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BeamdiameterFromWikipedia,thefreeencyclopediaBeamwidthredirectshere.Forcasesrelatedtoradioantennas,seebeamwidth.Thebeamdiameterorbeamwidthofanelectromagneticbeamisthediameteralonganyspecifiedlinethatisperpendiculartothebeamaxisandintersectsit.Sincebeamstypicallydonothavesharpedges,thediametercanbedefinedinmanydifferentways.Fivedefinitionsofthebeamwidthareincommonuse:D4,10/90or20/80knife-edge,1/e,FWHM,andD86.Thebeamwidthcanbemeasuredinunitsoflengthataparticularplaneperpendiculartothebeamaxis,butitcanalsorefertotheangularwidth,whichistheanglesubtendedbythebeamatthesource.Beamdiameterisusuallyusedtocharacterizeelectromagneticbeamsintheopticalregime,andoccasionallyinthemicrowaveregime,thatis,casesinwhichtheaperturefromwhichthebeamemergesisverylargewithrespecttothewavelength.Beamdiameterusuallyreferstoabeamofcircularcrosssection,butnotnecessarilyso.Abeammay,forexample,haveanellipticalcrosssection,inwhichcasetheorientationofthebeamdiametermustbespecified,forexamplewithrespecttothemajororminoraxisoftheellipticalcrosssection.Thetermbeamwidthmaybepreferredinapplicationswherethebeamdoesnothavecircularsymmetry.Contentshide1Widthdefinitionso1.1Fullwidthathalfmaximumo21.21/ewidtho1.3D4borsecondmomentwidtho1.4Knife-edgewidtho1.5D86width32Measurement3Seealso4ReferencesWidthdefinitionseditFullwidthathalfmaximumeditFormoredetailsonthistopic,seeFullwidthathalfmaximum.Thesimplestwaytodefinethewidthofabeamistochoosetwodiametricallyoppositepointsatwhichtheirradianeeisaspecifiedfractionofthebeamspeakirradianee,andtakethedistaneebetweenthemasameasureofthebeamswidth.Anobviouschoiceforthisfractionis?(-3dB),inwhichcasethediameterobtainedisthefullwidthofthebeamathalfitsmaximumintensity(FWHM).Thisisalsocalledthehalf-powerbeamwidth(HPBW).1/e2widthedit22The1/ewidthisequaltothedistaneebetweenthetwopointsonthemarginaldistributionthatare1/e=0.135timesthemaximumvalue.Inmanycases,itmakesmoresensetotakethedistaneebetweenpointswherethe22intensityfallsto1/e=0.135timesthemaximumvalue.Iftherearemorethantwopointsthatare1/etimesthemaximumvalue,thenthetwopointsclosesttothemaximumarechosen.The1/e2widthisimportantinthemathematicsofGaussianbeams.TheAmericanNationalStandardZ136.1-2007forSafeUseofLasers(p.6)definesthebeamdiameterasthedistaneebetweendiametricallyopposedpointsinthatcross-sectionofabeamwherethepowerperunitareais1/e(0.368)timesthatofthepeakpowerperunitarea.Thisisthebeamdiameterdefinitionthatisusedforcomputingthemaximumpermissibleexposuretoalaserbeam.Inaddition,theFederalAviationAdministrationalsousesthe1/edefinitionforlasersafetycalculationsinFAAOrder7400.2F,ProceduresforHandlingAirspaceMatters,February16,2006,p.29-1-2.2Measurementsofthe1/ewidthonlydependonthreepointsonthemarginaldistribution,unlikeD4andknife-edgewidthsthatdependontheintegralofthemarginaldistribution.1/e2widthmeasurementsarenoisierthanD4cwidthmeasurements.Formultimodalmarginaldistributions(abeamprofilewithmultiplepeaks),the1/ewidthusuallydoesnotyieldameaningfulvalueandcangrosslyunderestimatetheinherentwidthofthebeam.Formultimodaldistributions,theD4crwidthisabetterchoice.Foranidealsing-modeGaussianbeam,2theD4c,D86and1/ewidthmeasurementswouldgivethesamevalue.ForaGaussianbeam,therelationshipbetweenthe1/e2widthandthefullwidthathalfmaximumis,21whereisthefullwidthofthebeamat1/e.D4corsecondmomentwidtheditTheD4cwidthofabeaminthehorizontalorverticaldirectionis4timesc.sdieoterddeviiatliloeofthehorizontalorverticalmarginaldistribution,respectively.Mathematically,theD4cbeamwidthinthex-dimensionforthebeamprofileisexpressedas辺whereisthecentroidofthebeamprofileinthex-direction.Whenabeamismeasuredwithalaserbeamprofiler,thewingsofthebeamprofileinflueneetheD4cvaluemorethanthecenteroftheprofilesineethewingsareweightedbythesquareofitsdistanee,x2,fromthecenterofthebeam.Ifthebeamdoesnotfillmorethanathirdofthebeamprofilerssethentherewillbeasignificantnumberofpixelsattheedgesofthesensorthatregisterasmallbaselinevalue(thebackgroundvalue).Ifthebaselinevalueislargeorifitisnotsubtractedoutoftheimage,thenthecomputedD4cvaluewillbelargerthantheactualvaluebecausethebaselinevalueneartheedgesofthesensorareweightedintheD4cintegrafbTherefore,baselinesubtractionisnecessaryforaccurateD4ccwidth,unliketheFWHMandwidths,ismeaningfulformultimodalmarginaldistributionsthatis,beamprofileswithmultiplepeaksbutrequirescarefulsubtractionofthebaselineforaccurateresults.TheD4beamwidth.o-istheISOinternationalstandarddefinitionforKnife-edgewidtheditBeforetheadventoftheCCDbeamprofiler,thebeamwidthwasestimatedusingtheknife-edgetechnique:slicealaserbeamwitharazorandmeasurethepoweroftheclippedbeamasafunctionoftherazorposition.Themeasuredcurveistheintegralofthemarginaldistribution,andstartsatthetotalbeampoweranddecreasesmonotonicallytozeropower.Thewidthofthebeamisdefinedasthedistaneebetweenthepointsofthemeasuredcurvethatare10%and90%(or20%and80%)ofthemaximumvalue.Ifthebaselinevalueissmallorsubtractedout,theknife-edgebeamwidthalwayscorrespondsto60%,inthecaseof20/80,or80%,inthecaseof10/90,ofthetotalbeampowernomatter2whatthebeamprofile.Ontheotherhand,theD4p-nt/eWHMwidthsencompassfractionsofpowerthatarebeam-shapedependent.Therefore,the10/90or20/80knife-edgewidthisausefulmetricwhentheuserwishestobesurethatthewidthencompassesafixedfractionoftotalbeampower.MostCCDbeamprofilerssoftwarecancomputetheknife-edgewidthnumerically.D86widtheditTheD86widthisdefinedasthediameterofthecirclethatiscenteredatthecentroidofthebeamprofileandcontains86%ofthebeampower.ThesolutionforD86isfoundbycomputingtheareaofincreasinglylargercirclesaroundthecentroiduntiltheareacontains0.86ofthetotalpower.Unlikethepreviousbeamwidthdefinitions,theD86widthisnotderivedfrommarginaldistributions.Thepercentageof86,ratherthan50,80,or90,ischosenbecauseacircularGaussianbeamprofileintegrateddownto21/eofitspeakvaluecontains86%ofitstotalpower.TheD86widthisoftenusedinapplicationsthatareconcernedwithknowingexactlyhowmuchpowerisinagivenarea.Forexample,applicationsofhigh-energylaserweaponsandlidarsrequirepreciseknowledgeofhowmuchtransmittedpoweractuallyilluminatesthetarget.ISO11146beamwidthforellipticbeamseditThedefinitiongivenbeforeholdsforstigmatic(circularsymmetric)beamsonly.Forastigmaticbeamshowever,amorerigorousdefinitionofthebeamwidthhastobeused,andThisdefinitionalsoincorporatesinformationaboutx-y-correlation,butforcircularsymmetricbeams,bothdefinitionsarethesame.Somenewsymbolsappearedwithintheformulas,whicharethefirst-andsecond-ordermomentsandthebeampowerandUsingthisgeneraldefinition,alsothebeamsazimutal-anglecanbeexpressed.Itistheanglebetweenthebeamsdirectionsofminimumandmaximumelongation,knownasprincipalaxis,andthelaboratorysystem,beingthe-and-axisofthedetectorandgivenbyMeasurementeditInternationalstandardISO11146-1:2005specifiesmethodsformeasuringbeamwidths(diameters),divergeneeanglesandbeampropagationratiosoflaserbeams(ifthebeamisstigmatic)andforgeneralastigmaticbeamsISO11146-2isapplicable.迴TheD4beamwidthistheISOstandarddefinitionandthemeasurementoftheM2beamqualityparameterrequiresthemeasurementoftheD4crwidths.TheotherdefinitionsprovidecomplementaryinformationtotheD4c.TheD4candkriife-edgewidthsaresensitivetothe2baselinevalue,whereasthe1/eandFWHMwidthsarenot.Thefractionoftotalbeampowerencompassedbythebeamwidthdependsonwhichdefinitionisused.SeealsoeditBeamdivergeneeLase匚beam.profilerReferenceseditJumpupAHill,Dan(April4,2007).HowtoconvertFWHMmeasurementsto1/e-squaredhalfwidths.RadiantZemaxKnowledgeBase.RetrievedNov15,2012.1. JumpupASiegman”A.E.(October1997).Howto2. (Maybe)MeasureLaserBeamQuality(pdf).ArchivedfromtheoriginalonJune4,2011.RetrievedJuly2,2014.TutorialpresentationattheOpticalSocietyofAmericaAnnualMeeting,LongBeach,CaliforniaJumpupA_ISO11146-3:2004(E),Lasersandlaser-relatedequipmentTestmethodsforlaserbeamwidths,divergeneeanglesandbeampropagationratios3. Part3:Intrinsicandgeometricallaserbeamclassification,propagationanddetailsoftestmethods.abAJumpupto:-ISO11146-1:2005(E),Lasersandlaser-relatedequipmentTestmethodsforlaserbeamwidths,divergeneeanglesandbeampropagationratiosPart1:Stigmaticandsimpleastigmaticbeams.abaJumpupto:-ISO11146-2:2005(E),Lasersandlaser-relatedequipmentTestmethodsforlaserbeamwidths,divergeneeanglesandbeampropagationratiosPart2:Generalastigmaticbeams.JumpupAISO11146-3:2005(E),Lasersandlaser-relatedequipmentTestmethodsforlaserbeamwidths,divergeneeanglesandbeampropagationratiosPart3:Intrinsicandgeometricallaserbeamclassification,propagationanddetailsoftestmethods.Categories:*Antennas_(radio)Optics
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