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1、13.FresneldiffractionRemind!DiffractionregimesFresnel-KirchhoffdiffractionformulaEexp(ikr)0E()PF=()θdA0∫∫irλ∑rzObliquityfactor:F()cosθθ==rzEexp(ikr)Ex,y0dd()=ξη∫∫2irλ∑Aperture(ξ,η)Screen(x,y)222rzx=+?+?()()ξyη2222??11????xy??ξη()xy??ξ()η≈+zz??1????+=++????22????zz22zz222
2、2??xy??ξη??xyξη=z++++?+????????22zz??22zzzz??E0??k22Exy(),e=+xp()ikzexp??i()xyizλ??2z??kk22??×+∫∫exp??ii()ξηξexp???()x+yηddξη∑??2zz??Exy(),e=+E0xp()ikzexp??ik()xy22r??izλ??2z??kk22??×+∫∫exp??ii()ξηξexp???()x+yηdξdηAperture(ξ,η)Screen(x,y)∑??2zz????kk22??=+Ci∫∫exp??()ξηξe
3、xp???i()x+yηdξdη∑??2zz??Fresneldiffraction??kk22??E()xy,(=+CU∫∫ξ,ηξ)exp??i()ηexp???i()xξ+yηddξη??2zz??k22?j()ξη+?Exy(,)U,e2z∝F?()ξη???Fraunhoferdiffraction??kExyCU(),(=?∫∫ξη,)exp??ix()ξ+yηddξη??z=?CU(,)expξηξ??ik()sinθ+ηsinθddξη∫∫??ξηExy(,)∝F{U(ξ,η)}Fresnel(near-field)di
4、ffractionThisismostgeneralformofdiffraction–Norestrictionsonopticallayout?near-fielddiffractionk22?j()ξη+??curvedwavefrontUxy(,)FU,e2z≈?()ξη?–Analysissomewhatdifficult??Curvedwavefront(parabolicwavelets)ScreenzFresnelDiffractionAccuracyoftheFresnelApproximation3π222z??[(
5、)()x?ξ+y?η]max4λ?AccuracycanbeexpectedformuchshorterdistancesforU(,)ξηξsmooth&slowvaringfunction;x2?=≤D4λz2Dz≥Fresnelapproximation16λInsummary,Fresneldiffractionis…13-7.FresnelDiffractionbySquareApertureFresnelDiffractionfromaslitofwidthD=2a.(a)Shaded2w2aareaisthegeometr
6、icalshadowoftheaperture.ThedashedlineisthewidthoftheFraunhoferdiffractedbeam.(b)Diffractionpatternatfouraxialpositionsmarkedbythearrowsin(a)andcorrespondingtotheFresnelnumbersN=10,F1,0.5,and0.1.Theshadedarearepresentsthegeometricalshadowoftheslit.Thedashedlinesatx=(λrepr
7、esentthe/D)dwidthoftheFraunhoferpatterninthefarfield.Wherethedashedlinescoincidewiththeedgesofthegeometricalshadow,theFresnelnumberN=0.5.F2Naz=/λ:FresnelnumberFjkz∞()e()?k[()()22]?Ux,y=∫∫Uξ,ηexp?jx?ξ+y?η?dξdηjλz?∞?2z?2Δ=vNaz=/λ:FresnelnumberFFresneldiffractionfromawireFr
8、esneldiffractionfromastraightedgeFromHuygens’principletoFresnel-KirchhoffdiffractionHuygens’principleEv
