光学检测CH01PPT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 cos y sin 1 2AberrationFreeSystem Iftheopticalsystemisunaberratedordiffraction limited forapointobjectatinfinitytheimagewillnotbea point butanAiryDisk ThedistributionoftheirradianceontheimageplaneofAiryDiskiscalledPointSpreadFunctionorPSF SincePSFisverysensitivetoaberrationsitisoftenusedasanindicatoroftheopticalperformance DiametertothefirstzeroringiscalledthediameterofAiryDisk workingwavelengthF fnumberofthesystem Finiteconjugate NA numericalApertureNA nsinu F W WorkingFnumber Ruleofthumb forvisiblelight 0 5 m DAiry F 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 iftheimageplaneisshiftedalongtheopticalaxistowardthelensanamount z zisnegative achangeinthewavefrontrelativetotheoriginalsphericalwavefrontis DepthofFocus Ruleofthumb forvisiblelight 0 5 m 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 Itdoesn tchangetheshapeofthewavefrontandhasnoeffectontheimage 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 W040 4 W W040 4 W W020 2 W 1W020 2 W040 4 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 Snell sLaw 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 Onedependsonlyontheradialcoordinate andtheotherdependsonlyontheangularcoordinate nandlareeitherbothevenorbothodd Ithasrotationalsymmetryproperty Rotatingthecoordinatesystembyanangle doesn tchangetheformofthepolynomials canbeexpressedas wherem n l n 2m SoZerniketermUnmcanbeexpressedas Where sinfunctionisusedforn 2m 0cosfunctionisusedforn 2m 0 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 Ittellsnothingaboutthewholeareaoverwhichtheerrorareoccurring Anopticalsystemha