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PROCEDUREFORPERFORMINGFLATNESSMEASUREMENTFLATNESSMEASUREMENTSAREPERFORMEDTOCHECKTHEFLATNESSOFCMMTABLESANDSURFACEPLATESITDETERMINESWHETHERANYSIGNIFICANTPEAKSORTROUGHSEXISTANDQUANTIFIESTHEMIFTHESEERRORSARESIGNIFICANTTHENREMEDIALWORK,SUCHASLAPPING,MAYBEREQUIREDTOUNDERSTANDTHEBASICPRINCIPLESANDTECHNIQUESOFFLATNESSMEASUREMENTREFERTOTHEPRINCIPLESOFFLATNESSMEASUREMENTSTANDARDMETHODSOFASSESSINGFLATNESSPRINCIPLEOFFLATNESSMEASUREMENTTHEFLATNESSMEASUREMENTKITISUSEDTOMEASUREFLATNESSTHEANGULARINTERFEROMETERISATTACHEDTOTHETURNINGMIRRORANDTHEANGULARREFLECTORISATTACHEDONTOPOFTHESELECTEDFLATNESSBASETHEANGULARINTERFEROMETERISPLACEDINTHEPATHBETWEENTHELASERHEADANDTHEANGULARREFLECTORFIGURE1PRINCIPLEOFMEASUREMENTTHELASERBEAMISSPLITINTOTWOBYTHEBEAMSPLITTERINSIDETHEANGULARINTERFEROMETERONEPARTOFTHEBEAMTHEMEASUREMENTBEAMA1PASSESSTRAIGHTTHROUGHTHEINTERFEROMETERANDISREFLECTEDBYONEOFTHETWINREFLECTORSOFTHEANGULARREFLECTORBACKTHROUGHTHEINTERFEROMETERANDINTOTHELASERHEADTHEOTHERBEAMMEASUREMENTBEAMA2PASSESTHROUGHTHEPERISCOPEPARTOFTHEANGULARINTERFEROMETERTOTHESECONDREFLECTORFROMWHEREITRETURNSTHROUGHTHEINTERFEROMETERANDINTOTHELASERHEADANANGULARMEASUREMENTISPRODUCEDBYCOMPARINGTHEPATHDIFFERENCEBETWEENTHEBEAMSA1ANDA2,IETHEMEASUREMENTISINDEPENDENTOFTHEDISTANCEBETWEENTHELASERANDTHEINTERFEROMETERTHEFLATNESSREADINGDISPLAYEDBYTHESOFTWAREISTHEINCREMENTALHEIGHTBETWEENTHEFRONTANDBACKFEETOFTHEFLATNESSBASEPLATEONWHICHTHEANGULARREFLECTORISFITTEDTHISINCREMENTALHEIGHTISCALCULATEDFROMTHEANGULARMEASUREMENTANDKNOWLEDGEOFTHEDISTANCEBETWEENTHECENTRESOFTHEFRONTANDBACKFEETOFTHEFLATNESSBASEPLATETHISDISTANCE,TERMEDTHEFOOTSPACING,MUSTBEENTEREDINTOTHECALIBRATIONSOFTWAREBEFOREMEASUREMENTSTARTSFOREACHMEASUREMENTLINESEESTANDARDMETHODSFORASSESSINGFLATNESS,THEANGULARINTERFEROMETERMOUNTEDONTHEFLATNESSTURNINGMIRRORSTAYSSTATIONARY,WHILETHEREFLECTORMOUNTEDONAFLATNESSBASEMOVESALONGTHELINEININCREMENTALSTEPSDEFINEDBYTHEFOOTSPACINGAFLATNESSMEASUREMENTISCARRIEDOUTBYTAKINGASERIESOFINCREMENTALHEIGHTREADINGSASTHEANGULARREFLECTORISMOVEDALONGTHEMEASUREMENTPATHFIGURE2INCREMENTALMEASUREMENTSDRAWINGCHANGESINFIGURE2ABOVEPOSITIONIISTHEINITIALPOSITIONATWHICHTHEINTERFEROMETERREADINGISNORMALLYDATUMEDPOSITIONIIISONEFOOTSPACINGBEYONDPOSITIONITHEINTERFEROMETERREADINGWILLBETHEINCREMENTALDISTANCED1,WHICHISTHEDIFFERENCEINHEIGHTWITHRESPECTTOTHEDATUMLINEOFTHEFRONTANDBACKFEETOFTHEFLATNESSBASEPLATEPOSITIONIIIISONEFOOTSPACINGBEYONDPOSITIONIITHEINTERFEROMETERREADINGWILLBED2,IETHEDIFFERENCEINHEIGHTBETWEENTHEFRONTANDBACKFEETOFTHEBASEPLATEINITSNEWPOSITIONSIMILARLY,THEREADINGATPOSITIONIVWILLBED3,ANDSOONFORALLSUBSEQUENTPOSITIONSONTHEMEASUREMENTLINETHEACTUALFLATNESSOFTHEMEASUREMENTLINEWILLBETHEALGEBRAICSUMOFTHEREADINGD1,D2ETCPLUSTHEREADINGATTHE‘DATUM’POSITIONIIFITHADNOTBEENZEROEDNOTEENVIRONMENTALCOMPENSATIONISNOTREQUIREDWHENTAKINGFLATNESSMEASUREMENTS,ASTHEDIFFERENCEINPATHLENGTHSBETWEENTHETWOBEAMSISSOSMALLTHATTHEERRORDUETOENVIRONMENTALEFFECTSISNEGLIGIBLESTANDARDMETHODSFORASSESSINGFLATNESSTOMEASURETHEFLATNESSOFASURFACE,ANUMBEROFMEASUREMENTLINESNEEDTOBETAKENOVERTHESURFACETHEREARETWOSTANDARDMETHODSOFCARRYINGOUTFLATNESSMEASUREMENTSMOODYMETHODGRIDMETHODTHEFLATNESSOFASURFACECANBEDEFINEDASTHESEPARATIONOFTWOPLANESWHICHAREPARALLELTOTHEGENERALTRAJECTORYOFTHESURFACEANDWHICHJUSTENCLOSETHEMEASUREDSURFACEASSHOWNINFIGURE1FIGURE1FLATNESSSPECIFICATIONFLATNESSDEVIATIONSFORASURFACEPLATEOFAKNOWNSIZECANBECOMPAREDWITHPERMITTEDDEVIATIONSINNATIONALSTANDARDSMOODYMETHODWITHTHEMOODYMETHOD,MEASUREMENTISRESTRICTEDTOTHEEIGHTPRESCRIBEDLINESASSHOWNINFIGURE2FIGURE2MOODYMAPOFSURFACEPLATETHEMOODYMETHODWASFIRSTPROPOSEDBYJCMOODYIN1955ANDHASSUBSEQUENTLYACHIEVEDWIDEACCEPTANCETHEMETHODPROVIDESARELATIVELYQUICKMETHODOFCALIBRATINGASURFACEPLATE,WITHTHERESULTSBEINGPRESENTEDASACONTOURPLOTALONGTHEEIGHTMEASUREMENTLINESTESTED,INAFORMATACCEPTABLEFORCERTIFICATIONTHISMETHODDOESHAVEONEDISADVANTAGEALLOFTHEPOINTSONALLOFTHEEIGHTLINESMUSTBEMEASUREDANDPLOTTEDTHISCANCAUSEPROBLEMSINDEFININGAFOOTSPACINGWHICHWILLMEETTHISREQUIREMENT,PARTICULARLYONSLOTTEDTABLES/SURFACESWHERETHEPOSITIONOFONEORMORESLOTSMAYCOINCIDEWITHTHEREQUIREDPOSITIONOFONEOFTHEFEETOFTHEFLATNESSBASEGRIDANDHALFGRIDMETHODWITHTHEGRIDMETHOD,ANYNUMBEROFLINESMAYBETAKENINTWOORTHOGONALDIRECTIONSACROSSTHESURFACEASSHOWNINFIGURE3FIGURE3GRIDMAPOFSURFACEPLATEWITHTHEGRIDMETHOD,WHILSTTHEINCREMENTALNATUREOFTHEMEASUREMENTTECHNIQUEREQUIRESTHATALLPOINTSONAGIVENLINEAREMEASURED,ITISNOTNECESSARYTOTAKEMEASUREMENTSONALLLINESTHISALLOWSTHEMEASUREMENTLINESTOBECONFIGUREDTOAVOIDOBSTRUCTIONSEGSLOTSORTOPROVIDEGREATERDETAILINAGIVENAREATHEHALFGRIDMETHODASSHOWNINFIGURE4ISASPECIALCASEOFTHEGRIDMETHODWHEREANUMBEROFMEASUREMENTLINESARETAKENINONEDIRECTIONEGTHEXAXIS,BUTONLYTHEPERIMETERLINESAREUSEDFORTHEORTHOGONALDIRECTIONFIGURE4HALFGRIDMAPOFSURFACEPLATEADISADVANTAGEWITHBOTHGRIDMETHODSISTHATTHEYREQUIREAREFERENCEPLANETOBEDEFINEDANALTERNATIVETECHNIQUESUCHASTHEMOODYMETHODISNEEDEDTODEFINETHISREFERENCEPLANETOPERFORMFLATNESSMEASUREMENTSUSINGTHEMOODYMETHOD,CARRYOUTTHEFOLLOWINGSTEPS