文档介绍：该【ultraprecision real-time displacements calculation algorithm for the grating interferometer system weinan ye资料 】是由【宝钗文档】上传分享，文档一共【9】页，该文档可以免费在线阅读，需要了解更多关于【ultraprecision real-time displacements calculation algorithm for the grating interferometer system weinan ye资料 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eamMB,Splitter;MeasuringMB,Beams;MeasuringRB,ReferenceBeams;RB,Beams;ReferenceIS,InterferenceBeams;IS,-DOWSmodel,thegratinginterferometersystemofthewaferToestablishtheprecisephaseshift-DOWSmodel,thegratinginterferometersystemofthestageshowninFigure1isreducedtosomecoordinatesystems(CSs)andpoints,(CSs)andpoints,asshowninThe6--DOFDOWSCS??
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relativetotheprojectionlensCS??
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isthemeasured(Dxl,Dyl,Dzl,Rxl,Ryl,Rzl).PointsA,B,andCrepresentthekeypointsinwhichthemeasuringbeamsDOWS
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.PointsA,B,,thechange???ofSensors2019,19,,19,ofxallkeypointsandtheDOWSisdetermined,thechange?Lofthetotallength3ofofall9??,thetotallengthofallmeasuringbeamsanddiffractionspotdisplacements???inthe??directionthephaseshift?ofinterferencesignalcanbegivenby
,thephaseshift??ofinterferencesignalcanbegivenby2πα?2πn?=?22πα?S+?πn?L,(1)?=?ΔSL+λΔ,pxλ(1)pxwhereαisthedi?ractionorder,pisthegratingpitchintheXdirection,nistherefractiveindexinwhere??isthediffractionorder,??xisthegratingpitchinthe??gidirection,??istherefractiveindextheair,andλisthewavelengthof
thelaser.
intheair,and??????
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fixedtotheCS??
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representsgratingofthegratinginterferometer#i,andtheCSOEiXEiYEiZEi?xedtotheCSOsXsYsZsrepresentsthegratingofthegratinginterferometer#i,andtheCS??
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fixedtotheCS??
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encoder#(z-y-xextrinsic)betweentheCSOXYZandtheCSOXYZisrepresentsencoder#(z-y-xextrinsic)betweengithegiCSgigi????????andllthelCSl?
(txi,tyi,tzi).Theredarrowsrepresentthetypicalinternalandexternaleectiveopticalpathofthe??
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.,,andthedi??L,?Sismoreintuitive,andtherefore,DOWSisTherelationshipbetweentheDOEand???,???ismoreintuitive,andtherefore,DOWSisfirst???
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.RotationaldisplacementscanbetransformedbythebythetransformationmatrixbetweentheCSOlXlYlZlandCSOgiXgiYgiZgi,andthetranslationaltransformationmatrixbetweentheCS??
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andCS??
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,andthetranslationaldisplacementsaretransformedbyEquation(2).WhentheDOEdxgi,dygi,dzgi,rxgi,rygi,rzgiisdisplacementsaretransformedbyEquation(2).WhentheDOE
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iscomputed,thetransformationfromCSOgiXgiYgiZgitoCSOEiXEiYEiZEicanberepresentedbycomputed,githetransformationfromCS??
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toCS??
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canberepresentedbymatrix
,thehomogeneousmatrixofpointAthatdoesnotchangematrix
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Ei,thehomogeneousmatrixofpointAthatdoesnotchangewithwiththeDOEisaconstantmatrix
??.putationofthehomogeneousEimatrixofpointBrequiresonstraintsforbeamAB:thedirectionvectorDABof
beamABcanbecalculatedtheuseofgeometricπconstraintsforbeamθAB:thedirectionvector??
ofbeamABcanbebytheazimuthandtheLittrowanglel;??andtheLittrowangle??
;githeZcoordinateofpointBintheCSAccordingtotheseconstraints,Equation(3)issettosolveB.
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,Equation(3)issettosolve??.hiTgiTl??1lsiE=gi=dx??gidygidzgi1==l1QlsisQEEQQE??dxgidygidzgi1gigishTiTsisi==···E=Emx????mxsisimymysisimzsisi11,21,iK,i=?1,2K??Tl?Rot()tx,,tytzh??mxmymziT?Q?=??(iii)??sisisi,?,(2)(2)l=gi?Rottxi,tyi,tzi