水肺-2旋光仪光学设计报告

TechnicalReportOPTICALDESIGNOFTHESCUBA-2POLARIMETERSC2/POL/OPT/002Version0.3INO040193RN/ASubmittedto:Mr.PierreBastienDirector,ObservatoiredumontMegantic

Departementdephysique,UniversitedeMontreal

B.P.6128,Succ.Centre-villeMontreal,(Quebec),CanadaH3C3J7Preparedby:MelanieLeclercPresentedby:MelanieLeclercResponsabledeprojetPresentedby:MelanieLeclercResponsabledeprojetJonnyGauvinResponsabledeprogrammeconceptionoptiqueiINOJanuary14INO•2740,rueEinstein,Sainte-Foy(Quebec)CanadaG1P4S4TableofContentTOC\o"1-5"\h\z\o"CurrentDocument"Introduction 1\o"CurrentDocument"OpticaldesignofthepolarimeterwithZemax(DeliverableB1) 1Opticaldesign 1Preliminarystudytoevaluatethepossibilityofgettingtheopticalcomponentsnearerthecryostatwindow(DeliverableA3) 3Footprintoftheunvignettedbeamatpolarimeteropticalsurfaces 3Studyoftheeffectsofghostsinthepolarimeter (DeliverableB3) 10Toleranceanalysis 30\o"CurrentDocument"Analysisoftheeffectofinstrumentalpolarizationonthepolarimeter(DeliverableB2) 31Perfectpolarizerinacollimatedbeam 31Real polarizerinacollimatedbeam 35Real waveplateandrealmirrorsurfaces effect onthepolarizationstate 40Real polarimeterwiththetelescopeand the SCUBA-2camera 42Impactofthepolarimeterontwoorthogonalpolarizationstates 45IntroductionThestudyofpolarizedradiationistheprimarymeanofinvestigatingthegeometryofmagneticfieldswithinastronomicalsources.Thesefieldsareprevalentthroughoutgalaxies,fromthelargestscalestothesmallcoresthatarecollapsingtoformstarswithinmolecularclouds.Understandingthegeometryofthesefields,bothataglobalandadetailedlevels,iscrucialtoourunderstandingofstarformationprocessesandthephysicsofmolecularclouds.TheSCUBA-2PolarimeterwillbebuiltandwillbefixedinfrontoftheSCUBA-2camera,tostudypolarizedradiationsinthesub-millimeterwavelengthrange.TheSCUBA-2cameraisdesignedfortheJamesClerkMaxwellTelescope(JCMT).TheSCUBA-2polarimeterwillbethemostsensitiveinstrumentforthedetectionofpolarizedradiationinthesub-millimeterregime,thatbeingmadepossiblebythegreatsensitivityandlargeformatoftheSCUBA-2detectors.ThisdocumentdetailsdesignissuesrelativetotheSCUBA-2polarimeteranditsintegrationintotheexistingdesignsfortheJCMTandtheSCUBA-2camera.Thepresenceofthepolarimeterinthebeamanditseffectonimagequality,vignetting,ghostimages,instrumentalpolarization,andtolerancingwillbestudied.OpticaldesignofthepolarimeterwithZemax(DeliverableB1)OpticaldesignThenominalfileSC2_POL_OPT_001.ZMXwasmodifiedastheSCUBA-2camerawindowthicknesswaschangedfrom6mmto8mm.Thepositionofthesecondarymirrorwasthenre-optimizedandwentfrom-128.6mmto-128.595262mm.ThenewdesignwassavedasSC2_POL_OPT_003.ZMX.Inthisnewdesign,theconfiguration1representsthecamerawiththepolarimeterelementsoutofthebeam.Theconfiguration2istheoperationmodeofthepolarimeter,andtheconfiguration3isthecalibrationmodeofthepolarimeter.WesubsequentlymodifiedSC2__POL_OPT_003.ZMXtohavemorerealisticpolarizersandhalfwaveplateparameters,simulatingthepolarizersisolationandthewaveplatematerialandsurfaces.Wealsoaddedcircularaperturestorepresentthepolarimeteropticalelementsmounts.Thethreeconfigurationsremainedunchanged.ThismodifieddesignwassavedunderSC2_POL_OPT_004.ZMX.ZemaxFileSC2_POL_OPT_001.ZMXSC2_POL_OPT_003.ZMXConfiguration1(Withoutpolarimeter)SC2_POL_OPT_003.ZMXConfiguration2and3(Withpolarimeterinoperationandincalibrationmodes)Windowthickness(mm)688Positionofsecondarymirror(mm)-128.6-128.595262-128.536090Field#Fieldcoord.(deg)SpotRMSradiusrelativetocentroid(pm)SpotRMSradiusrelativetocentroid(pm)SpotRMSradiusrelativetocentroid(pm)1(0.0)106.232106,739143.0012(0.0652,0.0652)152.343119.627127.3423(0.0652,-0.0652)120.502113.767110.1634(-0.0652,0.0652)122.002127.440172.3165(-0.0652,-0,0652)155.402127.289117.2906(0,0.0652)119.150150.949227.4697(0,-0.0652)104.42999.478111.2878(0.0652,0)125.22598.530113.1069(-0.0652,0)121.770100.937107.100Table1-Impactofthepolarimeterontheimagespotsize-078•10UNAcocSMS•5

700

X00

821QlARCMINF工ELD\850MICRONS/ \l——I! 2000,0办/工l_L工METERSSC2_POL_OPT_00M.ZMX.CONFIGURATION：ALL3、、、Figure1-JCMTtelescopewithSCUBA-2camera,andpolarimeterlocationAPERTUREDIAMETER：368.B802SCUBA27.MONF1PR25SURFACE39：8X7.8ARCMINFIELD.2D05RAYXMINAPERTUREDIAMETER：368.B802SCUBA27.MONF1PR25SURFACE39：8X7.8ARCMINFIELD.2D05RAYXMINRAYYMINPOLARISEURCALIBRATION-90,Q9H9RRYXMAX-133.2078RRYYMAXMICRONS79.L112L69.8938M5D,0D0<3SC2_POL_OPT_00H.ZMXCONFXCURATION1DF3Preliminarystudytoevaluatethepossibilityofgettingtheopticalcomponentsnearerthecryostatwindow(DeliverableA3)Theopticalcomponentswereplacedasnearthewindowaspossibleconsideringthemechanicalpartssizeandlocation.Wedidnotimplementanysystemwithatranslationstagealongthezaxis,togetthepolarimeteropticalcomponentsnearerthewindowintheoperationmode,duetovolumeconstraints.FootprintoftheunvignettedbeamatpolarimeteropticalsurfacesToobtainthefootprintofthebeamatthelocationoftheopticalsurfacesofthepolarimetercomponentsanddeterminethecomponentsclearaperture,weconsideredafieldofviewof±0.09221°fortheJamesClerkMaxwellTelescope(JCMT).ThisfieldofviewisdefinedbytheZemaxfilefieldsasshowninTable1.XRAYSTHROUGH=96,99XFODTPRINTDIRGRRMFigure2-Footprintofthebeamatthecalibrationpolarizer5aul.LulxH」」Hz昌aoaez:APERTUREDIAMETER：289.DH39XRAYSTHROUGH=96,99XFOOTPRINTDIRGRRMUNRYYXCOUAAASMSRRM75232MNNUIIIREMMD2FCRARAXYR8X7.8ARCMINFIELD.2D05MICRONSkJAUEPLATE-69.3299-98.937113M.HM57RRYX5aul.LulxH」」Hz昌aoaez:APERTUREDIAMETER：289.DH39XRAYSTHROUGH=96,99XFOOTPRINTDIRGRRMUNRYYXCOUAAASMSRRM75232MNNUIIIREMMD2FCRARAXYR8X7.8ARCMINFIELD.2D05MICRONSkJAUEPLATE-69.3299-98.937113M.HM57RRYXMAX=RRYYMAX=WRVELENGTH=6H,028H131.9790M5D,0000SC2_POL_OPT.00M.ZMXCONFXCURATZON1DF3Figure3-FootprintofthebeamatthehalfwaveplatefirstsurfaceXRAYSTHROUGH=96.99XSC2_POL_OPT.00M.ZMXCONFTCURATION1DF3APERTUREDIAMETER：250.BH52FiJDTPRINTDIRGRRMSCU0A27.8X7.8ARCMINFIELD48SDMICRONSMONAPR252005SURFACE32：POLARISEURFIXERAYXMIN=-67.1268RRYXMAX= 62,8677RAYYMIN=-33,HHHMRRYYMAX=L1H.5339MAXRADIUS= 118.M6111WAVELENGTH= H50.0000Figure4-FootprintofthebeamattheanalyzerpolarizerThebeamfootprintisofanovalshapewithageometriccenterslightlyofftheopticalaxis.

ClearApertureneededtoavoidVignettingDecenteredclearapertureneededtoavoidvignettingCalibrationpolarizer369mm*21.5mmdecenter,326mmdiameterHalfwaveplate289mm~18mmdecenter,253mmdiameterAnalyzerpolarizer251mm~18mmdecenter,215mmdiameterTable2-BeamgeometryatpolarimeteropticalsurfacesTheavailablevolumeforthepolarimeterconstraintthemaximumclearaperturethatitispossibletohaveforeachopticalcomponent.Manufacturingprocessesfortheopticalcomponentsthemselvesarealsotobeconsideredtosetamaximumapertureforeachopticalcomponent.Followingisthefootprintofthebeamforthefollowingdesignoption:Clearapertureof:ocalibrationpolarizer=300mm,ohalfwaveplate=270mm,oanalyzerpolarizer=200mm.Wealsoincludedatabledetailingthevignettingeffectforthefollowingtwooptions:Clearapertureofallopticalcomponents=200mmClearapertureofallopticalcomponents=300mmFootprintforthehalfwaveplatewithclearaperture=270mmandanalyzerclearaperture=200mm,inoperationmodeAPERTUREDIAMETER：APERTUREDIAMETER：270.D00D%RAYSTHROUGH=9H,a5XFUDTPRINTDIRGRAM75232U-NNUIIIREMMD2FCRA-MRXYRBFUNRYYXCOUAARSMSPPM75232U-NNUIIIREMMD2FCRA-MRXYRBFUNRYYXCOUAARSMSPPM,8X7,8ARCMINFIELD.9SD2005MICRONSJMAUEPLATE=-65,9H56=-98.93H8=1LH,57B2RRYXMAX=RRYYMAX=WRVELENGTH=63.9B09L1H.29MSSC2_POL_OPT_00M,ZMXCONFXCURRTION2DF3-Firstapertureatthehalfwaveplate,inoperationmodeAPERTUREDIAMETER：200,000。/RAYSTHROUGH=9H.95XFOOTPRINTDIRGRAMSCU0A27.MONAPR25SURFACE62!RAYXMIN=RAYYMIN=MAXRRDIU3=8X7.8ARCMINFIELD.9S02B05POLARISEURFIXE-6H.9066RRYXAPERTUREDIAMETER：200,000。/RAYSTHROUGH=9H.95XFOOTPRINTDIRGRAMSCU0A27.MONAPR25SURFACE62!RAYXMIN=RAYYMIN=MAXRRDIU3=8X7.8ARCMINFIELD.9S02B05POLARISEURFIXE-6H.9066RRYXMAX93.9759RRYYMAX.6558WRVELENGTH=MICRONS62.8H7299,5307H5D.0D0GSC2_POL_OPT_00M,ZMXCONFXCURATION2DF3-Vignettingofthebeamattheanalyzer,inoperationmode2.3.2Footprintforthecalibrationpolarizerwithclearaperture=300mm,halfwaveplatewithclearaperture=270mmandanalyzerclearaperture=200mm,incalibrationmodeInthecalibrationmode,theopticalelementcausingthevignettingisthecalibrationpolarizer,asseeninFigure7.However,acalibrationpolarizerof300mmdiameterandananalyzerpolarizerof200mmdiametercauseasimilarvignettingeffect.300mmseemstobethemaximumdiameterfortheopticalelementsifweconsiderthemanufacturingaspectofthosecomponents.salillulzHTlHW&日DsaGz:UJ」au5XRAYSTHROUGH=9H.6HXUNRYYXCOUAAASMSRRM759323NNUIIIREMMD2FCRARAXYR8X7.8ARCMINFIELD.2005POLARISEURCALIBRATION-80.1113RRYXXRAYSTHROUGH=9H.6HXUNRYYXCOUAAASMSRRM759323NNUIIIREMMD2FCRARAXYR8X7.8ARCMINFIELD.2005POLARISEURCALIBRATION-80.1113RRYXMAX=-133.28BMRRYYMAX=1M8,3597WRVELENGTH=MICRONS79,1512IH2.2012SC2_POL_OPT.00M.ZMXCONFXCURATZON3DF3Figure7-Firstvignettingsurfaceatthecalibrationpolarizer,incalibrationmodeAPERTUREDIAMETER：300,0000FOOTPRINTDIRGRAMXRAYSTHROUGH=9H.6HXSCUBA2 7.MONAPR25SURFACEM2：RAYXMIN=RAYXRAYSTHROUGH=9H.6HXSCUBA2 7.MONAPR25SURFACEM2：RAYXMIN=RAYYMIN=MRXRADIUS=8X7.8ARCMINFIELD.85。2D05MAUEPLATE-65.9H56-98.93H8112,6371RRYXMAX=RRYYMAX=WRVELENGTH=MICRONS63.9B09L0B,9767M5D.0D0OSC2_POL_OPT_00M.ZMXCONFrCURATION3DF3Figure8-Beamatthefirstsurfaceofthehalfwaveplate,incalibrationmodeAPERTUREDIAMETER：27(3.0000FOOTPRINTDIAGRAM/RAYSTHROUGH=9H.6HXAPERTUREDIAMETER：200,000/RAYSTHROUGH=9H.6HXFOOTPRINTDIRGRAMSCU0A27.MONAPR25SURFACE62!RAYXMIN=RAYYMIN=MAXRRDIU3=8X7.8ARCMINFIELD.9S02B05POLARISEURFIXE-6H.9066RRYXMAX93.9759RRYYMAX.6558WRVELENGTH=MICRONS62.8H729M.H972SC2_POL_OPT_00M,ZMXCONFXCURATION3DF3Figure9-Beamattheanalyzerpolarizer,incalibrationmodeTheproportionofraysthrougheachapertureisdetailedinthefollowingtable,forpolarimeteropticalcomponentsofvariousdiameters.ThefieldsofTable1areconsidered.ModeSurfaceOption1:300mm0calibrationpolarizer,270mm0halfwaveplate,200mm0analyzerpolarizerOption2:200mm0opticalelementsOption3:300mm0opticalelementsCalibrationRayscomingfromtelescope(allfields)97.86%97.86%97.86%Atcalibrationpolarizer94.64%79.71%94.81%Atdetector94.64%79.71%94.81%OperationRayscomingfromtelescope(allfields)97.86%97.86%97.86%Athalfwaveplatefirstsurface94.85%92.88%96.85%Atdetector94.85%92.88%96.85%Table3-Vignettingwith200mmand300mmapertures

9B7rsrnzI

SAk叱口归」LNDIANnLEJNEJILU京L9B7rsrnzI

SAk叱口归」LNDIANnLEJNEJILU京LOPERATIONMODE□RLIBRFITIONMDDE一□.000000.0^221PZELDINDEGREESUJGNETTINGDjnQPRMSCUBA2P.BXT.BFlRCMLNFIELD.050MICRONSMQNnPQ252(2)131SD2_FDL_OrT.ZMX□□NPIGURPTinN2OP2UZGNETTINGDZOGRRMFigure10-Vignettingplotforthetwomodes,fora300mm0calibrationpolarizer,270mm0halfwaveplateanda200mm0analyzerpolarizerUZGNETTINGDZOGRRMFigure10-Vignettingplotforthetwomodes,fora300mm0calibrationpolarizer,270mm0halfwaveplateanda200mm0analyzerpolarizerqB7C]U1—0SAk此口旧1」皿NUIANnL口ZOMr^E^n-SCUBA2MQN口PCSCUBA2MQN口PCSC2_FDL_QPT_D0r.ZNX□□NPiGuiTnTiDN幺arg-Vignettingplotforthetwomodes,for200mm0componentsUJGNETTING口二口个口R)MSX7.0HRCMLNFIELD.BS0MICRONSQB76c-M32I0tn叱口LE3二口1匚京=|202PnnnUNCQSMSC2_尸Di__art_D0m，znxCDNPIGUROTIDN2QP2-Vignettingplotforthetwomodes,for300mm0components2.4Studyoftheeffectsofghostsinthepolarimeter(DeliverableB3)Thewaveplatematerialwasassumedtobeuncoatedsapphireatthetimeofthestudy.ThetransmissioncoefficientforthewholewaveplateincludingA/Rcoatingsbecameavailableduringthepreliminarydesignphaseandwasconsideredinsomeoftheanalysis.WherevertheA/Rcoatingsandupdatedtransmissiondatawasused,thereisindicationstothiseffectinthetext.Thefinalwaveplatewillhowevernotbemadeofsapphire,butthedataforthenewmaterialwasnotavailableduringthepreliminaryanalysisphase.Theghostsanalysisw川havetobeupdatedwhendataonthefinalwaveplatematerialbecomeavailable.Theparametersofthenominaldesign,fromtheSC2__POL_OPT__004.ZMXZemaxfile,are:Configuration2of3EffectiveFocalLength: 110486.6(inairatsystemtemperatureandpressure)EffectiveFocalLength: 110486.6(inimagespace)BackFocalLength : -7316.98TotalTrack: 11284.92ImageSpaceF/# : 7.465308StopRadius: 188.422ExitPupilDiameter : 85.44894ExitPupilPosition: -16.48413FieldType:AngleindegreesMaximumField: 0.09220672AngularMagnification: 190.7192

Themajorghostsimagesarecreatedbytheretro-reflectionbetweenthefollowingsurfaces:thetwopolarizersduringcalibration,thefrontsurfaceofthecamerawindowandthecalibrationpolarizer.the frontandbacksurfacesofthehalfwaveplate,the frontsurfaceofthe camerawindowandtheanalyzerpolarizer,the frontsurfaceofthe camerawindowandthelastsurface ofthehalfwave plate,the frontsurfaceofthe camerawindowandthefirstsurface ofthehalfwave plate,Ghostfocusfromretro-reflectionbetweenthetwopolarizersFigure13-Ghostimageproducedbytheretro-reflectionbetweenthetwopolarizersFigure13-Ghostimageproducedbytheretro-reflectionbetweenthetwopolarizersFZ#=6.53RMSspotradiusonaxis=37.169mmDistancetoghostpupil=-297.8855mmDistancetoghostfocus=268.43mmEffectivefocallength=103806.1936mmInthecalibrationmode,aretro-reflectionwillbeproducedbetweenthetwopolarizerssurfaces.Theghostimageisdefocusedby250mmrelativetoimageplane.

THICKNESSINMILLIMETERSDNSURFACE106THPQUGHFQCUE，THICKNESSINMILLIMETERSDNSURFACE106THPQUGHFQCUE，RMSGPQTF旧口工USFELHTPJET。CHIEFPRYGHDSTREFLECTIONOFFSURFACE52THEN39.THURPR2B2005QI。日NQOQ.ZMXCONFIGURATION1DF1Figure14-Ghostimagecreatedbytheretro-reflectionbetweenthetwopolarizers,defocusedof250mminfrontoftheimageplaneThespotsizeofthisghostimageonthedetectorisalmostaslargeasthedetectoraperture:FCDTPP工NTDIRGPRMGHDSTREFLECTIONOFFSURFACE52THEN39.THURFR2B2D05SURFACE1FCDTPP工NTDIRGPRMGHDSTREFLECTIONOFFSURFACE52THEN39.THURFR2B2D05SURFACE1吟IMACE5awlluzM」一KnQGaGaGr；RAYXMINRAYYMINMRXRRDIU3-55.9H67RRYXMAX-H2.5839RRYYMAX60,3850WAVELENGTH56.7H205H,2965M5D.0B0GGI0日ZOO夕.NEXCONFICURATION1OF1Figure15-Footprintoftheghostbeamattheimageplaneforcentralfield(0,0)°Weassumeapolarizertransmission>95%whenthebeampolarizationislinearandalignedwiththepolarizersaxisandof0.01%whenthebeampolarizationislinearandperpendiculartothepolarizersaxis.IfthesapphirehalfwaveplateisleftwithoutanyA/Rcoating,theinterfaceair/sapphirehasatransmissioncoefficientT=0.7413.However,ifwetakeintoaccountthe5elementsofthehalfwaveplateandtheA/Rcoating,Cardiffuniversitysimulationsonthehalfwaveplateindicateatransmissionof94.7%at850micronsandof82.8%.IfweassumeahalfwaveplatewithoutanyA/Rcoating,theghost/imageratiowillbe:ifthepolarizationislinearandalignedwiththepolarizersaxis:&3,=(1—0.95)2(0.7413尸=7.55x107=0.08%oranerrorof0.08%overanimageintensityof(0.95)2(0.7413)2=0.4959oftheintensitymeasuredwithonlythetelescopeandthecamera.ifthepolarizationislinearandperpendiculartothepolarizersaxis:T油加=d-0.0001)2(0.7413)4=3.02xl0-1=30.19%oranerrorof30%overanimageintensityof(0.0001)2(0.7413)2=5x1O_9oftheintensitymeasuredwithonlythetelescopeandthecamera.Ifweassumeatransmissionof94.7%at850pmand82.8%at450pmforCardiffsapphirehalfwaveplate,theghost/imagepowerratiowillbe:ifthepolarizationislinearandalignedwiththepolarizersaxis:小(450〃,〃)=(1-0.95)2(0.828)2=171xl0-3=0.2%加(850网i)=(1-0.95)2(0.947)2=2.24x10-3=0.2%oranerrorof0.2%overanimageintensityof0.747-0.855oftheintensitymeasuredwithonlythetelescopeandthecamera.ifthepolarizationislinearandperpendiculartothepolarizersaxis:Tghusl(450///7?)=(1-0.0001)2(0.828)2=6.85x10-'=68.5%7纲,(850〃加)=(1-0.000(0.947尸=8.97x10-1=89.7%oranerrorof69-90%overanimageintensityof8x1O'9-9x10-9oftheintensitymeasuredwithonlythetelescopeandthecamera.Thisghostbeamwillalsosufferimportantvignettingthatwillreducetheintensitybymorethanhalfatthecoldstop:0.0000Q0.011618FIELDINDEGREES0.09221VIGNETTINGOIRGRRMI.0.0000Q0.011618FIELDINDEGREES0.09221VIGNETTINGOIRGRRMI.号87653-3210SACILolul»-luNDI>NnILDNDHluBallGHDSTREFLECTIONOFFSURFACE52THEN39,THURPR282D0S,NEXCONFIGURATION1DF1Figure16-VignettingoftheghostbeamcomingfromthetwopolarizersGhostfocusfromretro-reflectionbetweenthefirstsurfaceofthewindowandthecalibrationpolarizerSurfaces57and39:F/#=5.787207Figure17-Ghostimageproducedbytheretro-reflectionbetweenthefirstsurfaceofthewindowandthecalibrationpolarizerRMSspotradiusonaxis=59.994mmDistancetoghostpupil=-359.8403mmDistancetoghostfocus=-3253.2155mmEffectivefocallength=-17314.0353mmIfweassumeahalfwaveplatewithoutanyA/Rcoating,theghost/imageintensityratiowillbe:Figure17-Ghostimageproducedbytheretro-reflectionbetweenthefirstsurfaceofthewindowandthecalibrationpolarizerifthepolarizationislinearandalignedwiththecalibrationpolarizeraxis:,6。“=(1-0.9568)(1—0.95)(0.95)2(0.7413/=5.89x1。T=0.06%oranerrorof0.06%overanimageintensityof0.4959oftheintensitymeasuredwithonlythetelescopeandthecamera.ifthepolarizationislinearandperpendiculartothecalibrationpolarizeraxis:Tghost=(1-0.9568)(1-0.0001)(0.0001)2(0.7413)4=1.30xl0-,°=lxl0-8%oranegligibleerroroveranimageintensityof5x1O_9oftheintensitymeasuredwithonlythetelescopeandthecamera.TheresultswillbesimilarifweusethetransmissioncoefficientforthewholewaveplateincludingA/RcoatingsfromCardiffsimulations,andtheghosteffectfromtheretroreflectionbetweenthewindowandthecalibrationpolarizercanbeconsiderednegligible.Ifweassumeatransmissionof94.7%at850pmand82.8%at450|imforCardiffsapphirehalfwaveplate,theghost/imagepowerratiowillbe:ifthepolarizationislinearandalignedwiththepolarizersaxis:Tgluisl(450〃，”)=(1-0.9568)(1-0.95)(0.95)2(0.828)2=1.34xl0-3=0.1%小(850〃m)=(1-0.9568)(1-0.95X0.95)2(0.947)2=1.75X10-3=0.2%oranerrorof0.2%overanimageintensityof0.747-0.855oftheintensitymeasuredwithonlythetelescopeandthecamera.ifthepolarizationislinearandperpendiculartothepolarizersaxis:小(450〃加)=(1-0.9568)(1-0.000lXO.0001)2(0.828)2=2.96x10-10=3x1O-8%Tghnst(850/zm)=(l-0.9568)(1-0.000iXO.OOOl)2(0.947)2=3.87x10-1°=4x10-8%oranegligibleerroroveranimageintensityof8x1O'9-9x1O_9oftheintensitymeasuredwithonlythetelescopeandthecamera.Theghostimageisdefocusedof367mmrelativetotherealimage.

0UA工'qmxx-I"IIJAHM・nu(Lz(I:0UA工'qmxx-I"IIJAHM・nu(Lz(I:s•工MioM-6.00DE+-D02 -3.0D0E*D02 D,000E*D0QTHICKNESSINMILLIMETERSONSURFACE116THROUGHFOCUSPMSSPOTER□工USEELRTIVE丁口CHIEFERYGHDSTREFLECTIONOFFSURFACE57THEN39.FRIAPR292B05GI0日7000.NMXCONFICURRTION1OF1-GhostimagedefocusThespotdiameteris185mmattheimageplane.出 41♦ 1 怎强—除普尔融APERTUREDIAMETER：129,2139 /RRYSTHROUGH=92.6BXFOOTPRINTDIRGRRMGHDSTREFLECTIONOFFSURFACE57THEN39.FRIHPR292D05SURFACE117!IMACERAYXMIN=-76.9H37RRYXMAX= 76,3793RAYYMIN=-69.2261RRYYMAX= 8B.9953MAXRADIUS= 92.5231WRVELENGTH=M5D,0D0QQI。日70。夕,NMXCONFZCURATION1DF1-Ghostcentralfieldfootprintattheimageplane

Thevignettingoftheghostbeamatthecoldstopisimportant.Only27.4%ofthebeamintensitygetsthroughtothedetector:0.0QD0Q0.0H61QFIELDINDEGREES0.0922LVIGNETTINGDIAGPRM90.0QD0Q0.0H61QFIELDINDEGREES0.0922LVIGNETTINGDIAGPRM9£*QUJllUJNuI>NnULDZOHHOSUGHOSTREFLECTIONOFFSURFACE57THEN39.FRIRPR292005GI0曰70。夕,NN1XCONFICURRTION1DF1-Ghostvignetting2.4.2Ghostfocusfromretro-reflectionbetweenthetwosurfacesofthehalfwaveplateAghostimageiscreatedbytheretro-reflectionatthetwosurfacesofthehalfwaveplate.Thisghostimageisdefocused2mmrelativetotheimageplane.Thespotsizeofthisghostimageattheimageplaneistwotothreetimeslargerthanthatoftherealimage.IllIHI11SeeenlargedpicturebelowHalfwaveplateSurfaces48and42:RMSspotraduisonaxis=0.26825mmtoghostpupil=-19~dancetoqhostfocus=617.2989mmEffeXSlength=110419.0969mmFigure21褊-nbetweenthetwospaces“thehaKwave语(040193)fl.fltm.QI3O3DDEC ・ • ・・ e11Q.ahsz.o.atszdbc ♦ ♦ .、、a.flbSS. DEC ， • ♦♦.-D.M52.0.D652DEG-E膜2.・Q,Q图OGG % • ・、、Q,(3M3. DBG • • •••O.QEVQ,-9.D6S3DEG ♦ ・ ♦♦・纺3.D.QEJQDOBC ♦ • •♦♦-D.CMez^e.mmdec . • .・•-HD0G -2000 a200B H0G0SURFACETMA：IMADETHROUGHFOCUSSPOTDIAGRAMGHDSTREFLECTIONOFFSURFACEHBTHENH2.THUAPRZB2005UNITSRREJQ.FBnt i 】 】 q i ， ？ i ，流血E： 风0以“球⑶hH语WBill视旧超盘那IEme：a,G甯再氏HRM㈱孵限旧副国公物BM3Hg8H2.1NX3CFLEBFF； M3。 FEFE间CE；CHIEFWHCONFIGURATION1DF1-Throughfocusspotdiagramfortheghostimagecreatedbytheretro-reflectionatthewaveplatesurfacesdh>t'qhxtG.M9B7&dh>t'qhxtG.M9B7&5000Q00THICKNESSINMILLIMETERSONSURFACE92THROUGHFOCUSRMSSPOTRADIUSRELATIVETDCHIEFRflYGHDSTREFLECTIONOFFSURFACEHBTHENH2.THURPR2B2005GI0H日。IN.ZMXCONFIGURATION1DF1

-ThroughfocusRMSspotradiusforthecentralfieldIfweassumeanair/sapphire(withoutanyA/Rcoating)interfacetransmissionof74.13%,wewillhaveaghost/imageintensityratioof:——i="0.7413)2=6.69x10-2=6.69%Ifweassumeatransmissionof82.8%at450pmand94.7%at850pmforthewholewaveplatewithA/Rcoating:TkImsi(450/z/n)=(1-Vo.828)2=8.1xl0-3=0.81%7；tos,(850Aw)=(l-V0^947)2=7.2xl0-4=0.07%Thisghostbeamwillalsosuffersomevignettingatthecoldstopthatwillreducetheintensity:0,000000.0H610FIELDINDEGREES0.09221Vltf^ETTINEQIRGRRM^87^543210SAC*aILJllluN0,000000.0H610FIELDINDEGREES0.09221Vltf^ETTINEQIRGRRM^87^543210SAC*aILJllluNuI>NnILDZOHHOaauGHOSTREFLECTIONOFFSURFACEHBTHENH2.THURPR2B2D05GMOM©0 2.NEXCONFICURATION1DF1-VignettingoftheghostbeamcomingfromthetwosurfacesofthewaveplateTheresultingghost/imageintensityratiowillbe:心。“四加0,=6.69x10".0.902=6.04x10"=6%Theintensityoftheghostcomingfromtheretro-reflectionbetweenthetwowaveplatesurfacesmightbereducedifaA/Rcoatingofsomesortisused.Thepolarizationstateoftheghostbeamcomparedwiththeimagebeamcanbedefinedasfollows:

Thehalfwaveplatecanbemodeledasa2x2matrix:Fl01HWP=B

0-1whereB2=TandTisthetransmissioncoefficientofthewholewaveplateincludinginternalabsorptionandA/Rcoatings.Ifthewaveplaterotatesaroundtheopticalaxiswiththeangle0:HWP\0)=R(-0)HWPl(0)HWPf{e}=Bcos(-e)-sin(-^)HWPf{e}=Bcos(-e)-sin(-^)sin(-^)Tl0-cos(-6)0-1cos(e)

一sin®)sin⑹ cos(26)sin(28)cos(6) sin(26)-cos(2^)Thepartofthebeamthatisretro-reflectedhasitsphaseoffsettedby180°ateachretro-reflectionatasapphire/airinterface.Theghostgoesthroughthree(3)timesthewaveplatethickness.Thefirstghosttrajectoryintothewaveplatecanbemodeledas:HWPr(0)=B2(1-B)2[HWPXff^Phaseshift^80。)1"卬尸'(一的[Phases帅Q8(F)I"WP®]sin(66)sinsin(66)sin（6。）-cos（66）cos(-ff) sin(-6)-101cos®)sin®)]--1o'-sin(-6)cos(-0}0-1J-sin(e)cos(^)J0-1cos⑻sin(^)T1oTcos(-e)sin(-ey「10--sin®)cos(^)J|_0-[-;in(-6)cos(-O)[o-1,cos(-^)sin(-6)I-cos®)sin(^)-sin(-^)cos(-0][o-1.[-sin®)cos(e)~HWP\0)=B2(\-B)2sin((sin((2+4〃“-cos((2+4〃)。)0cos((2+4〃W)

sin((2+4〃0Thebeamthengoesthroughtheanalyzer.Thispolarizercanbedefinedasarealpolarizer(notperfect),anditexhibitsanextinctionratioofapproximately100.Theparametersforthepolarizerare:PowerTransmissionReference:SCUBA-2PolarimeterPolarizerSpecificationsSC2/POL/SRE/007Version1.0,November182004.:EReference:SCUBA-2PolarimeterPolarizerSpecificationsSC2/POL/SRE/007Version1.0,November182004.EFieldparalleltowires:0.01Anon-idealpolarizercanberepresentedby:1 「〃0] I I—— 1 1P=/ wherea=J0.95,b=V0.01andA=/ =/yla2+b2L°b\ yla2+b2Vo^6

andtheresultingpolarizationstateis:-t-J1rJ2_yla2-\-b2£（1-犷n=0qcos（（2+4〃）6）asin（（2+4〃W）[Z?sin（（2+4〃⑼-/?cos（（2+4〃⑼J-，一fA.B2y[a2+b2M=0tz（cos（（2+4〃.）J[+sin（（2+4〃⑼JJ/?（sin（（2+ -cos（（2+4〃W），2）*Therefore,theresultingmatrixafterthewholepolarimeterinoperationmodeis:"⑹…恪""0cos（（2+4Therefore,theresultingmatrixafterthewholepolarimeterinoperationmodeis:"⑹…恪""0cos（（2+4〃⑼/J[sin（（2+4〃W）sin（（2+4〃⑼-cos（（2+4〃W）M⑻£（1-Bp7+b~1”=o4cos（（2+4〃⑼

/?sin（（2+4〃）6）asin（（2+4〃H）-bcos（（2+4〃⑼Thecorrespondingintensityis:cos（（2+4/z?）^）cos（（2+4/7）0）（a~JX*4+/?2J2*J2）,上_ （…）+sin（（2+4W^）sin（（2+4nrt^2*-/2 *J,）-a2+b2' +sin（（2+4w^）cos（（2+4n）^）（a2J2*-b2Jt*J2）<+cos（（2+4/n）^）sin（（2+4n）^）（a2Jl*J2-b2J2*/）Themainbeamintensitycorrespondstom=n=0.Whenmornisgreaterthan0,thatcorrespondstoaghostintensity.Ifweconsiderthefollowingparameters,foranimperfectpolarizerandawaveplatewithA/Rcoatings,thattransmits0.828oftheincidentdepolarizedbeamat450pm:Sumcoefficients: m：=0..10 n:=0..10Polarizertransmission: a:=0.95 b:=（）.（）]Polarizationstateinfrontofthepolarimeter: j:=1.0.B:=T0,5Transmissivityofhalfwaveplate: tB:=T0,5w