第五章--高分辨(相位)衬度的起源与理论

2004.91-Boersch19461947ScherzerdefocusScherzerMenter195620501.219701957ArizonaCowley1971CowleyIijima4CowleyIijimaCscorrectorexitwavereconstruction2004.92(phasecontrast):fringes1.(phasecontrast)HRTEM1AbbeAbbe1873ErnstAbbeABCFraunhofer2004.93AbbeFourierTransfer51Abbe{})()(rqFuQ={})()()(1rquQFr==−ψ)(rq2004.942.}}),(),(yxSqayxqaSiiiiii=∑∑3.(Kirchhoff)(Helmholtz){}∫∫−−−=σθθππλdrikrrikriPFqqqcoscos)2exp()2exp(4)(θθqdσrrqrrψ(x,y)Q2004.95),(YXqP{}∫∫+−−=dXdYrikrYXqrikriyxqqqθθππλψcoscos)2exp(),()2exp(2),(XYZFresnelR{}∫∫+−=dXdYrikrYXqiyx1cos)2exp(),(2),(θπλψ2222)()(RYyXxr+−+−=()R(X,Y)(x,y)cosθ≅1rRrRYyXxRRYyXxr22222)()()()(−+−+≈+−+−=π/22004.96∫∫−+−−−=dXdYRYyXxikYXqZikZiyx2])()[(2exp),()2exp(),(22πλπψ),(*),(yxPyxqR=(4-8)q(x,y)Ψ(x,y)RPR(x,y)+−−=RyxikRiyxPR2)(2exp2),(2πλπ4.(TransferFunction)-pointx,yextendedregion2:()()()()''''')(rrhrfdrrrhrfrg−⊗=−=∫f(x,y)x,yg(r)fgx,y(r)h(r-r’)2004.97Fourier),(sin),(cos)'(22yxyxrrh+=−52CTF123x,yfx,yAB,fA(x,y)fB(x,y)gAgBgAgB(x,y)2004.98gx,yFouriergx,y∑∑⋅=+==uuyxyxr)iG(u)exp(2))yui(xu)exp(2u,G(ug(r)y)g(x,yx,kππuFourierG(k)g(x,y)Fourierf(x,y)F(k)f(x,y)Fourier()h(x,y)H(k)h(r)Fourierh(x,y)H(k)CTFG(k)=H(k)F(k)H(k)≡1,,:1y)(x,exp(-iy)(x,I22==Ψ=tVσ,,2004.99,(transferfunction)H(u)53H(k)H(k)A(k)E(k)B(uk)A(k)B(u)=exp{iχ(u)}E(u)=R(u)G(u),R(u)G(u)H(u,v)Ψ(x,y)Ψ(u,v)q(x,y)Q(u,v)2004.910B(u)=exp{iχ(u)}χ(u)432uC21uf(u)λπλπχs+∆=uf(x,y)(phasecontrast)(phase-object)(transmissionfunction)y))(x,y)exp(-iA(x,y)f(x,tφ=2004.911A(x,y)y)(x,tφt11A(x,y)1V(x,y,z)tdz∫=t0tz)y,V(x,y)(x,V:2meEh/=λ:)),,(2me(Eh/'zyxV+=λdz:dzzyxVEzyxVdz),,()1E),,(E(2)dz1-1(2'λπλπλλπφ≈−+==∆σλπ=E(σ)dzzyxV),,(σφ=∆2004.912V(x,y,z)tφdy)(x,Vz)dzy,V(x,0t)1-1(2t0'σσλλπφ≅==∫∫dzdtVt(x,y)=∫t0V(x,y,z)dzz(projectionpotential)σ5454σCowley2004.913µ(x,y))],(),(exp[),(yxyxViyxftµσ−−=(POA)2~3nmVt(x,y)1,exp1µ),(1),(yxViyxftσ−=(WPOA)2(diffractionfunction):Q(u)=F[ψ(x,y)]))(exp(]),([)()}(exp(),(1{)(),({uizyxViFuuixyxViFuHyxfFttχσδσ∆+=⊗−=⊗=uFFourierHuHuA(u)E(u)B(u)B(u)2004.914(u)2sin(u))exp(iB(u)χχ≈=Hu(u)2sin)()(T(u)χuEuA=TuHuTuTuCTFE(u),Tu(u)sin)(2T(u)χuA=A(u)≥≤=)(,0)(,1)(00rrrruAr0Fourierϕϕ001)(2)}({krkrJuAF=J1ϕ2004.915(u)χ(u)χ(aberration,Cs)defocus,z∆astigmatism,Caλπ2×=λπχ2(u)T(u)(u)χπ(u)χ2/π±(u)χπ±T(u)u5555T(u)~u0~u1u1uu1T(u)T(u)u1u02004.916u1uθ)(θδθθθδfCs∆+=3)(Bragg24)()(240θθθθδθθfCdDs∆+==∫BraggλθndB=sin2Bθ1°λλθudB=≈2ud1=(u)χ×λπ2(u)χ)24(2)(22244λλλπθλπufuCDs∆+==21)/(*λλsCf∆=∆)*2(*)(2*4*ufuu∆+=πχT(u)(T(u)))(sin(2uχCsλ∆fu2004.91756T(u)u56T(u)u200KeV;Cs=1mm;∆f=-58nm57Cs58∆f2004.91857CsT(u)2004.9192004.92058∆f,Csλχ(u)∆f∆fsinχ≈1rr0.,:I(r)=Ψ’(r)2≈1-2σVt(r)1946Scherzer∆fScherzerScherzer∆f*2)(sinθχm1∆f*12121)(2.1)34(λλssCCf−=−=∆ScherzerScherzer434166.0λsSchertzerCr=2004.921T(u)E(u)T(u)T(u)E(u)E(u)E(u))}(exp{2uaqπ−θ)}(exp{)(22θπθqaE−=a]2[][)(3234642233uiuufuCuqs∆−+∆−=λπλπλλ3226242232)(θπλθπθθθ∆−∆+∆−=ifCqsE(u)FourierE(u)E(u)∆−22)(21expuπλ2004.922θE(θ))21exp(242λθπ∆−Fourier5ab2004.923591(point-to-pointresolution)2(informationresolution)3(lineresolution)dp=1/upup2004.924sin[χ1(u)]exp[-χ2(u)]J1[χ3(u)]/χ3(u)=0.u.Scherzerds=1/us=0.65Cs1/4λ3/4.di=1/ui,uiexp[-χ2(ui)]J1[χ3(ui)]/χ3(Hui)=0.3()()()yxhyxViyxhyxfyxt,)],(1[,,),(⊗−=⊗=Ψσ()),sin(),cos(,yxiyxyxh+=()()yxyxVyxyxVyxtt,cos),(,sin),(1),(⊗−⊗+=Ψσσ2Ψ=ΨΨ=∗Iσ200kVσ0.00728V-1nm-1;1000kVσ0.00539V-1nm-1σ2004.925()yxyxVIt,sin),(21⊗+=σAbell,:Ψ(x,y)=F-1[Q(u)]=F-1{F[ψ(x,y)]},,(structureimage),(atomicimage).,.(1.23)..200kV,ϕp(r)1.2×103VÅ.2004.926,ϕ0(r)20V,ϕp(r)=tϕ0(r)1.2×103VÅt60Å.,(1/4)×60Å(,),(1.23)15Å!,,,.1Multi-slicemethod(PseudopotentialMethod)1X,4.,2004.927f(x,y)Q(u)=F{f(x,y)};T(u)Q(u)ψ(u)T(u)Q(u);FourierFFTψ(u)),(yxΨF{ψ(u)};I),(yxΨ),(yxΨ*phasegrating0.2~0.5nmzVt(x,y)itizyxVyx∆=),(),(ϕ}),(exp{y)q(x,itzyxVi∆=σiz∆ii11z∆2004.928FresnelP1}2(exp{2211izyxikziP∆+∆=λ),(),(),(111yxPyxqyx⊗=ψ),(1yxψ),()],(),()[,(),()],(),([),()],(),([),(21122112122yxPyxPyxqyxqyxqyxPyxqyxPyxyxqyx⊗⊗=⊗=⊗=ψψ..2004.929510.,i),(})]...,()],(),()[,(...[{),([),()],(),([),(112112111yxPyxPyxPyxqyxqyxqyxqyxPyxyxiiiiiiii−−−−−⊗⊗⊗=⊗=ψψii1Q(u)](u)P[(u)⊗=−iiψψψι(u)iPiuiQi(u)i.,2,:,,tc2004.93023””