foueieroptics课件c4fresnelandfraunhoferdiffra

CHAPTER4,FresnelandFraunhoferDiffraction,Reviewofphysicaloptics_1,FirstRayleigh-sommerfelddiffractioninrectangularcoordinates,Reviewofphysicaloptics_2,Fresneldiffraction,Reviewofphysicaloptics_3,ConvolutionformofFresneldiffraction,Reviewofphysicaloptics_4,FTformofFresneldiffraction,Positivevs.NegativePhases,Timedependenceisoftheformexp(-j2t)Ifwemoveinspaceinsuchawayastointerceptportionsofawavefieldthatwereemittedlaterintime,thephasorwillhaveadvancedintheclockwisedirection,andthereforethephasemustbecomemorenegative,Phasesignofsphericalwave,DivergentsphericalwaveConvergentsphericalwave,earlier,earlier,later,later,Phasesignofplanewave,PositiveangleNegativeangle,x,z,k,x,z,k,-,earlier,later,earlier,later,Distanceearlierpositive,TransferfunctionofFresneldiffraction,FTtheimpulseresponsefunctionofFresneldiffractionh(x,y)gets,ComparisonofstrictdiffractionandFresneldiffraction,Recalltransferfunctionofpropagationthroughfreespace,Theexpression(4-21)isclearlyanapproximationtothemoregeneraltransferfunction(4-20).,FresnelDiffractionBetweenConfocalSphericalSurfaces,ConfocalsphericalsurfacesTwospheresaresaidtobeconfocalifthecenterofeachliesonthesurfaceoftheother,Paraxialapproximation,Approximativeformula,ExpressionofFresneldiffractionaboutplanes,becomes,Fouriertransformform,Asidefromconstantmultipliersandscalefactors,thefieldobservedontheright-handsphericalcapistheFouriertransformofthefieldontheleft-handsphericalcap.KirchhoffratherthanRayleigh-Sommerfeldanalysisremainsvalidfordiffractionbetweentwosphericalcaps.,Reviewofphysicaloptics_5,Fraunhoferdiffraction,FraunhoferdiffractionFouriertransform,Asidefrommultiplicativephasefactorsprecedingtheintegral,FraunhoferdiffractionissimplytheFouriertransformoftheaperturedistribution,ExamplesofFraunhoferdiffraction_1,RectangularAperture,Lettheaperturesareilluminatedbyaunitamplitude,normallyincidentplanewave,thenthelightfieldbehindtheapertureU(,)=tA(,),Fraunhoferdiffractionofrectangleaperture,PlotofFraunhoferdiffraction_1,Thewidthofthemainlobeis,PlotofFraunhoferdiffraction_2,ExamplesofFraunhoferdiffraction_2,CircularApertureqisaradiuscoordinateintheplaneoftheaperturewithradiusw,ristheradiuscoordinateintheobservationplane,Fraunhoferdiffractionofcircularaperture,whereA=w2,Airypattern,ThisintensitydistributionisreferredtoastheAirypattern.Thewidthofthecentrallobeisgivenby,PlotofFraunhoferdiffraction_1,PlotofFraunhoferdiffraction_2,ExamplesofFraunhoferdiffraction_3,ThinSinusoidalAmplitudeGrating,CalculationofEq.4-33,DiffractionofsinusoidalamplitudeGrating,PlotofFraunhoferdiffraction,ThecentraldiffractionpatterniscalledthezeroorderoftheFraunhoferpattern,whilethetwosidepatternsarecalledthefirstorders.,DiffractionEfficiency,Definition:thefractionoftheincidentopticalpowerthatappearsinasinglediffractionorderForthesinusoidalamplitudegrating,wehavethreeDEswithvaluesof,ExamplesofFraunhoferdiffraction_4,ThinSinusoidalPhaseGrating,4-38,CalculationofEq.4-38,Diffractionofsinusoidalphasegrating,Iff01/w,theintensityhasapproximateform,Diffractionefficiencyofsinusoidalphasegrating,Diffractionefficiencyoftheq-thorderofthisgratingis,+1or-1ordermayhavediffractionefficiencyupto33.8%,fargreaterthanforthecaseofasinusoidalamplitudegrating,FresnelDiffractionbyaSinusoidalAmplitudeGrating,ObjectisperiodicstructureDiffractionlieswithintheregionofFresnelratherthanFraunhofer,Specialcaseofperiodicobject,Thegratingismodeledasatransmittingstructurewithamplitudetransmittance,TherearetwoapproachestocalculatingthefieldsbehindthegratingconvolutionformoftheFresneldiffractionequationFouriertransform,Analysisinfrequencydomain,Transferfunctionofwavepropagationinfreespace,Fouriertransformoftheamplitudetransmittance,FToftheFresneldiffractionfield,Nowtheabovetransferfunctionhasvalueunityattheorigin,andwhenevaluatedatfrequencies(fx,fy)=(1/L,0)yields,Fouriertransformofthefieldbecomes,Fresneldiffractionfield,Inversetransformingthisspectrumwefindthefieldatdistancezfromthegratingtobegivenby,Interestinginterpretations_1,Supposethatthedistancezbehindthegratingsatisfies,Thentheintensityobservedatthisdistancebehindthegratingis,ItisanexactimageofthegratingwithoutalensTalbotimage,Interestinginterpretations_2,Supposedistancezbehindthegratingsatisfies,Thentheintensityobservedatthisdistancebehindthegratingis,Thisisalsoanimageofthegrating,butthistimewithaspatialphaseshiftphasereversedTalbotimage,Inter