光学元件应用实例.docx

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