FresnelLenses-菲涅尔透镜原理

PositiveFocalLengthFresnelLensUsedasaCollectorPositiveFocalLengthFresnelLensUsedasaCollimatorNegativeFocalLengthFresnelLensUsedasaDivergerHIGHQUALITYFRESNELLENSESINAVARIETYOFSIZES&FOCALLENGTHS©CopyrightFresnelTechnologies,Inc.20032TheFresnelLensCenturiesago,itwasrecognizedthatthecontouroftherefractingsurfaceofaconventionallensdefinesitsfocusingproperties.Thebulkofmaterialbetweentherefractingsur-faceshasnoeffect(otherthanincreasingabsorptionlosses)ontheopticalpropertiesofthelens.InaFresnel(pointfocus)lensthebulkofmaterialhasbeenreducedbytheextractionofasetofcoaxialannularcylindersofmaterial,asshowninFigure1.(PositivefocallengthFresnellensesarealmostuniversallyplano-convex.)Thecontourofthecurvedsurfaceisthusapproximatedbyrightcircularcylindricalportions,whichdonotcontributetothelens’opticalproper-ties,intersectedbyconicalportionscalled“grooves.”Nearthecenterofthelens,theseinclinedsurfacesor“grooves”arenearlyparalleltotheplaneface;towardtheouteredge,theinclinedsurfacesbecomeextremelysteep,especiallyforlensesoflowf–number.Theinclinedsurfaceofeachgrooveisthecorrespondingportionoftheoriginalasphericsurface,translatedtowardtheplanosurfaceofthelens;theangleofeachgrooveismodifiedslightlyfromthatoftheoriginalasphericprofiletocompensateforthistranslation.Theearlieststepped-surfacelenswassuggestedin1748byCountBuffon,whoproposedtogrindoutmaterialfromtheplanosideofthelensuntilhewasleftwiththinsectionsofmaterialfollowingtheoriginalsphericalsurfaceofthelens,asshownschematicallyinFigure2a).Buffon’sworkwasfollowedbythatofCondorcetandSirD.Brewster,bothofwhomdesignedbuilt-uplensesmadeofsteppedannuli.TheasphericFresnellenswasinventedin1822byAugustinJeanFresnel(1788–1827),aFrenchmathematicianandphysicistalsocreditedwithresolvingthedisputebetweentheclassicalcorpuscularandwavetheoriesoflightthroughhiscarefulexperimentsondiffraction.Fresnel’soriginallenswasusedinalighthouseontheriverGironde;themaininnovationembodiedinFresnel’sdesignwasthatthecenterofcurvatureofeachringrecededalongtheaxisaccordingtoitsdistancefromthecenter,soaspracticallytoeliminatesphericalaberration.Fresnel’soriginaldesign,includingthespherical-surfacedcentralsection,isshownschematicallyinFigure2b).TheearlyFresnellenseswerecutandpolishedinglass–anexpensiveprocess,andonelimitedtoafewlargegrooves.Figure3showsaFresnellens,constructedinthisway,whichisusedinthelighthouseatStAugustine,Florida,USA.ThelargeapertureandlowabsorptionofFresnellenseswereespeciallyimportantforusewiththeweaklampsfoundinlighthousesbeforetheinventionofhigh-brightnesslightsourcesinthe1900s.Theillustratedsystemiscatadioptric:theglassringsaboveandbelowtheFresnellensbandinthecenterofthelightaretotally-internally-reflectingprisms,whichservetocollectanadditionalfrac-tionofthelightfromthesource.Theuseofcatadioptricsys-temsinlighthouseswasalsoduetoFresnel.Untilthe1950’s,qualityFresnellensesweremadefromglassbythesamegrindingandpolishingtechniquesusedin1822.CheapFresnellensesweremadebypressinghotglassintometalmolds;becauseofthehighsurfacetensionofglass,Fresnellensesmadeinthiswaylackedthenecessarydetail,andwerepoorindeed.Inthelastfortyyearsorso,theadventofoptical-qualityplastics,compressionandinjectionmoldingtechniques,Figure1ConstructionofaFresnellensfromitscorrespond-ingasphere.EachgrooveoftheFresnellensisasmallpieceoftheasphericsurface,translatedto-wardtheplanosideofthelens.Thetiltofeachsur-facemustbemodifiedslightlyfromthatoftheoriginalportionofasphericsurface,inordertocompensateforthetranslation.Figure2Earlystepped–surfacelenses.Inbothillustrationstheblackareaismaterial,andthedashedcurvesrepresenttheoriginalcontoursofthelenses.a)showsthelenssuggestedbyCountBuffon(1748),wherematerialwasremovedfromtheplanosideofthelensinordertoreducethethickness.b)showstheoriginallensofFresnel(1822),thecen-tralringofwhichhadasphericalsurface.InFresnel’slens,thecenterofcurvatureofeachringwasdisplacedaccordingtothedistanceofthatringfromthecenter,soastoeliminatesphericalaberration.a)b)©CopyrightFresnelTechnologies,Inc.20033andcomputer-controlledmachininghavemadepossiblethemanufactureandwideapplicationofFresnellensesofhigheropticalqualitythanthefinestglassFresnellenses.Moderncomputer-controlledmachiningmethodscanbeusedtocutthesurfaceofeachconepreciselysoastobringallparaxialraysintofocusatexactlythesamepoint,avoid-ingsphericalaberration.Betterstill,newermethodscanbeusedtocuteachrefractingsurfaceinthecorrectasphericcontour(ratherthanasaconicalapproximationtothiscon-tour),thusavoidingeventhewidthofthegroove(typically0.1to1mm)asalimittothesharpnessofthefocus.Eventhougheachgrooveorfacetbringslightpreciselytoafocus,thebreakingupofthewavefrontbythediscontinuoussur-faceofaFresnellensdegradesthevisibleimagequality.Exceptincertainsituationsdiscussedlater,Fresnellensesareusuallynotrecommendedforimagingapplicationsinthevisiblelightregionofthespectrum.Thecharacteristicsoftheaspheric“correction”Thegrindingandpolishingtechniquesusedinthemanufac-tureofconventionalopticsleadtosphericalsurfaces.Spher-icalsurfacesproduceopticswithlongitudinalspheri