e-Chapter 4ppt课件

Chapter4MirrorandPrismSystems Contentsinthischapter TheimagingpropertiesandfeaturesofthemirrorandprismsystemsTheimagingdirectionsofprismsystemsTheconjunctionofmirrorandprismsystems 4 1ApplicationsofMirrorandPrismSystemsinOpticalInstruments Propertiesofcoaxialsphericalsystems Advantages a Beabletoformtheimageofanobjectasrequiredb Imagesinparaxialregionareperfectc Whiletheobjectplaneisnormaltotheaxis theimageplanewillbealsonormaltotheaxis andtheimageissimilartotheobject Defects Cannotchangedirectionsobject opticalsystem imagelocateonacommonline Applicationsofthemirrorandprismsystems a Theycanbeusedtoreducethedimensionandweightofaninstrument b Theycanbeusedtochangethedirectionoftheimage ormaketheimageinverted c Theycanbeusedtochangethelocationanddirectionoftheaxis producingacertainperiscopeheightortiltingtheaxisforanangle d Withthehelpofrotatingtheprismandmirror thedirectionoftheaxiscanbechangedcontinuously enlargingthefieldofview Examles Examples 4 2Imagingpropertiesofmirrors P A O N B D A I I O B pointAisimagedatpointA WecantakeincidentrayAOfrompointOarbitrarily TheincidentAOisarbitrary theequationhasnorelationshipwiththelocationofpointO AlloftheextendingraysofthereflectedrayfrompointAwillmeetatonecommonpointA 1 Imagingofanarbitrarypointthroughasinglemirror P O D O A A Conclusion a Theimageandobjectpointsaresymmetricaltothemirror b Theheightoftheimageisequaltothatoftheobject c Arealobjectformsavirtualimage andavirtualobjectformsarealimage d Asingleplanemirrorcanformidealimages Istheimagesimilartotheobject 2Imageofobjectinspacereflectedbyasinglemirror P x y z o y z x o a Thesizeoftheimageisequaltothatoftheobjectbutindifferentorientation b Therighthandcoordinatesinobjectspacewillbechangedtolefthandcoordinatesinimagespace c Facingdirectlytoaxeszandz separately whenxrotatesanticlockwisewecanseethatx willrotateclockwise Theimagesatisfyingthisrelationshipbetweentheobjectandimagespacesiscalledmirrorimage Summery a Asingleplanemirrorcanimageanyobjectpointsideallyinthewholespace b Theimageandobjectpointsaresymmetricaltothemirror c Thesizeoftheimageisequaltothatoftheobject d Formingamirrorimage theimageformedbyaplanemirrorisnotsimilartotheobject 3Imagingpropertiesofmirrorssystem FormingidealimagesAnimageformedbyoddmirrorswillbeamirrorimageandbyevenmirrorswillbeonesameastheobject Attentions 1 Theerectedorinvertedimagehasnorelationshipwiththemirrorimage 2 Theobjectandthemirrorimagehavedifferentshape andtheyarenotsimilar Generallyspeaking wealwaysexpecttheimageissimilartotheobject especiallyinthesystemsusedinmilitary 4 3RotationofMirrors P N O A B I I N B Conclusion Thereflectedanglewillbe2 ifthemirrorrotates 2 I 2I 2 1 Rotationofsinglemirror Advantage Enlargingtherangeobserved Defect Errorscausedbyrotation Example TheplanemirrorinRangeFinder 1 Rotationofsinglemirror 2 Rotationoftwomirrors P1 P2 A O1 O2 M B I1 I2 IntriangleO1O2M N thenormalsoftwomirrorsmeetatpointN IntriangleO1O2N accordingtotheprincipleofexternalangle Theanglebetweentheincidentandthereflectedraysistwiceoftheangleoftwomirrors 2 Rotationoftwomirrors P1 P2 A O1 O2 M B I1 I2 TherotationdirectionwillcoincidewiththatofrotationfromP1toP2accordingtotheorderofreflectionsontwomirrors N Therotatedangleoftheemergentraywillbeequaltotwiceangleofthetwomirrors regardlessoftheincidentray sdirection Application WecanusetwomirrorsinplaceofthesinglemirrorinRangeFinder anglemirror prism 4 4PrismandItsUnfolding 1 Advantagesanddefectsofprisms Prism Opticalelementwhichcanmakeuseofthereflectioninglasstochangethedirectionofrays Advantages Thelossofenergyissmall It shardtobreak Itiseasytoassembleandfix Defects It svolumeandweightarelarger Ithasstrictrequirementsformaterial Itisinfluencedbycircumstancegreatly 2 Unfoldingoftheprism methodofstudyingtheimagingpropertiesofprisms Right anglePrism Mainsection Theplaneorsectionwhichisperpendiculartoeachprism Themethod unfoldingthemainsectionofprismalongthereflectivesurfaceandcancelingthereflectionandreplacingprism srefractionsbyglassblock srefractions iscalledprismunfolding 1 2 3 FromLawofreflection wecanget Fromthesymmetricalrelationship wecanget So wecanget 3 Therequirementsforprisms 1 Afterunfoldingaprism thetwofacesoftheglassblockmustbeparalleltoeachother 2 Whenaprismlocatesinconvergingrays theaxismustbeperpendiculartobothincidentandemergentsurfaces 4 Typicalexamplesofunfoldingprisms a Right anglePrism Locatinginparallelrays A B C A Whentheprismworksinparallelraysthetwofacesoftheglassblockunfoldedbytheprismmustbeparalleltoeachother then AB A C Andthen 4 Typicalexamplesofunfoldingprisms a Right anglePrism Locatinginparallelrays A B C A FaceABneedstobeparalleltofaceA C then ABC A CB Sotheprismneeds ABC ACB Thatmeanstriangle ABCmustbeanisoscelestrianglebut Band Cdonotneedtoequal45 or Adoesnotneedtobearightangle Whenaprismlocatesinconvergingrays boththefirstandthesecondsurfacesshouldbeperpendiculartotheaxis A B C A Whentheaxisofthisprismisdeviatedthroughaxis90 Whendeviatingtheaxisthroughanyangle B C A Ifwewanttheraytodeviate thenthereflectivesurfacemustdeviatetheaxis ThiskindofprismiscalledIsoscelesprism Ifweneedtheaxisofthisprismbedeviated45 then 2 PentaPrism 3 BootPrism 45o 60 4 CubePrism A B C I I E a D Supposetheindexoftheprismisn thentherefractionangleI is FromthefigurewecanseethatthediameterDoftheraysis 4 CubePrism A B C I I E a D weget IftheglassisK9 orBK7 thenn 1 5163 wecanget Inordertoenlargethediameteroftherays ortoreducethesizeoftheDoveprismforagivendiameteroftherays twoDoveprismscanbecementedhypotenusetohypotenusewhichcanformtheCubeprism AttentionstouseCubePrismAbundleofrayswillbedividedintotwobundlesofraysafterenteringtheprism thentheywillbemergedtogethertoonebundleofrayafterpassingthroughtheprism SothehypotenusesofthetwoDoveprismsmustbeparalleltoeachotherpreciselytoavoidproducingtwoseparatedimages Iftheentrancepupiloftheraysiscircular theexitpupiloftherayswillbedividesintotworeversedhalfcircles Sothecubeprismcannotworkincircularrays Sincetheincidentandemergentfacesarenotnormaltotheaxis theCubeprismcanonlybeusedinparallellightrays 1 1 2 2 3 4 4 3 4 5RoofSurfacesandRoofprisms Roofsurfaces Usingtworightanglesurfacestoreplaceonereflectingsurface Roofprism Prismwhichcontainsfoorsurfaces RoofSurfacesandRoofprisms Effects Theadditionoftherooftoaprismistointroduceanextrainversiontotheimageorchangethetotalreflectingnumberfromoddtoeven keepingtheoriginalaxisandimageorientationinthemainsectionunchanged Inthiswaywecanaddareflectionandgetanimagesimilartotheobject y x z x1 y1 z1 y z x x2 y2 z2 Requirementforaroofprism Theroofanglemustbeequalto90 precisely otherwise theemergentrayswillbenotparallel producingdoubleimages unfoldingofroofprisms 4 6ImagingPropertyofParallelGlassBlockandPrismSizeCalculation 1 Imagingpropertiesoftheparallelglassblock 1 Thefinalimageposition A A A A L l1 l2 SupposetheobjectdistanceofthefirstsurfaceisL1 istheimagedistanceofthesecondsurface calculate CalculatearaybyusingtheGaussianequationforthetwosurfacesoftheparallelglassblockonebyone Substitutetotheaboveequation weget Sotheshiftofimageplaneis 2 Thesizeofimage A L l1 l2 u u Conclusion Aparallelglassblockonlymakestheimageplaneshiftacertaindistance havingnoinfluenceontheimagingproperty TheshiftingvalueisL L n Theemergentraywillbeparalleltotheincidentraywhenitpassesthroughaparallelglassblock So wecanget Intheair Andthen 2 TheequivalentairthicknessofAparallelglassblock A L l1 l2 P2 P1 K Q KP2 AA L L n KP2 QM L L nNQ L n M N L n A Fromthefigure AQ l1 L n l2 A M Theheightsoftherayatthetwosurfacesoftheparallelglassblockareequaltothoseoftherayatthetwosurfacesoftheequivalentairthickness ForaparallelglassblockwhosethicknessisLandindexisn L niscalledtheequivalentairthickness Thedistancefromthesecondsurfacetotheimageplaneisequaltothatofbypassingthroughanequivalentairthickness Theheightsoftherayatthetwosurfacesoftheparallelglassblockareequaltothoseoftherayatthetwosurfacesoftheequivalentairthickness Thesizeoftheimageformedbytheparallelglassblockisequaltothatformedbytheequivalentairthickness Theequivalences Thenonequivalences Theparallelglassblockmakestheimageplaneshift Thereisnoshiftofimageplaneformedbytheequivalentairthickness Theparallelglassblockintroducesaberrations Therearenoaberrationsbytheequivalentairthickness 2 Applications Givenathinlens effectivefocallengthis100mm diameteroftheraysis20mm theobjectisininfinity diameteroftheimageis10mm 50mmbehindthelensthereisaPentaprismwhichmakestheaxisdeviate90 Findoutthesizeoftheprismandthepositionoftheimage n 1 5163 Step1 Makethecorrespondingfigureofrays D y 100 50 D1 D2 Step2 Calculatethediameterofthefirstsurface D1 20 10 2 15 Step3 Calculatethethicknessesofglassblockandequivalentairthickness L 51 21 e L n 33 8 Step5 Calculatediameterofthesecondsurfaceoftheprism 10 5 100 50 D1 D2 33 8 x Step6 Calculatetheimagedistance fromthesecondsurfaceoftheprismtotheimageplane L2 50 33 8 16 2 Homework No 2 6onpage88 89 16 2 Example supposethediameterofarightangleprismis10mm whenrotatingtheprism45 theemergentraywillbeparalleltotheincidentrays findoutthediameteroftherays A B C 10 D A E D K K N 45 Thethicknessoftheglassblockis Theequivalentairthicknessis 4 7DeterminationofImageOrientationsforMirrorsandPrisms Intentions Findouttheorientationsoftheimageformedbymirrorsandprisms 2 Designamirrorsandprismssystemaccordingtotherequirementsoftheorientationsoftheaxisandimageofthesystem Methodsofrepresentingtheorientationsoftheobjectandimageinmirrorandprismsystem Takeanorthogonalcoordinatesxyzinobjectspace xorientationcoincideswiththeincidentaxis Yorientationliesinthemainsectionoftheprism Zorientationisnormaltothemainsection Similarly intheimagespacex y z areusedtorepresenttheorientationsoftheimage Methodsofdeterminingtheimageorientations 1 Determinex orientation Itcoincideswiththeexitaxis 2 Determinethey z orientations Opticaxissection Mainsectionthatcoincideswiththeopticaxis Mirrorandprismsystemswithsinglemainsection Allofthemainsectionsofthemirrorsandprismscoincidewitheachother Mirrorandprismsystemwithsinglemainsection Noroofsurface zandz havethesameorientations TheemergentaxisandincidentaxisCoincide a Ifthenumberofreflectorsisodd y willbeoppositetoy b Ifthenumberofreflectorsiseven y willhavethesameorientationasy Mirrorandprismsystemwithsinglemainsection Noroofsurface zandz havethesameorientations Theemergentaxisandincidentaxisarereversed a Ifthenumberofreflectorsisodd y willhavethesameorientationasy b Ifthenumberofreflectorsiseven y willbeoppositetoy Mirrorandprismsystemwithsinglemainsection noroofsurface Afterdeterminingtheorientationsofx andy wecanfindouttheorientationofz accordingtototalnumberofreflectors mirrorimageorsimilarimage Mirrorandprismsystemwithsinglemainsection Ifthereisaroofsurfaceinthesystem aboverulescanalsobeused However forthetotalnumberofreflectors theroofsurfaceshouldbecountedtwice Mirrorandprismsystemwithtwomainsectionsperpendiculartoeachother Themainsectionsofprism1andprism3areparallel butthemainsectionofprism2isverticaltothoseofprism1andprism3 Foraprismitcanonlychangetheorientationofthecoordinatewhichliesinitsmainsection andhasnoinfluenceuponthecoordinatewhoseorientationisnormaltothemainsection Prism2canonlychangetheorientationofz andcannotchangethatofy alsoprisms1and3canonlychangetheorientationofy anddonotaffectz Prism2orprisms1and3allbelongstothesystemswithsinglemainsectionandtheaboverulescanbeusedtofindouttheorientationsoftheimage However wecan tsimplyjudgebythefinalorientationofemergentaxis butshouldjudgebytheactualrotationsofopticalaxiscausedbyprism1and3 Fortheaxisinthissystem afterpassingthroughprism1theaxisrotates90 andafterpassingthroughprism3theaxisagainrotates90 rotatingalltogether180 Thatmeans wecandeterminetheorientationofy accordingtoprisms1and3 andtheaxisshouldbeconsideredreversed Nowwecandeterminetheorientationofy accordingtoprisms1and3 thenumberofreflectorsis2 y isreversedFortheorientationofz forprism2 theaxisisreversed thenumberofreflectorsis2 z isreversed Actually afterdeterminingtheoneoforientationsofeithery orz accordingtothetotalnumberofreflectors wecandeterminethecoordinateoftheobjectandimagespace thenfindouttheotherorientation Notethatfortheemergentandincidentaxes coincide and reverse areinbroadsense Coincide meansnotonlyforemergentaxisbeingparalleltotheincidentaxis butalsofortheaxialdeviationanglewithin0 and90 Reverse meanstheaxialdeviationanglegreaterthan90 Ifthedeviationangleisjustequalto90 both coincide and reverse canbeusedandcangetthesameresult 1 Accordingtotheseconditions twoprismscanbeusedtochangetheaxis90 twice andtheycanbemadeupbyaprismsystemwithasinglemainsection Fromthe HandbookofOpticalDesign wecanfindouttwotypesofprisms 90 1and90 2 inwhich90 1istheso calledrightangleprismand90 2arePentaprismandBootprism 2 Sincetheemergentandincidentaxesarerequiredtobeparallelandtheimageisrequiredtobeinvertedtotheobject thetotalnumberofreflectorsshouldbeodd Thatmeans thecombinationshouldbea90 1prismanda90 2prism othercombinationsareunacceptable Therearetwokindsofthecombinations Example Designaprismsystemwhichismadeupbytwoprisms Thesystemhasa800mmperiscopeheight Theaxisshouldalwaysliesinoneplaneandthesystemisrequiredtoproduceaninvertedimagesimilartotheobject 3 sincethetotalnumberofthereflectorsisodd theimageisamirrorimage sooneofthereflectingsurfaceshouldbechangedtoroofsurfaces Inthisway fourpossiblesystemsareshowninFig 4 31 Anyoneofthefoursystemscanbeacceptedaccordingtotheactualsituations Homework No 1 3 4 5onpage88 89 4 8ThePrismRotationLaw Themethodofrotatingmirrorsandprismsisusuallyusedtoenlargetheviewangle Therotationofmirrorsandprismscanbeusedtoadjusttheaxisofthesystemortheimagedirectionduringtheassemblyofthesystem Theprismrotationlawcanbeusedtostudytheproblem 中巴资源卫星红外多光谱扫描仪 图1方案一光学系统结构示意图 图2方案二光学系统结构示意图 Ifaprismworksinparallelraypathitissufficienttoconsideronlythedirectionsoftheimage However ifitdoesnotworkinparallelraypath boththedirectionandthepositionshouldbeconsidered Supposeistheunitvectorthatrepresentstherotatingdirectionandpositionoftheprism Similarlyrepresentstheimage srotatingdirectionandpositionoftheprism rotatinganglen reflectornumber Aspecialsymbol isusedtorepresenttherotation Wecaneasilygetthefollowingequations PrismRotationLaw Supposetheobjectspaceisfixed ifaprismrotatesangle aroundvector theimagewillfirstrotateangle 1 n 1 aroundvector andthenrotateangle aroundvector Step1 Supposetheprismisfixed theobjectspacerotatesangle aroundthevector accordingtotheimageproperties ifthereflectorisoddtheimageismirrorimage andifthereflectoriseventheimageissimilartotheobject Thatmeanstheimagespacewillrotateangle 1 n 1 aroundthevector Step2 Rotatetheobjectspace prismandtheimagespaceangle aroundthevector Then theobjectspacekeepsunchanged theprismrotates aroundthevector andtheimagespacefirstrotatesangle 1 n 1 aroundthevector andthenrotatesangle aroundthevector objectspaceprismimagespacestep1 rotate unchangerotate 1 n 1 Step2 rotate rotate rotate Totalresult unchangerotate rotate 1 n 1 rotate 1 Prismrotatesaroundtheaxiszintheparallelraypath Sincetheprismworksinparallelraypath wecanonlydeterminethedirectionoftheimage withoutconsideringtheposition Supposetherearenoroofsurfaces wehave Ifthereflectorniseven wewillget Ifthereflectornisodd wewillget Thatmeans whentheprismrotatesangle aroundaxisz ifthereflectoriseventheimagespacewillbeunchanged andifthereflectorisoddtheimagespacewillrotateangle2 aroundaxisz Supposetheprismcontainsroofsurfaces wehave Ifthereflectorniseven wewillget Ifthereflectornisodd wewillget Thatmeans whentheprismrotatesangle aroundaxisz ifthereflectorisoddtheimagespacewillbeunchanged andifthereflectoriseventheimagespacewillrotatesangle2 aroundaxisz 2 Prismrotatesaroundtheaxisxintheparallelraypath andtheincidentaxisisparalleltotheemittedaxis 1 Thedirectionoftheincidentaxisisassameasthatoftheemittedaxis Ifthereflectornisodd wewillget Ifthereflectorniseven wewillget Thatmeans whentheprismrotatesangle aroundaxisx ifthereflectoriseventheimagespacewillbeunchanged andifthereflectorisoddtheimagespacewillrotatesangle2 aroundaxisx 2 Thedirectionoftheincidentaxisisinoppositedirectionoftheexitaxis Ifthereflectorniseven wewillget Ifthereflectornisodd wewillget Thatmeans whentheprismrotatesangle aroundaxisx ifthereflectorisoddtheimagespacewillbeunchanged andifthereflectoriseventheimagespacewillrotatesangle2 aroundaxisx Example1 Designaprismsystem Theperiscopeheightbetweentheincidentandtheexitaxesis300mm theincidentaxis0O1canrotatearoundthehorizontalandverticalaxes theexitaxiskeepsunchanged theimageshouldbereversedandsimilartotheobject Tworightangleprismscanbeplacedtogettheperiscopeheight Theupperprismcanrotatesaroundthehorizontalandverticalaxes Inordertoavoidtherotationoftheexitaxis aprismofoddreflectorcanbeplacedbeneaththeupperprism Theprismbeneaththeupperprismshouldbeoddreflector Wecanchoosethesimplestprism Doveprism Sincethetotalreflectoristhree tworoofsurfacesshouldbeaddedonthebottomprism SupposetheupperprismandtheDoveprismrotatetogetheraroundtheverticalaxis theimageaxiswillrotatesimultaneously InordertoavoidtherotationtheDoveprismcanrotatereverselyhalftheangle Inotherwords theupperprismandtheDoveprismrotatetogetheraroundtheverticalaxis aslongasthespeedoftherotationoftheDoveprismishalfoftheupperprism 空军飞行模拟器 背景显示系统 3 Prismrotatesaroundtheincidentaxisx andtheincidentaxisisperpendiculartotheemittedaxis Ifthereflectorniseven wewillget Ifthereflectornisodd wewillget Thatmeans whentheprismrotatesangle aroundaxisx ifthereflectoriseventheimagespacewillfirstrotatesangle aroundaxisx andthenrotatesangle aroundaxisx Ifthereflectorisoddtheimagespacewillfirstrotatesangle aroundaxisx andthenrotatesangle aroundaxisx Example2 Aprismsystemconsiststhreeprisms asshowninFig Supposeprism2and3togetherrotateangle aroundaxisO1O2 thenprism3rotatesangle aroundaxisO4O3 Findoutthedirectionsoftheimage Determinethedirectionsoftheimage Theincidentaxisofprism2 3isO1O2 theexitaxisisperpendiculartotheincidentaxis Sincethereflectoris3andthetwoprismsrotateangle aroundtheincidentaxis accordingtothepreviousconclusiontheimagewillfirstrotatesaroundaxisx andthenrotatesangle aroundaxisO1O2 Aga