光学元件应用实例.docx
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光学元件应用实例.docx
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光学元件应用实例
OpticsApplicationExamples
Application1:
DetectorSystems
Figure1:
PCXLensasFOVLimitinDetectorApplication
Everyopticalsystemrequiressomesortofpreliminarydesign.Gettingstartedwiththedesignisoftenthemostintimidatingstep,butidentifyingseveralimportantspecificationsofthesystemwillhelpestablishaninitialplan.Thefollowingquestionswillillustratetheprocessofdesigningasimpledetectororemittersystem.
Goal:
WhereWilltheLightGo?
Althoughsimplelensesareoftenusedinimagingapplications,inmanycasestheirgoalistoprojectlightfromonepointtoanotherwithinasystem.Nearlyallemitters,detectors,lasers,andfiberopticsrequirealensforthistypeoflightmanipulation.Beforedeterminingwhichtypeofsystemtodesign,animportantquestiontoansweris"Wherewillthelightgo?
"Ifthegoalofthedesignistogetallincidentlighttofilladetector,withasfewaberrationsaspossible,thenasimplesingletlens,suchasaplano-convex(PCX)lensordouble-convex(DCX)lens,canbeused.
Figure1showsaPCXlens,alongwithseveralimportantspecifications:
Diameterofthelens(D1)andFocalLength(f).Figure1alsoillustrateshowthediameterofthedetectorlimitstheFieldofView(FOV)ofthesystem,asshownbytheapproximationforFullFieldofView(FFOV):
(1.1)
Or,bytheexactequation:
(1.2)
Fordetectorsusedinscanningsystems,theimportantmeasureistheInstantaneousFieldofView(IFOV),whichistheanglesubtendedbythedetectoratanyinstantduringscanning.
(1.3)
Figure2:
InstantaneousFOV
Figure3:
PCXLensasFOVLimitinEmitterApplication
Consideredinreverse,Figure1canalsorepresentanemittingsystem(Figure3),withthelensusedtocollimatethelight.Thissetupwillbethepremiseoftheapplicationexample.
LightTransmission:
HowMuchLightExistsInitially?
Knowingwherethelightwillgoisonlythefirststepindesigningalight-projectingsystem;itisjustasimportanttoknowhowmuchlightistransmittedfromtheobject,orthesource.Theefficiencyisbasedonhowmuchlightisreceivedbythedetector,therebyansweringthequestion"Howmuchlightexistsinitially?
"TheNumericalAperture(NA)andf-number(f/#)ofalensmeasuretheamountoflightitcancollectbasedonf,D,indexofrefraction(n),andAcceptanceAngle(θ).Figure4illustratestherelationshipbetweenf/#andNA.
Correspondingly,thisrelationshipcanbemathematicallyexpressedaccordingtoEquation1.5.ItisimportanttonotethatthelargertheDiameter,thesmallerthef/#;thisallowsmorelighttoenterthesystem.Tocreatethemostefficientsystem,itisbesttomatchtheemittedconeoflightfromthesourcetotheacceptanceconeofthelens,asthisavoidsoverorunderfillingthelensarea.
(1.4)
(1.5)
(1.6)
Figure4:
DCXLensShowingf/#andNA
Figure5:
DCXLensIllustratingThroughput
OpticalThroughput:
HowMuchLightgetsthroughtheSystem?
Whenusingalensasatooltotransferlightfromanemittertoadetector,itisimportanttoconsiderThroughput(TP),aquantitativemeasurementoftransmittedlightenergy.Inotherwords,answeringthequestion"Howmuchlightgetsthroughthesystem?
"dictatesthegeometryofthelensusedandtheconfigurationofthesystem.Becauseemittersanddetectorsareareasoflightandnotpointsources,thediameterofalensaffectsTPevenwhentheratiobetweenDiameterandFocalLength(specifiedbyf/#)remainsconstant.
Figure5showsthebasicdefinitionofthroughput(TP)asexpressedinEquation1.7,whereAistheAreaoftheobject,(lightsource),ΩistheSolidAngle,andzistheObjectDistance(withtheirconjugatesinimagespaceasA',Ω',andz').
(1.7)
SolidangleisdefinedasΩ=A/r2,withtheareaofthelenssurfaceandtheradius(r)beingthedistancefromthelenstotheobject(z)orimageplane(z'),forΩorΩ',respectively.
Theamountoflightreachingthedetectorcanbereducedbyvignetting,whichistheresultoflightbeingphysicallyblockedwithinthesystemduetolensaperturelimitations.However,somesystemsbenefitfromintentionalvignetting,asitcaneliminatestraylightthatwouldnegativelyaffectthequalityoftheimage.Itisimportanttonotethatproperlyaligningthesystemreducesstraylightandunintentionalvignetting.
Aberrations:
HowDoestheImageLook?
Determininghowmuchlightpassesthroughthesystemisimportant,butaberrationswithinthesystemalsoplayamajorrole.Answering"Howdoestheimagelook?
"canleadtoimprovingthesystem'sdesigninordertoreduceaberrationsandimproveimagequality.Aberrationsareerrorsinherentwithanyopticalsystem,regardlessoffabricationoralignment.Sinceeveryopticalsystemcontainsaberrations,balancingperformancewithcostisanimportantdecisionforanydesigner.Severalbasicaberrations,suchascoma(variationinmagnificationorimagesizewithaperture),spherical(lightraysfocusinginfrontoforbehindparaxialfocus),andastigmatism(havingonefocuspointforhorizontalraysandanotherforvertical)canbereducedbyalargef/#,asshowninthefollowingrelations.
(1.8)
(1.9)
(1.10)
ApplicationExample:
DetectorSystem
Asanexample,considerasysteminwhichlightisemittedfroma¼"diameterfiberopticlightguide,asshowninFigure3.
∙InitialParameters
NAofLightGuide=0.55
DiameterofSource(Emitter)=6.35mm
IndexofRefractionofAir=1
∙CalculatedParameters
F-Number(f/#)
(1.11)
APCXlensoff/1,meaningthef/#is1,wouldbeidealtoplaceinfrontofthelightguideinordertocollimateasmuchlightaspossible.AccordingtoEquation1.4,ifthef/#is1,thenthediameterandfocallengthofalensareequal.Inotherwords,ifweconsideralenswithadiameterof12mm,thenthefocallengthisalso12mm.
FullFieldofView(FFOV)
(1.12)
Throughput(TP)
(1.13)
(1.14)
(1.15)
Steradianscorrespondtoa2-dimensionalanglein3-dimensionalspace,astheanglefromtheedgetoedgeofthelensisintwodimensions.Ahighervalueinsteradiansisgivenbyashorterdistancefromemittertolens,oralargerdiameterofthelens.Thelargestvalueasolidanglecanhaveis4π,orabout12.57,asthiswouldbeequivalenttothesolidangleofallspace.
InordertocalculateThroughput(TP)ofthissystem,weneedtofirstcalculatetheAreaoftheSource(Equation1.11),theAreaoftheLens(Equation1.12)andtheSolidAngle(Equation1.13).Asaruleofthumbforcollimatinglightfromadivergentsource(i.e.thelightguideinthisexample),placethelensadistanceequaltoonefocallengthawayfromthesource.
(1.16)
Sincethesystemisinfreespace,wherenisapproximatedas1,n2doesnotfactorintothefinalcalculation.
Application2:
SelectingtheRightLens
Highimagequalityissynonymouswithlowaberrations.Asaresult,designersoftenutilizetwoormorelenselementsinordertoobtainhigherimagequalitycomparedtoasinglelenssolution.Manyfactorscontributetoselectingtherightlensforanapplication:
typeofsource,spaceconstraints,cost,etc.
Figures6a-6ecompareavarietyoflenssystemsforarelaylens,or1:
1imaging,application.Inthisspecificexample,outlinedinthefollowingseriesofcomparisons,itiseasytoseehowimagequalityisaffectedbytheinherentgeometryandopticalpropertiesofthelenseschosen.
Figure6a:
DCXLensRelaySystem:
25mmEFLx20mmEntrancePupilDiameter(LeftisColorandRightisMonochromatic)
Figure6b:
PCXLensRelaySystem:
50mmEFLx20mmEntrancePupilDiameter(LeftisColorandRightisMonochromatic)
Figure6c:
AchromaticLensRelaySystem:
50mmEFLx20mmEntrancePupilDiameter(LeftisColorandRightisMonochromatic)
Figure6d:
AspherizedAchromaticLensRelaySystem:
50mmEFLx50mmEntrancePupilDiameter(LeftisColorandRightisMonochromatic)
Figure6e:
AsphericLensRelaySystem:
50mmEFLx40mmEntrancePupilDiameter(LeftisColorandRightisMonochromatic)
ApplicationExample:
SingleElementLensSystem
Adouble-convex(DCX)lensisregardedasthebestsingleelementfor1:
1imagingbecauseofitssymmetricalshape,asbothsidesofthelenshaveequalpower,insteadofonesidebendingraysmorethantheother,suchasaplano-convex(PCX)lens.Sincethelenssystemismadeofjustonelens,theaperturestopisessentiallythelens,whichallowsforthereductionofmanyaberrations.Forthesereasons,aDCXlensispreferabletoasinglePCXlensfor1:
1imaging.However,itisimportanttokeepinmindthatatalowf/#,thereisstillsignificantsphericalaberrationandcoma.TheseaberrationsarecausedbytheShapeFactor(S)ofthesinglelens:
(2.1)
whereR1andR2aretheradiiofeachsurfaceofthelens.
Forapplicationsthatonlyneedonelens,withtheobjectorsourceatinfinity,abettershapefactorcanbefound,toreducewhicheveraberrationismostdetrimentaltothesystem.Forexample,toreducesphericalaberration,theidealshapefactorcanbecalculatedby:
(2.2)
(2.3)
(2.4)
WherenistheIndexofRefractionoftheGlassSubstrate,pisthePositionFactor,zisObjectDistance(measuredtobeanegativevalue),andz'isImageDistance(measuredtobeapositivevalue).
Toreducecomaforanobjectatinfinity,theShapeFactorcanbecalculatedby:
(2.5)
Forglassthathasanindexof1.5(N-BK7is1.517),withanobjectatinfinity,aShapeFactorofabout0.8willbalancethecorrectionsofbothcomaandsphericalaberrations.
ApplicationExample:
DoubleElementLensSystem
Inordertoimprovethesystem,asingleDCXlenscouldbereplacedwithtwoequalPCXlenseseachwitha
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