《光学检测CH》PPT课件

1.0BasicWavefrontAberrationTheoryForOpticalMetrology,ChangchunInstituteofOpticsandFineMechanicsandPhysics,Dr.ZhangXuejun,ThePrincipalpurposeofopticalmetrologyistodeterminetheaberrationspresentinanopticalcomponentoranopticalsystem.Tostudyopticalmetrologytheformsofaberrationsthatmightbepresentneedtobeunderstood.,Formostopticaltestinginstruments,thetestresultisthedifferencebetweenareference(unaberrated)wavefrontandatest(aberrated)wavefront.WeusuallycallthisdifferencetheOpticalPathDifference(OPD).,NotethattheOPDisthedifferencebetweenthereferencewavefrontandthetestwavefrontmeasuredalongtheray.,1.1SignConvention,TheOPDispositiveiftheaberratedwavefrontleadstheidealwavefront.Inotherword,apositiveaberrationwillfocusinfrontoftheparaxial(Gaussian)imageplane.,RightHandedCoordinates:ZaxisisthelightpropagationdirectionXaxisisthemeridionalortangentialdirectionYaxisisthesagittaldirection,Thedistanceispositiveifmeasuredfromlefttoright.TheangleispositiveifitisincounterclockwisedirectionrelativetoZaxis.,Sincemostopticalsystemsarerotationallysymmetric,usingpolarcoordinateismoreconvenient.,x=cosy=sin,1.2AberrationFreeSystem,Iftheopticalsystemisunaberratedordiffraction-limited,forapointobjectatinfinitytheimagewillnotbea“point”,butanAiryDisk.ThedistributionoftheirradianceontheimageplaneofAiryDiskiscalledPointSpreadFunctionorPSF.SincePSFisverysensitivetoaberrationsitisoftenusedasanindicatoroftheopticalperformance.,DiametertothefirstzeroringiscalledthediameterofAiryDisk,:workingwavelengthF#:fnumberofthesystem,Finiteconjugate,NA:numericalApertureNA=nsinu,F#W:WorkingFnumber,Ruleofthumb:forvisiblelight,0.5m,DAiryF#inmicrons,x,y:coordinatesmeasuredintheexitpupilx0,y0:coordinatesmeasuredinthefocalplaneI0:intensityofincidentwavefront(constant):wavelengthofincidentwavefrontf:focallengthoftheopticalsystemA:amplitudeintheexitpupil(x,y):thephasetransmissionfunctionintheexitpupil,Foraberrationfreesystem,thePSFwillbethesquareoftheabsoluteoftheFouriertransformofacircularapertureanditisgivenintheformof1storderBesselfunction.,Thefractionofthetotalenergycontainedinacircleofradiusraboutthediffractionpatterncenterisgivenby：,r,AngularResolution-RayleighCriterion,Generallyamirrorsystemwillhaveacentralobscuration.Ifeistheratioofthediameterofthecentralobscurationtothemirrordiameterd,andiftheentirecircularmirrorofdiameterdisuniformlyilluminated,thepowerperunitsolidangleisgivenby,isinlp/mm,TheCut-Offfrequencyofanopticalsystemis:,Features：MirrorsalignedonaxisAdvantages：SimpleandachromaticDisadvantages：CentralobscurationandlowerMTFSmallerFOVwithlongfocallength,ObscuredSystem,UnobscuredSystem,Features：MirrorsalignedoffaxisAdvantages：NoobscurationandhigherMTF；LargerFOVwithlongfocallengthAchromaticDisadvantages：Difficulttomanufactureandassembly,1.3SphericalWavefront,DefocusandLateralShift,AperfectlenswillproduceinitsexitpupilasphericalwavefrontconvergingtoapointadistanceRfromtheexitpupil.Thesphericalwavefrontequationis:,Sagequation,Defocus,Originalwavefront:,Newwavefront:,Defocusterm,IncreasingtheOPDmovesthefocustowardtheexitpupilinthenegativeZdirection.Inotherword,iftheimageplaneisshiftedalongtheopticalaxistowardthelensanamountz(zisnegative),achangeinthewavefrontrelativetotheoriginalsphericalwavefrontis:,DepthofFocus,Ruleofthumb:forvisiblelight,0.5m,Z(F#)2inmicrons,ByuseofRayleighCriterion:,ThesmallertheF#,orthelargertherelativeaperture,thesmallertheDepthofFocus,sotheharderthealignment.,Lateral(Transverse)Shift,InsteadofshiftingthecenterofcurvaturealongZaxis,wemoveitalongXaxis,then:,Forthesamereason,ifmovealongYaxis,then:,Ageneralsphericalwavefront:,Thisequationrepresentsasphericalwavefrontwhosecenterofcurvatureislocatedatthepoint(X,Y,Z).,TheOPDis:,Thisthreetermsareadditiveforthemisalignment,someorallofthemshouldberemovedfromthetestresultfordifferenttestconfigurations.,1.4TransverseandLongitudinalAberration,Ingeneral,thewavefrontintheexitpupilisnotaperfectspherebutanaberratedsphere,sodifferentpartsofthewavefrontcometothefocusindifferentplaces.Itisoftendesirabletoknowwherethesefocuspointsarelocated,i.e.,find(x,y,z)asafunctionof(x,y).,WavefrontaberrationisthedepartureofactualwavefrontfromreferencewavefrontalongtheRAY.,1.5SeidelAberrations,Inarealopticalsystem,theformofthewavefrontaberrationscanbeextremlycomplexduetotherandomerrorsindesign,fabricationandalignment.AccordingtoWelford,thiswavefrontaberrationcanbeexpressedasapowerseriesof(h,x,y):,a3termgivesrisetothephaseshiftoverthatisconstantacrosstheexitpupil.Itdoesntchangetheshapeofthewavefrontandhasnoeffectontheimage,usuallycalledPiston.b1tob5termshavefourthdegreeforh,x,ywhenexpressedaswavefrontaberrationorthirddegreeastransverseaberration,usuallycalledfourth-orderorthirdorderaberrations.,h:fieldcoordinatesx,y:coordinatesatexitpupil,Iflooktheopticalsystemfromtherearend,weseeexitpupilplaneandimageplane.,WavefrontAberrationExpansion,ClassicalSeidelAberrations,Whatdoaberrationslooklike?,FieldCurvature,Wheredoaberrationscomefrom?,Distortion,Astigmatism,W222,Coma,W131,WarrenSmith,ModernOpticalEngineering,P65,SphericalAberration,W=W0404,+,W=W0404,W=W0202,W=-1W0202+W0404,SphericalAberration+Defocus,Through-focusDiffractionImage(WithSphericalAberration),Wavefrontmeasurementusinganinterferometeronlyprovidesdataatasinglefieldpoint(oftenonaxis).Thiscausesfieldcurvaturetolooklikefocusanddistortiontolookliketilt.Therefore,anumberoffieldpointsmustbemeasuredtodeterminetheSeidelaberration.Whenperformingthetestonaxis,comashouldnotbepresent.Ifcomaispresentonaxis,itmightresultfromtiltor/anddecenteredopticalcomponentsinthesystemduetomisalignment.Acommonerrorinmanufacturingopticalsurfacesisforasurfacetobeslightlycylindricalinsteadofperfectlyspherical.Astigmatismmightbeseenonaxisduetomanufacturingerrorsorimpropersupportingstructure.,Importanttoknow,Caustic,Specifiesthesizeofaberration,Basicformofaberration,Theaberrationsofagivenopticalsystemdependonthesystemparameterssuchasaperturediameter,focallength,andfieldangle,aswellassomespecificconfigurationsofthesystem.,1.6AberrationCoefficients,TheLagrangeInvariant,TheLagrangeInvariantholdsatanyplanebetweenobjectandimage.,=,Forobjectatinfinity：,ParaxialRayTracing,SnellsLaw,L=,SeidelCoefficientTable,SeidelCoefficientCalculationforaSinglelet,CalculationbyZemax,CalculationbySeidelCoefficientFormula,TheThinLensForm,Theaberrationsofagivenopticalsystemdependonthesystemparameterssuchasaperturediameter,focallength,andfieldangle,aswellassomespecificconfigurationsofthesystem.Thesystemparameterscanbefactoredoutoftheaberrationcoefficients,leavingremainingfactorswhichdependonlyupontheconfigurationofthesystem.Theseremainingfactorswewillcallthestructuralaberrationcoefficients.,TheStructureAberrationCoefficient,RolandV.Shack,TheThinLensBending,Itispossibletohaveasetoflenseswiththesamepowerandthesamethicknessbutwithdifferentshapes.,X：,Minimumsphericalaberration,IfYisconstant,then,Ifobjectatinfinity,Y=1,n=1.5,then,Minimumcoma,Ifobjectatinfinity,Y=1,n=1.5,then,Forobjectatinfinity,stopatthinlens,whenlenspowerisfixed:,ZemaxResult,CalculationUsingThinLensForm,Forobjectatinfinity：,=,Forthinlensisinair,n=1，rearrangethethinlensformula:,1.7ZernikePolynomials,Ofteninopticaltesting,tobetterinterpretthetestresultsitisconvenienttoexpresswavefrontdatainpolynomialform.Zernikepolynomialsareoftenusedforthispurposesincetheycontaintermshavingthesameformsastheobservedaberrations(Zernike,1934).NearlyallcommercialdigitalinterferometersandopticaldesignsoftwaresuseZernikepolynomialstorepresentthewavefrontaberrations.,Zernikepolynomialshavesomeinterestingproperties,IfisZernikepolynomialtermsofnthdegreeandwediscusswithinaunitcircle:Thesepolynomialsareorthogonaloverthecontinuousinterioroftheunitcircle:,canbeexpressedastheproductoftwofunctions.Onedependsonlyontheradialcoordinateandtheotherdependsonlyontheangularcoordinate.nandlareeitherbothevenorbothodd.Ithasrotationalsymmetryproperty.Rotatingthecoordinatesystembyanangledoesntchangetheformofthepolynomials:,canbeexpressedas:,wheremn,l=n-2m.SoZerniketermUnmcanbeexpressedas:,Where:sinfunctionisusedforn-2m0cosfunctionisusedforn-2m0,SothewavefrontaberrationcanbeexpressedasalinearcombinationofZernikecircularpolynomialsofkthdegree:,WhereAnmisthecoefficientofZerniketermUnm.,4thZernikepolynomials,Re-orderedZernikepolynomials(first36terms),1,2,3,5,4,6,7,8,PlotsofZernikepolynomials#1#8,9,10,11,12,13,14,15,PlotsofZernikepolynomials#9#15,PlotsofZernikepolynomials#16#24,16,17,18,19,20,21,22,23,24,33,PlotsofZernikepolynomials#25#36,25,26,28,27,29,30,32,31,35,34,Zernikepolynomialsareeasilyrelatedtoclassicalaberrations.W(,)isusuallyfoundthebestleastsquaresfittothedatapoints.SinceZernikepolynomialsareorthogonalovertheunitcircle,anyoftheterms:alsorepresentsindividuallyabestleastsquaresfittothedata.Anmisindependentofeachother,sotoremovedefocusortiltweonlyneedtosettheappropriatecoefficientstozerowithoutneedingtofindanewleastsquaresfit.,AdvantagesofusingZernikepolynomials,CautionsofusingZernikepolynomials,Midorhighfrequencyerrorsmightbe“smoothedout”.ForexampletheDiamondTurnedsurfaceprofilecannotbeaccuratelyexpressedbyusingreasonablenumberofZerniketerms.Zernikepolynomialsareorthogonalonlyoverthecontinuousinteriorofanunitcircle,generallynotorthogonaloverthediscretesetofdatapointswithinaunitcircleoranyotherapertureshape.,RelationshipBetweenZernikepolynomialsandSeidelAberrations,Thefirst9Zernikepolynomialsareexpressedas:,ThesameaberrationcanbeexpressedinSeidelform:,Usingtheidentity:,1.8PeaktoValleyandRMSWavefrontAberration,PeaktoValley(PV)issimplythemaximumdepartureoftheactualwavefrontfromthedesiredwavefrontinbothpositiveandnegativedirections.WhileusingPVtospecifythewavefronterrorisconvenientandsimple,butitcanbemisleading.Ittellsnothingaboutthewholeareaoverwhich