应用光学ch.2.10-2.17

Review:1.ChartIllustrationForImageFormation(7)2.ImagePositionAndSizeGaussianequationNewtonianequation)25.2(1lflf)26.2(lflf)22.2('''fxxfyy)23.2(''ffxx-xx’-ff’-ll’-yy’2.10MagnificationOfOpticalSystemsFF’HH’B’BAA’-x-f-l-y’f’l’ObjectplaneImageplaneX’yU2’U1’-U2-U1Fig.2.32•Lateral(ortransverse)magnification垂轴放大率•Longitudinalmagnification轴向放大率•Angularmagnification角放大率MagnificationOfOpticalSystems2.10.1Lateral(ortransverse)magnificationAccordingtoNewtonianequationandGaussianequationwecanhave)22.2('''fxxfyy)26.2(lflf2.10.2Longitudinalmagnification•Supposetheobjectplaneofanopticalsystemmoveasmalldistancedxalongthesystemaxis,theimageplaneofthesystemwillalsomoveasmalldistancedx’alongtheaxis.dxdx'(1)Gaussianequation•Differentiating(微分)onbothsidesoftheaboveequationandaccordingtotheFig.2.32,wehave)25.2(1'lflf’)27.2(''''22lflfdldldxdx(2)Newtonianequation•Differentiating(微分)onbothsidesoftheaboveequation,wehave)23.2(''ffxx)28.2(''xxdxdx(3)AngularmagnificationInparaxialregionUUtan'tanInfig.2.32）（29.2'uuGaussianequation:Newtonianequation:11()flffflffxffx)32.2(''xffx)22.2('''fxxfyy)30.2()(lltgUUtglhUtglhUtg；)30.2('tan'tanllUU(4)Relationshipamongthethreemagnificationor)33.2(2221flfflf1()ff2.11Optical(Lagrange)Invariant(物像空间不变式)hhuullulul，）（15.2'''lnlyynInparaxialregion:lluu'''''unuyynuyyunJn'''Optical(Lagrange)Invariant）（34.2'''uyyunJn）（35.2'tan''tanUUynyJnTheopticalinvariantforidealopticalsystems:Iftheindicesofobjectandimagespaceareequal,wehaveytgUytgUForareflectedsurfaceytgUytgUytgUytgUoddnumberreflectionevennumberreflection2.12relationshipbetweenfandf’）（34.2'''unuyyn)26.2(''lflf）（alluu36.2''）（bnnff36.2''）（bnnff36.2''Iftheindicesofobjectandimagespaceareequal,wehaveff位于空气中的光学系统，其像方焦距和物方焦距大小相等，符合相反(EFF)2.12.1ImagePosition(n’=n,f’=-f)AccordingNewtonianEquation,wehave)37.2(''2fxxAccordingGaussianEquation,wehave)25.2(11'1fll2.12.2Magnification(n’=n,f’=-f)•Lateral(ortransverse)magnification•Longitudinalmagnification•Angularmagnification)39.2(lllflf)40.2('''''2222lllflfdldldxdx)30.2('tan'tanllUU2.12.3Relationshipamongthethreemagnification1uuunnuyy)42.2(1)44.2(12AccordingtoEqu.(2.33),wehave)43.2(2Thecoupleofplaneswhoseangularmagnificationisequalto1arecallednodalplanes.Theplaneintheobjectspaceiscalledthefirstnodalplaneandtheplaneintheimagespaceiscalledthesecondnodalplane.2.13NodalPlanesAndNodalPoints(节平面和节点)1''lluu•Theintersectionpointsofthetwonodalplanesandtheaxisarecalledthefirstnodalpointandthesecondnodalpointseparately,denotedbyJandJ’.Properties:•AnyincidentlightraywhichpassesthroughthefirstnodalpointJ,afterpassingthroughthesystem,willpassthroughthesecondnodalpointJ’andparalleltoitsoriginaldirection,asshowninFig.2.35.1''xffxAccordingtoEqu.(2.32),wehave)45.2(;'/fxfxJJ??Whenanopticalsystemisboundedonbothsidesbyair(n’=n),wehave';/fxfxJJOnthiscondition,JcoincideswithHandJ’coincideswillH’,thatistosay,thenodalpointscoincidewiththeprincipalpoints,asshowninfig.2.36.(7)Anyincidentrayswhichpassthroughthefirstprincipalpointwillemitfromthesecondprincipalpointandparalleltotheincidentray.＊TheseventhConclusionofChartillustration：Thefirstapplicationofthepropertyofnodalpoints:tofindtheimageoftheobjectH(J)H’(J’)FABB’A’HH'JJ'F'(A1’)12θThesecondapplication:tomeasuretheothernodalpointofanopticalsystem?HH'JJ'A1'F'A2'θIftherotatingaxispassedthroughthesecondnodalpointJ’,theimagepointwillnotshiftAB'B1'A1'A'A1B1BJ'JObjectlensθThethirdapplication:tousepanoramiccamera(全景、周视)照相ObjectImageHomeworkP62,1-8,12-152.14ImageHeightOfTheObjectAtInfinity•Weusethefieldangleω(视场角)todenotetheobjectpositionwhichisatinfinity.•ω:startfromtheaxistotheray.Itispositiveiftheanglerotatesright-handedandnegativeifleft-handed.-ω-ff’HH’II’FF’y’Fig.2.39Imageheightofinfinityobject•Fromfig.2.39weknowtan'f)tan(--fIHy(2.46)Ifthesystemisboundedonbothsidesbyair,thenf’=-f,weget）（’47.2'tan-fyω’-ff’HH’II’FF’yFig.2.40Objectheightanditsinfinityimage）（’’48.2tanfy2.15TheCombinationOfIdealOpticalSystemsf,f’,F,F’,H,H’?2.15.1positionoffocalpoints(twolens)F1H1H’1F1'F2-f1d2f1'-f2H2H’2F’2f2’‘D•Supposethefocallengthsoftwoknownsub-systemsarefandf’•thedistancebetweenthesecondfocalpointF’1ofthefirstsystemandthefirstfocalpointF2ofthesecondsystemisdenotedbyΔ.ThesignconventionofΔ•Δ:startsfromF’1toF2,positiveifitgoesfromlefttoright.•Accordingtothepropertiesofthefocalpoints,anyparallelincidentraywillcrosspointF’1afterpassingthroughthefirstsystem,andtheintersectionpointoftheemergingrayandtheaxisafterpassingthroughthesecondsystemisthesecondfocalpointF’ofthecombinedsystem.HA1FuF1A1’H1H1’F1'F2-f112d22f1'A2'H'-f2H2H’2F2'F'-u'f2'f-f’-xF-xH-lF-lHxF’xH’lF’lH’A2ObjectImageDFig.2.41Thecombinationoftwoidealsystems12xF:startfromF1toFxH:startfromF1toHxF’:startfromF2’toF'xH’：startfromF2’toH'lF’：startfromH’2toF’lH’:startfromH2’toH'lF：startfromH1toFlH:startfromH1toH•positiveiftheygofromlefttor