopetomaintainaparallelbeampathwithinthecorrectorandtoenabletheoperatortousethemicroscopecontrolsasusual.Throughintegrationoftheaberrationcorrector,thechromaticaberrationcoefficientofthecorrectedmicro-scopeincreasedfromavalueof1.3mmfortheuncorrectedinstrumentto1.7mm.Theresultingsmalldeteriorationoftheinformationlimitwascompensatedbydecreasingtheenergyspreadofthesourceto0.7eVFWHM,measured Figure3.Distortionofaraybundlethroughahexapolefield,withaviewalongtheopticalaxis.Thepolesaremarkedbyplusandminussigns,theraysbeforeandafterdeflectionbyemptyandfilledcircles,respectively. Figure4.Operationmodesofadouble-hexapolecorrector.Thetwoelementsinthecenterdenoteroundlenses;thetwoelementstotheleftandrightdenotehexapolefields.Hexapolesswitchedoff:Apairofrays,enteringfromtheleft,leavesthedeviceun-deflected,withamagnificationofShortHexapolefield:Apairofraysleavesthedeviceundeflected,becausethedeflectionsofthetwohexapolefieldscancel.Longhexapolefield:Apairofraysleavesthedevicewithapuredivergence,becausethetwohexapoledeflectionscancelandthetwodivergencesaddup.MarkusLentzen ormultipolesScherzer,1936.Theuseofspacechargesandfieldsvaryingwithtimeprovedtobeimpracticalfortrans-missionelectronmicroscopy,andtheuseofmultipolefieldswasnotaccessibleforalongtimeduetothestringentrequirementsforelectricalstability.Aprojectonthecorrectionofatransmissionelectronmicroscopestartedinthemid-1970sBastianetal.,1971;Rose,1971;Heinzerling,1976;Koopsetal.,1976;Kuck,1979;Bernhard,1980;Fey,1980;Hely,1982,1982,wherethedemandsonthecorrectinglenssystemwereparticularlyhigh,becausenotonlydidimagingfromasinglepointintheobjectplanehavetobesuccessfullycorrectedbutalsoimagingofawidefieldofsuchpoints.Theprojectaimednotonlyatsphericalaberrationcorrectionbutalsoatthesimultaneouscorrectionofchromaticaberrationatanac-celeratingvoltageof40kV.Thelayoutofthecorrectorsystemconsistedoffivemagneticoctupoles;thethreecenterelementswerecombinedmagneticandelectricoctu-poles.Sphericalaberrationcorrectionandchromaticaber-rationcorrectionweresuccessfullydemonstrated.Thecorrectedinstrumentreachedaninformationlimitof1.5nmimposednotbyresidualaberrations,butbytheelectricalandmechanicalinstabilitiesoftheuncorrectedmicroscope.Asecondprojectstartedin1992withtheaimofcorrectingsphericalaberrationina200-kVtransmissionelectronmicroscopeRose,1990;Haideretal.,1995.Thecorrectingsystemconsistedoftwohexapolesandfouraddi-tionalroundlenses.Itsadvantageovertheformerlayoutwasastabilityrequirementforthehexapolefieldsofabout10ppm,whichwastwoordersofmagnitudelowerthanforquadrupolefieldsHaideretal.,1998.Thelackofchro-maticaberrationcorrectioninthislayoutwaspartlycom-pensatedbytheuseofamicroscopeequippedwithafield-emissiongun,thusprovidingasmallerelectronenergyspreadandhenceamuchsmallercontributiontothetem-poralcoherenceenvelope.Theprincipleofsphericalaberrationcorrectionusingthedouble-hexapolecorrectorBeck,1979;Rose,1990;Haideretal.,1995canbeunderstoodbyconsideringfirsttheactionofahexapolefieldonarayparalleltotheopticaxis.Iftherayentersthefield,havingathreefoldsymmetry,atadistancefromtheopticaxis,itexperiencesasmalldeflectionproportionalto.Withinalonghexapolefield,thechangeofthedistancetotheopticaxishastobeconsideredaswell,whichintroducesaverysmalladditionaldeflectionoftherayproportionalto.Apairofraysatoppositesidestotheopticaxiswillbedeflectedproportionaltointhesamedirection,duetothethree-foldsymmetryofthefield,butsmalldeflectionspropor-tionaltopointtooppositedirections.Figure2displaysraydiagramsfordeflectionbyshortandlonghexapolefields.Thenetactionofahexapolefieldonabundleofrays,eachwithdistancetotheopticaxis,isthenasmalldivergencebetweenraysatoppositesidestotheaxis,butatthecostofstrongthreefolddistortionofthewholeraybundle.Inthepictureofrayaberrations,thethreefolddeflectionrepresentsathreefoldastigmatism,andthediver-genceisnegativesphericalaberration.Figure3displaysthecorrespondingraydisplacementsinthehexapoleexitplane.Thekeyideaofsphericalaberrationcorrectionbyadoublehexapoleisnowthecombinationoftwohexapolefields,sothatthestrongthreefolddistortionscancelandthetwodivergingdeflectionsadd.Thisisachievedbyatransferdoubletofroundlenseswithamagnificationof1be-tweenthetwohexapoleplanesintroducingapointinver-siontotheraybundle.Anothertransferdoubletofroundlensesisintroducedbetweentheobjectivelensofthemicro-scopeandthefirsthexapoleplane.Itspurposeistoimagethecoma-freepointoftheobjectivelensintotheplaneofthefirsthexapole.Thusthewholeassemblyofobjectivelensandcorrectorbecomessemi-aplanatic,thatis,off-axialab-errationsareminimized,andawidefieldofimagepointsisspherical-aberrationcorrectedRose,1990.Figure4dis-playsraydiagramsillustratingpointinversionbythefirsttransferdoubletandthedeflectionofapairofraysbyshortandlonghexapolefields.Thetwohexapoleelementsareusuallyassembledas12-polestoleavesomefreedomforthecompensationofsmallrelativemisorientationofthetwohexapolefieldsduetolimitedprecisionofthemachiningsetup.Forthesamereason,anumberofdeflectioncoilsisaddedinorderto Figure2.RaypathsthroughahexapolefieldforapairofraysparalleltotheopticalaxisO.A.Theraysenterthefieldatdistancesinadipoleplane.DeflectionthroughashorthexapolefieldproportionaltoDeflectionproportionaltoadditionaldivergenceproportionaltothroughalonghexapoleProgressinAberration-CorrectedHRTEM Therewasstillaneedforadirectsolutiontothedelocalizationproblem:Theindirectexit-wavereconstruc-tionmethodswerenotabletoprovidethemicroscopeoperatorwithafastanddirectviewoftheobjectstructureatthelocationofinterest.Directlenscorrectionwasex-pectedtorevealsuchanimage,andaprojectonlensaberrationcorrectionofamedium-voltagetransmissionelectronmicroscopestartedin1992withtheaimofshow-ingthepotentialoflenscorrectionforhigh-resolutionmaterialsscienceinvestigationsHaideretal.,1995.TheprojectwasbasedonanoutlineforanaberrationcorrectorbyRose1990,1994ORRECTOR Formanyyears,sphericalaberrationcorrectionoftheimag-ingsystemofatransmissionelectronmicroscopeseemedtobeimpossible.Scherzerhadalreadyshownthatsuchcorrec-tionofaroundobjectivelenscannotbemade,inprinciple,withouttheuseoffieldsvaryingwithtime,spacecharges, Figure1.Typicalphasecontrasttransferfunctionsforanaccelerationvoltageof200kV.Scherzerdefocus,LaBsource,largepositivesphericalaberration.Scherzerdefocus,FEGsource,largepositivesphericalaberration.Lichtedefocus,FEGsource,largepositivesphericalaberration.Scherzerdefocus,FEGsource,smallpositivesphericalaberration.ScherzerdefocusLichtedefocus,FEGsource,smallpositivesphericalaberration.ScherzerdefocusLichtedefocus,FEGsource,smallnegativesphericalaberration. Table1.,for200kVMicroscopeswithLaBandFEGSources,andforDifferentSettingsofDefocus,,andSphericalAberration, Scherzerdefocus,LaB641.230.65Scherzerdefocus,FEG641.234.2Lichtedefocus,FEG3711.232.5ExtendedScherzerdefocus,FEG170.0830.33ScherzerdefocusLichtedefocus,FEG110.0370.07MarkusLentzen Intraditionalelectronmicroscopy,aberrationcorrec-tionislimitedfirsttofindingthecoma-freeaxisoftheobjectivelensbyusinganintentionalilluminationtiltandtheneliminatingtwofoldastigmatismbyusingtheobjectivelensstigmators.Thelarge,positive,andfixedthird-ordersphericalaberration,whichisontheorderofthefocallengthoftheobjectivelens,iscombinedwithafavorabledefocussettingtoformtheScherzer4phaseplate,SchwiththepointresolutionSchsothatobjectinformationuptoaspatialfrequency1Schtransferredwiththesamesignoftheaberrationfunction,yieldingdark-atomcontrastforathinspecimen.Theuseoffactorsintheaboveequationsextendsthepointresolutionslightly,asinthetreatmentofEisenhandlerandSiegel,comparedwiththeoriginalScherzerdefocusScherzer,1949.TheScherzerphaseplateistheequivalentoftheZernikephaseplateinlightopticsZernike,1942,1955:Theweakpotentialofthinspecimensimposesaphasechangeofthescatteredelectronwaveby2withrespecttothetransmittedwave,andtheadditionalphasechangeoftheobjectivelensbyanother2producesastructureimagewithpositivephasecontrast.Inaddition,LichteÕsdefocusofleastconfusionLichte,denotestheimagingplanewherethelargestraydisplace-insideanaperturegivenbytheinformationhasaminimum,thatis,therespectivebundleofraysinsidetheaperturehasaminimumdelocalizationofAnotherimportantsettingistheminimumphase-contrastdefocusHeinemann,1971transferringinformationfromathinobjectuptoaspatialfrequencywithcontrastclosetozero.ThisdefocusisimportanttoestablishinganeasilydetectablereferenceinordertosettheobjectivelenseithertoScherzerdefocusorLichteÕsdefocusofleastconfusion.Astheinformationlimitoftransmissionelectronmi-croscopeshasimproved,chieflybytheuseoffield-emissionelectronguns,theimportanceofcorrectingthreefoldastig-matismbecameapparentTypke&Dierksen,1995.ThisproblemwassoonsolvedbyincorporatingarespectivestigmatortocompensateforthefixedthreefoldastigmatismoftheobjectivelensWangetal.,1999.Atthesametime,theinfluenceofhigher-orderaberrations,suchasthird-orderstaraberration,,orfourfoldastigmatism,,didnotseemtobeimportantforhigh-resolutionmaterialsscienceinvestigations.Becauseoftheimprovinginformationlimitoffield-emissioninstruments,thediscrepancybetweeninformationlimitontheonehandandpointresolutionandminimumdelocalizationontheotherhandincreased.Foramodern300-kVinstrumentwith0.6mmandaninformationlimitof0.1nm,thepointresolutionamountstoonly0.17nmandthesmallestdelocalizationtoeven1.2nm!ForsuchaninstrumentoperatedatScherzerdefocus,rapidcontrastreversalsoccuratspatialfrequenciesbetweentheScherzerlimitandtheinformationlimit,impairingintu-itivestructureinterpretationforathinobjectLichte,1991;Coene&Jansen,1992.AtLichteÕsdefocus,minimizingdelocalization,anumberofcontrastreversalsappearovertheentirefrequencyrangeLichte,1991.Thecomparablypoorpointresolutionandthecontrastreversalsareduetothestrongsphericalaberration,whichintheabovecasecontributes12fullcyclesoftheaberrationfunction.Figure1AÐCprovidesanoverviewofphasecontrasttransferfunctionsforScherzerdefocusandaninstrumentequippedwithaLaBsource,forScherzerdefocusandimprovedspatialcoherencewithanFEGsource,andLichteÕsdefocusofleastconfusion.Thecalculationsassumeanaccelerationvoltageof200kVandalargesphericalaberra-tionof1.23mm.Table1givesthecorrespondingdefocussettingsandtheresultingvaluesforthedelocalizationintheimageplane.Twoindirectmethodsforaberrationcorrection,andinparticularforspherical-aberrationcorrection,becamefeasibleinthe1990s:high-resolutionelectronholographyLichte,1986;Tonomura,1993andthrough-focusseriesreconstructionsee,e.g.,Coeneetal.,1992,1996;Saxton,1994;Thustetal.,1996,1996.Bothmethodsmeasuretheexitwavefunctionintheimageplane,,whichisthenusedtorestoretheexitwaveintheobjectplane,,byapplyinganumericalphase-plateexpdeter-minedfromanindependentmeasurementoftheaberrationThustetal.,1996;Lehmann,2000;Saxton,.Therestoredexitwaveintheobjectplaneisalmostfreeofdelocalizationandyieldsatomicstructuredetailouttotheinformationlimitofthemicroscope.Averysmallresidualdelocalization,whichis,inpractice,smallerthantheblurringduetothefiniteinformationlimit,resultsfromthesmall,unavoidableerrorsoftheaberrationmeasurement.ProgressinAberration-CorrectedHRTEM structureimage.GaborÕsconceptsoonyieldedfruitinlightLeith&Upatnieks,1962,1963,1964,butnotuntil40yearslaterwiththeadventofelectronsourceswithimprovedcoherenceinhigh-resolutionelectronmicroscopyLichte,1986;Tonomura,1993Avariantoftheholographicrestorationoftheundis-turbedscatteredelectronwavewasproposedbySchiskein1968,withtheideaofchangingthelensdefocussystemati-callyandmeasuringtheimageintensityatmanyimagingSchiske,1968,2002;Saxton,1978,1988;VanDycketal.,1993.Eachimagerepresentsanin-linehologram,intermsofGaborÕsformalism,andanunambiguoussolutionofthereconstructionproblemcanbefoundbyusingasetoffilterstodeducethecomplexelectronwavefromtheimageseries.Themethodanditsvariantsbecameusefulforhigh-resolutionstructureinvestigationsinthe1990s,whenmorepowerfuldigitalcomputersbecameavailableCoeneetal.,1992,1996;Saxton,1994;Thustetal.,1996Adirectinstrumentalapproachtothespherical-aberrationproblemwasalreadyproposedbyScherzer:Theuseofmultipolelensesprovidesawaytoproduceadiverg-inglenssystemwithnegativesphericalaberration,thuscompensatingthepositivesphericalaberrationoftheobjec-tivelensScherzer,1947.Duetotechnicaldifficulties,how-ever,severalattemptstoimprovetheopticalperformanceofahigh-resolutiontransmissionelectronmicroscopehaveThisreviewreportsontherecentsuccessfulattemptatmultipoleaberrationcorrectionofamedium-voltagetrans-missionelectronmicroscope,thePhilipsCM200FEGST,operatedatanacceleratingvoltageof200kVHaideretal.,.Anoverviewoftheimportantlensaberrations,theprincipleofsphericalaberrationcorrectionwithamulti-poleaberrationcorrector,aberrationmeasurement,andcor-rectoralignment,contrasttransferandnewimagingmodesinthecorrectedmicroscope,hintsforpracticalwork,andmaterialsscienceapplicationsarealsodescribed.Thespherical-aberrationproblemexistsaswellintherelatedtechniqueofscanningtransmissionelectronmiscos-copy,whichisbeyondthescopeofthisreviewduetothedifferentelectron-opticalconstructionofthatmicro-scopesandduetothedifferentelectron-opticalapproachtospherical-aberrationcorrectionDellbyetal.,2001;Batsonetal.,2002 Foranideallens,raysoriginatingfromanobjectpointconvergeatasingleimagepoint.Intheequivalentwavepicture,thesphericalwaveoriginatingfromapointobjectistransformedbytheideallenstoasphericalwaveconverg-ingtowardtheimagepoint.ImperfectlensesaredescribedinthefirstsystembyrayaberrationsandinthesecondsystembywaveaberrationsBorn&Wolf,1980.Therayaberrationofarayleavingtheobjectpointwithadiffrac-tionvectorisgivenbythedisplacementvectorfromtheidealGaussianimagepointtothepointwheretheray,afterpassingthroughthelens,intersectstheimageplane.Thewaveaberrationisthedeviationofthewavefront,imposedbythelens,fromtheidealreferencesphereconverg-ingtowardtheidealimagepoint.ThedeviationofthewavefrontisexpressedbyanadditionalphaseshiftbetweenthewavefunctionintheobjectplaneandthewavefunctionintheimageplaneexpTheaberrationfunctioncanbewrittenincompactform,ifisexpressedasacomplexnumber,andtherelatedcomplexscatteringangle,,withbeingtheelectronwavelength,isusedsee,e.g.,Uhlemann&Haider,1998.Expandingtofifthorderinyieldswiththelensaberrationcoefficientsdefocus,twofoldastigmatism,second-ordercoma,threefoldastigma-,third-ordersphericalaberration,third-orderstaraberration,fourfoldastigmatism,fourth-ordercoma,three-lobeaberration,fivefoldastigmatism,fifth-ordersphericalaberration,fifth-orderstaraberration,rosetteaberration,andsixfoldastigma-.ThelensaberrationcoefficientsarecomplexnumbersdenotingthetwoCartesiancomponents,except-,and,whicharerealnumbers,anddenotesthecomplexconjugateofDifferentsystemscanbefoundintheliteraturetodenoteaberrationcoefficientse.g.,compareBernhard,1980;Uhlemann&Haider,1998;Saxton,2000.Inthisreview,wehaveusedindicestodenoteorderandazimuthalsymmetryoftheaberration.FollowingthesuggestionofSaxton,factors1wereusedforallcontri-butionstothethorder.Therayaberrationislinkedtothewaveaberrationby]x~Lichte,1991;Coene&Jansen,1992MarkusLentzen ©MICROSCOPYSOCIETYOFAMERICA2006 ProgressinAberration-CorrectedHigh-ResolutionTransmissionElectronMicroscopyUsingHardwareAberrationCorrectionMarkusLentzen*InstituteofSolidStateResearch,ErnstRuskaCentreforMicroscopyandSpectroscopywithElectrons,ResearchCentreJŸlich,52425JŸlich,GermanyAbstract:Thedesignandconstructionofadouble-hexapoleaberrationcorrectorhasmadeitpossibletobuildtheprototypeofaspherical-aberrationcorrectedtransmissionelectronmicroscopededicatedtohigh-