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33520125ChineseJournalofScientificInstrumentVol.33No.5May．20122010-12ReceivedDate2010-12*“”2010ZX04014-091、50627501、PHR201006104*11211001242230009。、、、、5。、、、、、。。。。TB92A460．2010Re-visittotheAbbeprincipleShiZhaoyao1ZhangBin1FeiYetai21CollegeofMechanicalEngineeringandAppliedElectronicsTechnologyBeijingUniversityofTechnologyBeijing100124China2SchoolofInstrumentScienceandOpto-electronicsEngineeringHefeiUniversityofTechnologyHefei230009ChinaAbstractToexploretheadaptabilityoftheAbbeprincipleinmodernultra-precisionmanufacturingandmeasure-menttheAbbeprincipleanditsextensionarereviewedthefirstordererrorsduetotheconfigurationoftheele-mentsareanalyzedandtheAbbeprinciplefortwodimensionallengthmeasurementisdiscussed．Throughanalyzingtheerrorsgeneratedbythedifferentconfigurationsoffiveelementssuchasreferencemeasurandsensingpointref-erencepointandguidingsurfaceitisdiscoveredthatthefirstordererrorsarefoundwhenthesensingpointrefer-encepointandguidingsurfacearenotinthesamelinewhilethereferenceandmeasurandarecollinearastheAbbeprinciplerequires．TheconceptsofcollinearsensingpointcollinearreferencepointandcollinearguidingsurfacearepresentedandtheAbbeoffseterrorsenseoffseterrorreferenceoffseterrorguidingoffseterrorandAbbecompre-hensiveerroraredefined．TheimpliedconditionsoftheAbbeprinciplearerevealedandanewstatementofAbbeprincipleispresented．TheadaptabilityoftheAbbeprincipleinstack-upandco-planartwodimensionalstructuresisdiscussed．Asapplicationsaconcisestructureforimprovingtheaccuracyoftoolmicroscopesisproposedandaco-planartwodimensionalprecisionstageisintroducedinwhichtheAbbeerrorisreduced．Throughre-understandingtheAbbeprincipleitispossibletoupdatethedesignphilosophyforthedesignofnewultra-precisioninstrumentsandmachineryandfortheupgradeoftypicalmetrologyinstruments．KeywordsAbbeprinciplefirstordererrorAbbeerror2DAbbeprinciple5112911890·ErnstAbbe1。SiegfriedCzapski《》23。μm。4-56。7-11。3nm。。。。22．11212。1。LφφΔLΔL=Lcosφ－1≈－12L·φ2L=500mmφ=10″ΔL=－0．00000059mm。。1Fig．1ConfigurationcompliedwiththeAbbeprinciple2Fig．2ConfigurationnotcompliedwiththeAbbeprinciple2。Aφαα=Atanφ≈AφA=100mmφ=4″α=0．00195mm。。。2．2。OttoEppenstein。、、。。J．B．Bryan13。。14。。。15、。、、。16。1130332。17nm。。2．3。、、、5。33．1。“”。2“”。。3．2。“”。“”。3Sδ=Stanφ≈S·φ。。3Fig．3Senseoffseterror4Rθ=Rtanφ≈Rφ。。4Fig．4Referenceoffseterror3．3。2。、“”。5GGξ≈G·φ。。5Fig．5Guidingoffseterror44．1。、。、、。4．251131、。“”。、、。5。。。2218619-207。。YYYXX。、、、。XY。XXXXYXX、、、、YYYYXYY、、、、。XY。。66．18。。μm。8Fig．8Classicaltoolmicroscopeconfiguration9。。19nm、。9Fig．9Animprovedtoolmicroscopeconfiguration1132336．2H、、。10H21。HXY。10HFig．10HstyletwodimensionalprecisionstageXY。X0．93μmY0．93μm0．9722。7。、、、、。、、、“”。H。。1ABBEE．MessapparatefuerPhysikerJ．ZeitsfuerIn-strumentenkunde189010446-448．2CZAPSKIS．GrundzuegedertheoriederoptischenInstru-mentenachAbbeM．LeipzigVerlagvonJohannAm-brosiusBarth1904．3EVANSC．PrecisionengineeringAnevolutionaryviewM．BedfordEnglandCranfieldPress1989．4LUCC．J．20113271655-1659．XUSANLIDSHLUCCetal．Researchofnanopo-sitioningmethodbasedonphase-controlheterodyneinter-ferometrictechniqueJ．ChineseJournalofScientificInstrument20113271655-1659．5．J．20113251138-1144．XUQXHOUWMSHENGSHJetal．3-dimension-alprofilerbasedondigitalmicromirrordeviceJ．Chi-neseJournalofScientificInstrument20113251138-1144．6．M．．2011—2020．2010288-315．ZENGLJZHAOWQZHUJG．MeasurementscienceofmanufacturalandoperationalparametersofmachinesM．DepartmentofEngineeringandMaterialsScienceofNationalNaturalScienceFoundationofChina．Strategicreportonmechanicaldisciplinedevelopment2011—2020．BeijingSciencePress2010288-315．7．———J．2011375648-656．SHIZHYZHANGBLINJCHetal．Halfcenturyofcoordinatemetrologytechnology—EvolutionandtrendsJ．JournalofBeijingUniversityofTechnology2011375648-656．8JAEGERG．Ananopositioningandnanomeasuringma-chineoperationmeasuredresultsJ．NanotechnologyandPrecisionEngineering20042Suppl．81-84．9RUIJLT．UltraprecisioncoordinatemeasuringmachineDesigncalibrationanderrorcompensationD．TheNetherlandsTechnischeUniversiteitEindhoven20017-84．10FANKCLIUCLWUPTetal．Thestructurede-signofamicro-precisionCMMwithAbbeprincipleJ．Proceedingsofthe35thInternationalMATADORConfer-ence200712297-300．11SPAANHAMWIDDERSHOVENI．Isara400ultra-precisionCMMJ．Proc．SPIE2011816981690T．doi10．1117/12．902237．5113312．M．2004．LIQXWANGDSHLIYH．Designofmodernpreci-sioninstrumentsM．BeijingTsinghuaUniversityPress2004．13BRYANJB．Designandconsructionofanultra-precision84inchdiamondturningmachineJ．PrecisionEngi-neering19791113-18．14BRYANJBCARTERDL．Designofanerror-correctedco-ordinatemeasuringmachineJ．PrecisionEngineer-ing197913125-128．15ZHANGGX．AstudyontheAbbeprincipleandAbbeerrorJ．CIRPAnnals-ManufacturingTechnology1989381525-528．16．-J．B．BryanJ．1993142212-215．NIEHJ．Aamendideaforthestraightnessmeasurementprinciple-J．B．BryanadviceJ．ChineseJournalofSci-entificInstrument1993142212-215．17FEIYTSHANGPCHENXetal．TheAnalysisandcomplementarityofAbbeprincipleapplicationlimitedincoordinatemeasurementC．ProceedingsoftheWorldCongressonEngineeringLondonU．K．2010．18．J．2011194828-835．WANGSHZHXIETBCHANGSP．Combinedpro-filometerforultra-precisionsurfacetopographyJ