水肺-2旋光仪光学设计报告

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TechnicalReportOPTICALDESIGNOFTHESCUBA-2POLARIMETERSC2/POL/OPT/002Version0.3INO040193RN/ASubmittedto:Mr.PierreBastienDirector,ObservatoiredumontMeganticDepartementdephysique,UniversitedeMontrealB.P.6128,Succ.Centre-villeMontreal,(Quebec),CanadaH3C3J7Preparedby:MelanieLeclercPresentedby:MelanieLeclercResponsabledeprojetAuthorizedby:JonnyGauvinResponsabledeprogrammeconceptionoptiqueiINOJanuary14INO•2740,rueEinstein,Sainte-Foy(Quebec)CanadaG1P4S4

1TableofContent1Introduction12OpticaldesignofthepolarimeterwithZemax(DeliverableB1)12.1Opticaldesign12.2Preliminarystudytoevaluatethepossibilityofgettingtheopticalcomponentsnearerthecryostatwindow(DeliverableA3)32.3Footprintoftheunvignettedbeamatpolarimeteropticalsurfaces32.4Studyoftheeffectsofghostsinthepolarimeter(DeliverableB3)102.5Toleranceanalysis303Analysisoftheeffectofinstrumentalpolarizationonthepolarimeter(DeliverableB2)313.1Perfectpolarizerinacollimatedbeam313.2Realpolarizerinacollimatedbeam353.3Realwaveplateandrealmirrorsurfaceseffectonthepolarizationstate403.4RealpolarimeterwiththetelescopeandtheSCUBA-2camera423.5Impactofthepolarimeterontwoorthogonalpolarizationstates451IntroductionThestudyofpolarizedradiationistheprimarymeanofinvestigatingthegeometryofmagneticfieldswithinastronomicalsources.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.2OpticaldesignofthepolarimeterwithZemax(DeliverableB1)2.1OpticaldesignThenominalfileSC2_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)-128.6-128.595262-128.536090

2Field#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

3-078•10UNAcocSMS•5700X00821QlARCMINF工ELD\850MICRONS/\l——I!2000,0办/工l_L工METERSSC2_POL_OPT_00M.ZMX.CONFIGURATION：ALL3、、、Figure1-JCMTtelescopewithSCUBA-2camera,andpolarimeterlocation

4APERTUREDIAMETER：368.B802SCUBA27.MONF1PR25SURFACE39：8X7.8ARCMINFIELD.2D05RAYXMINRAYYMINPOLARISEURCALIBRATION-90,Q9H9RRYXMAX-133.2078RRYYMAXMICRONS79.L112L69.8938M5D,0D0<3SC2_POL_OPT_00H.ZMXCONFXCURATION1DF31.1Preliminarystudytoevaluatethepossibilityofgettingtheopticalcomponentsnearerthecryostatwindow(DeliverableA3)Theopticalcomponentswereplacedasnearthewindowaspossibleconsideringthemechanicalpartssizeandlocation.Wedidnotimplementanysystemwithatranslationstagealongthezaxis,togetthepolarimeteropticalcomponentsnearerthewindowintheoperationmode,duetovolumeconstraints.1.2FootprintoftheunvignettedbeamatpolarimeteropticalsurfacesToobtainthefootprintofthebeamatthelocationoftheopticalsurfacesofthepolarimetercomponentsanddeterminethecomponentsclearaperture,weconsideredafieldofviewof±0.09221°fortheJamesClerkMaxwellTelescope(JCMT).ThisfieldofviewisdefinedbytheZemaxfilefieldsasshowninTable1.XRAYSTHROUGH=96,99XFODTPRINTDIRGRRMFigure2-Footprintofthebeamatthecalibrationpolarizer

55aul.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.

6ClearApertureneededtoavoidVignettingDecenteredclearapertureneededtoavoidvignettingCalibrationpolarizer369mm*21.5mmdecenter,326mmdiameterHalfwaveplate289mm~18mmdecenter,253mmdiameterAnalyzerpolarizer251mm~18mmdecenter,215mmdiameterTable2-BeamgeometryatpolarimeteropticalsurfacesTheavailablevolumeforthepolarimeterconstraintthemaximumclearaperturethatitispossibletohaveforeachopticalcomponent.Manufacturingprocessesfortheopticalcomponentsthemselvesarealsotobeconsideredtosetamaximumapertureforeachopticalcomponent.Followingisthefootprintofthebeamforthefollowingdesignoption:1.Clearapertureof:ocalibrationpolarizer=300mm,ohalfwaveplate=270mm,oanalyzerpolarizer=200mm.Wealsoincludedatabledetailingthevignettingeffectforthefollowingtwooptions:2.Clearapertureofallopticalcomponents=200mm3.Clearapertureofallopticalcomponents=300mm3.1.1Footprintforthehalfwaveplatewithclearaperture=270mmandanalyzerclearaperture=200mm,inoperationmodeAPERTUREDIAMETER：270.D00DForthisoptionandmode,itistheanalyzerpolarizeraperturethatiscausingthevignettingofthebeam,asseenonFigure6.Ifpossible,theclearapertureofthispolarizercouldbeaugmentedto251mmandthehalfwaveplatediametercouldbeaugmentedto289mmtominimizethevignetting(seethebeamdiameterinTable2).%RAYSTHROUGH=9H,a5XFUDTPRINTDIRGRAM75232U-NNUIIIREMMD2FCRA-MRXYRBFUNRYYXCOUAARSMSPPM,8X7,8ARCMINFIELD.9SD2005MICRONSJMAUEPLATE=-65,9H56=-98.93H8=1LH,57B2RRYXMAX=RRYYMAX=WRVELENGTH=63.9B09L1H.29MSSC2_POL_OPT_00M,ZMXCONFXCURRTION2DF3Figure5-Firstapertureatthehalfwaveplate,inoperationmode

7APERTUREDIAMETER：200,000。/RAYSTHROUGH=9H.95XFOOTPRINTDIRGRAMSCU0A27.MONAPR25SURFACE62!RAYXMIN=RAYYMIN=MAXRRDIU3=8X7.8ARCMINFIELD.9S02B05POLARISEURFIXE-6H.9066RRYXMAX93.9759RRYYMAX.6558WRVELENGTH=MICRONS62.8H7299,5307H5D.0D0GSC2_POL_OPT_00M,ZMXCONFXCURATION2DF3Figure5-Vignettingofthebeamattheanalyzer,inoperationmode2.3.2Footprintforthecalibrationpolarizerwithclearaperture=300mm,halfwaveplatewithclearaperture=270mmandanalyzerclearaperture=200mm,incalibrationmodeInthecalibrationmode,theopticalelementcausingthevignettingisthecalibrationpolarizer,asseeninFigure7.However,acalibrationpolarizerof300mmdiameterandananalyzerpolarizerof200mmdiametercauseasimilarvignettingeffect.300mmseemstobethemaximumdiameterfortheopticalelementsifweconsiderthemanufacturingaspectofthosecomponents.

8salillulzHTlHW&日DsaGz:UJ」au5XRAYSTHROUGH=9H.6HXUNRYYXCOUAAASMSRRM759323NNUIIIREMMD2FCRARAXYR8X7.8ARCMINFIELD.2005POLARISEURCALIBRATION-80.1113RRYXMAX=-133.28BMRRYYMAX=1M8,3597WRVELENGTH=MICRONS79,1512IH2.2012SC2_POL_OPT.00M.ZMXCONFXCURATZON3DF3Figure7-Firstvignettingsurfaceatthecalibrationpolarizer,incalibrationmodeAPERTUREDIAMETER：300,0000FOOTPRINTDIRGRAMXRAYSTHROUGH=9H.6HXSCUBA27.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

9/RAYSTHROUGH=9H.6HXAPERTUREDIAMETER：200,000。FOOTPRINTDIRGRAMSCU0A27.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

109B7rsrnzISAk叱口归」LNDIANnLEJNEJILU京LOPERATIONMODE□RLIBRFITIONMDDE一□.000000.0^221PZELDINDEGREESUJGNETTINGDjnQPRMSCUBA2P.BXT.BFlRCMLNFIELD.050MICRONSMQNnPQ252(2)131SD2_FDL_OrT.ZMX□□NPIGURPTinN2OP2

11UZGNETTINGDZOGRRMFigure10-Vignettingplotforthetwomodes,fora300mm0calibrationpolarizer,270mm0halfwaveplateanda200mm0analyzerpolarizerqB7C]U1—0SAk此口旧1」皿NUIANnL口ZOMr^E^n-SCUBA2MQN口PCSX?.BRRCMLNFIELD.日50MICRONS2(21130SC2_FDL_QPT_D0r.ZNX□□NPiGuiTnTiDN幺argFigure11-Vignettingplotforthetwomodes,for200mm0components

12UJGNETTING口二口个口R)MSX7.0HRCMLNFIELD.BS0MICRONSQB76c-M32I0tn叱口LE3二口1匚京=|202PnnnUNCQSMSC2_尸Di__art_D0m，znxCDNPIGUROTIDN2QP2Figure11-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

13Themajorghostsimagesarecreatedbytheretro-reflectionbetweenthefollowingsurfaces:1.thetwopolarizersduringcalibration,2.thefrontsurfaceofthecamerawindowandthecalibrationpolarizer.3.thefrontandbacksurfacesofthehalfwaveplate,4.thefrontsurfaceofthecamerawindowandtheanalyzerpolarizer,5.thefrontsurfaceofthecamerawindowandthelastsurfaceofthehalfwaveplate,6.thefrontsurfaceofthecamerawindowandthefirstsurfaceofthehalfwaveplate,Ghostfocusfromretro-reflectionbetweenthetwopolarizersFigure13-Ghostimageproducedbytheretro-reflectionbetweenthetwopolarizersSurfaces52and39:FZ#=6.53RMSspotradiusonaxis=37.169mmDistancetoghostpupil=-297.8855mmDistancetoghostfocus=268.43mmEffectivefocallength=103806.1936mmInthecalibrationmode,aretro-reflectionwillbeproducedbetweenthetwopolarizerssurfaces.Theghostimageisdefocusedby250mmrelativetoimageplane.

14THICKNESSINMILLIMETERSDNSURFACE106THPQUGHFQCUE，RMSGPQTF旧口工USFELHTPJET。CHIEFPRYGHDSTREFLECTIONOFFSURFACE52THEN39.THURPR2B2005QI。日NQOQ.ZMXCONFIGURATION1DF1Figure14-Ghostimagecreatedbytheretro-reflectionbetweenthetwopolarizers,defocusedof250mminfrontoftheimageplaneThespotsizeofthisghostimageonthedetectorisalmostaslargeasthedetectoraperture:FCDTPP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%.

15IfweassumeahalfwaveplatewithoutanyA/Rcoating,theghost/imageratiowillbe:1.ifthepolarizationislinearandalignedwiththepolarizersaxis:&3,=(1—0.95)2(0.7413尸=7.55x107=0.08%oranerrorof0.08%overanimageintensityof(0.95)2(0.7413)2=0.4959oftheintensitymeasuredwithonlythetelescopeandthecamera.2.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:1.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.2.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.

16Thisghostbeamwillalsosufferimportantvignettingthatwillreducetheintensitybymorethanhalfatthecoldstop:0.0000Q0.011618FIELDINDEGREES0.09221VIGNETTINGOIRGRRMI.号87653-3210SACILolul»-luNDI>NnILDNDHluBallGHDSTREFLECTIONOFFSURFACE52THEN39,THURPR282D0S,NEXCONFIGURATION1DF1Figure16-Vignettingoftheghostbeamcomingfromthetwopolarizers2.4.1Ghostfocusfromretro-reflectionbetweenthefirstsurfaceofthewindowandthecalibrationpolarizerSurfaces57and39:F/#=5.787207Figure17-Ghostimageproducedbytheretro-reflectionbetweenthefirstsurfaceofthewindowandthecalibrationpolarizerRMSspotradiusonaxis=59.994mmDistancetoghostpupil=-359.8403mmDistancetoghostfocus=-3253.2155mmEffectivefocallength=-17314.0353mmIfweassumeahalfwaveplatewithoutanyA/Rcoating,theghost/imageintensityratiowillbe:1.ifthepolarizationislinearandalignedwiththecalibrationpolarizeraxis:,6。“=(1-0.9568)(1—0.95)(0.95)2

17(0.7413/=5.89x1。T=0.06%oranerrorof0.06%overanimageintensityof0.4959oftheintensitymeasuredwithonlythetelescopeandthecamera.1.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:1.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.2.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.

180UA工'qmxx-I"IIJAHM・nu(Lz(I:s•工MioM-6.00DE+-D02-3.0D0E*D02D,000E*D0QTHICKNESSINMILLIMETERSONSURFACE116THROUGHFOCUSPMSSPOTER□工USEELRTIVE丁口CHIEFERYGHDSTREFLECTIONOFFSURFACE57THEN39.FRIAPR292B05GI0日7000.NMXCONFICURRTION1OF1Figure18-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,NMXCONFZCURATION1DF1Figure19-Ghostcentralfieldfootprintattheimageplane

19Thevignettingoftheghostbeamatthecoldstopisimportant.Only27.4%ofthebeamintensitygetsthroughtothedetector:0.0QD0Q0.0H61QFIELDINDEGREES0.0922LVIGNETTINGDIAGPRM9£*QUJllUJNuI>NnULDZOHHOSUGHOSTREFLECTIONOFFSURFACE57THEN39.FRIRPR292005GI0曰70。夕,NN1XCONFICURRTION1DF1Figure18-Ghostvignetting2.4.2Ghostfocusfromretro-reflectionbetweenthetwosurfacesofthehalfwaveplateAghostimageiscreatedbytheretro-reflectionatthetwosurfacesofthehalfwaveplate.Thisghostimageisdefocused2mmrelativetotheimageplane.Thespotsizeofthisghostimageattheimageplaneistwotothree

20timeslargerthanthatoftherealimage.

21IllIHI11SeeenlargedpicturebelowHalfwaveplateSurfaces48and42:RMSspotraduisonaxis=0.26825mmtoghostpupil=-19~dancetoqhostfocus=617.2989mmEffeXSlength=110419.0969mmFigure21褊-nbetweenthetwospaces“thehaKwave语(040193)

22fl.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-2000a200BH0G0SURFACETMA：IMADETHROUGHFOCUSSPOTDIAGRAMGHDSTREFLECTIONOFFSURFACEHBTHENH2.THUAPRZB2005UNITSRREJQ.FBnti】】qi，？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；CHIEFWHCONFIGURATION1DF1Figure22-Throughfocusspotdiagramfortheghostimagecreatedbytheretro-reflectionatthewaveplatesurfacesdh>t'qhxtG.M9B7&5000Q00THICKNESSINMILLIMETERSONSURFACE92THROUGHFOCUSRMSSPOTRADIUSRELATIVETDCHIEFRflYGHDSTREFLECTIONOFFSURFACEHBTHENH2.THURPR2B2005GI0H日。IN.ZMXCONFIGURATION1DF1

23Figure22-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*aILJllluNuI>NnILDZOHHOaauGHOSTREFLECTIONOFFSURFACEHBTHENH2.THURPR2B2D05GMOM©02.NEXCONFICURATION1DF1Figure23-VignettingoftheghostbeamcomingfromthetwosurfacesofthewaveplateTheresultingghost/imageintensityratiowillbe:心。“四加0,=6.69x10".0.902=6.04x10"=6%Theintensityoftheghostcomingfromtheretro-reflectionbetweenthetwowaveplatesurfacesmightbereducedifaA/Rcoatingofsomesortisused.Thepolarizationstateoftheghostbeamcomparedwiththeimagebeamcanbedefinedasfollows:

24Thehalfwaveplatecanbemodeledasa2x2matrix:Fl01HWP=B0-1whereB2=TandTisthetransmissioncoefficientofthewholewaveplateincludinginternalabsorptionandA/Rcoatings.Ifthewaveplaterotatesaroundtheopticalaxiswiththeangle0:HWP\0)=R(-0)HWPl(0)HWPf{e}=Bcos(-e)-sin(-^)sin(-^)Tl0-cos(-6)0-1cos(e)一sin®)sin⑹cos(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)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((2+4〃“-cos((2+4〃)。)Ifwetakeintoaccountthemultipleretro-reflectionsbetweenthetwosurfacesofthewaveplate,weobtainthesum:〃二0cos((2+4〃W)sin((2+4〃W)Thebeamthengoesthroughtheanalyzer.Thispolarizercanbedefinedasarealpolarizer(notperfect),anditexhibitsanextinctionratioofapproximately100.Theparametersforthepolarizerare:PowerTransmissionReference:SCUBA-2PolarimeterPolarizerSpecificationsSC2/POL/SRE/007Version1.0,November182004.:EFieldperpendiculartowires:>0.95EFieldparalleltowires:0.01Anon-idealpolarizercanberepresentedby:1「〃0]II——11P=/wherea=J0.95,b=V0.01andA=/=/yla2+b2L°b\yla2+b2Vo^6

25andtheresultingpolarizationstateis:-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+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..10n:=0..10Polarizertransmission:a:=0.95b:=（）.（）]Polarizationstateinfrontofthepolarimeter:j:=1.0.B:=T0,5Transmissivityofhalfwaveplate:t:=0.82^5

26weobtainthefollowingtotalintensity:andtheghostspartifthetotalintensityis:

27Ifwehavearighthandedcircularpolarizationstatebeforethepolarimeter,thesameanalysiscanbeperformed.Thetotalintensityis:Thepercentageoferrorinducedbyghostsis:0e2-nTheghostintensitymaximumscorrespondstotheprincipalbeamintensityminimums,andtheerroristhereforemoreimportantinthatcase.TheperformanceoftheA/Rcoatingusedonthewaveplatehasadirecteffectontheghostintensity.Ifweconsideratransmissionof0.947at850pminsteadofatransmissionof0.828at450pm,themaximumpercentageoferrorinducedbyghostsasinthefigureabovedropsfromapproximately3.5%toabout0.025%.

282.4.3Ghostfocusfromretro-reflectionbetweenthefirstsurfaceofthewindowandtheanalyzerpolarizerSurfaces57and52:F/#=6.269735RMSspotradiusonaxis=22.061mmDistancetoghostpupil=-89.0308mmDistancetoghostfocus=-3144.8305mmEffectivefocallength=-18116.7539mmFigure25-Ghostimageproducedbytheretro-reflectionbetweenthefirstsurfaceofthewindowandtheanalyzerpolarizer-2.000E*D02-J.000E*D02D.0D0E+-D00THICKNESSINMILLIMETERSDNSURFACE90THROUGHFOCUSRMSSPOTRADIUSRELRTIUETDCHIEFRRVGHDSTREFLECTIONOFFSURFACE57THEN52.FRIAPR292B05GI0日7。日2.ZMXCONFICURATION1DF1Figure26-ThroughfocusRMSspotradiusforthecentralfieldIfweassumeanair/HDPE_300interfacetransmissionof95.68%andapolarizertransmission>95%,wewillhaveaghost/imageintensityratioof:

29Tghost=(1-0.9568)(1-0.95)=2.I6X10-3=0.22%Theghostimageisdefocusedof150mmrelativetotherealimage.Thespotdiameteris70mmattheimageplane.Thevignettingoftheghostbeamatthecoldstopisimportant.0.00D000.0H6100.0922LVIGNETTINGDIRGRRM弓8765X3210SAUMQlu»-lluNuH>NnLDZOHHOaauGHDSTREFLECTIONOFFSURFACE57THEN52.FRIRPR292D05GI0日7■。日2.ZMXCONFXCURRTION1DF1Figure26-VignettingoftheghostbeamcomingfromthewindowandanalyzerTheresultingghost/imageintensityratiowillbe:Toh..t.=2.16x10-3•0.601=1.30x10-3=0.13%

302.4.4Ghostfocusfromretro-reflectionbetweenthefirstsurfaceofthewindowandthelastsurfaceofthehalfwaveplateSurfaces57and48:F/#=6.089175RMSspotradiusonaxis=32.754mmDistancetoghostpupil=-167.9461mmDistancetoghostfocus=-3182.5819mmEffectivefocallength=-17875.1293mmFigure28-Ghostimageproducedbytheretro-reflectionbetweenthefirstsurfaceofthewindowandthelastsurfaceofthehalfwaveplateWewillhaveaghost/imageintensityratioof:Tghos,=(1-0.9568)(1-0.7413)(0.95)2=l.OlxlO_2=1.01%-3.00DE*D02-j.5D0E*0020,0D0E*-D00THICKNESSINMILLIMETERSDNSURFACE98Theghostimageisdefocusedof220mmrelativetotherealimage.Thespotdiameteris105mmattheimageplane.THROUGHFOCUSRMSSPOTRADIUSRELATIVETDCHIEFRAYGHOSTREFLECTIONOFFSURFACE57THENHQ.FRIRPR2D05GI0曰J曰.NEXCONFXCURATION1DF1Figure29-Ghostimagedefocus

310.000000.0H610FIELDINDEGREES0.0922L1.,'IC.NETTINGDIRGRRM987653-3210SAC*oluFl-iuNuH>NnILDZDHlQBaULGHDSTREFLECTIONOFFSURFACE57THEN43.FRIRPR292B05GI0曰TC3T曰.NMXCONFXCURRTION1DF1Figure29-GhostvignettingTheresultingghost/imageintensityratiowillbe:Tghosl=1.01xl0-2-0.463=4.68x10-3=0.47%2.4.5Ghostfocusfromretro-reflectionbetweenthefirstsurfaceofthewindowandthefirstsurfaceofthehalfwaveplateSurfaces57and42:F/#=6.064942RMSspotradiusonaxis=33.113mmDistancetoghostpupil=-170.6000mmFigure31-Ghostimageproducedbytheretro-reflectionbetweenthefirstsurfaceofthewindowandthefirstsurfaceofthehalfwaveplateDistancetoghostfocus=-3183.6187mmEffectivefocallength=-17867.3064mm

32Wewillhaveaghost/imageintensityratioof:TghoS,=(1-0.9568)(1-0.7413)(0.95)2(0.7413)2=5.54x10"=0.55%Theghostimageisdefocusedof221mmrelativetotherealimage.Thespotdiameteris106mmattheimageplane.THROUGHFOCUSRMSSPOTRADIUSRELRT工呼TDCHIEFRRYGHDSTREFLECTIONOFFSURFACE57THENH2.FRIRPR292B050.000000.04610FIELDINDEGREES0.0922LFigure32-Ghostimagedefocus弓8765X3210SAC*oUJllUJNuI>NnLDZOHFOaau'.71ENETTINEDIAGPRMGHDSTREFLECTIONOFFSURFACE57THENH2-FRIRPR292B05GI0曰7Q.NMXCONFICURATJON1DP1Figure33-GhostvignettingTheresultingghost/imageintensityratiowillbe:兀.=5.54x10-3•0.479=2.65x10-3=0.27%2.5ToleranceanalysisThefollowingtoleranceswereincludedinthetolerancedataeditor,andthefileSC2_POL_OPT_006tolerancing.ZMXwascreated.Rayaimingwasswitchedon.Foreachofthetwopolarizers,andforthehalfwaveplate:

33Defocus:±0.1mmDecenterX:±0.1mmDecenterY:±0.1mmTiltX:±0.4°TiltY:±0.4°AMonte-Carloanalysisover20trialsconsideringthetolerancesaboveshowsanincreaseofRMSspotradiusof0.15pmasaworstcase,thenominalRMSspotradiusbeing11411m.Thetolerancewiththemajoreffectonthespotsizeisthehalfwaveplatetilt.Asensitivityanalysisshowsthattheimageofastarinthecenterofthefieldwillmoveby20pmfromitsnominalpositionontheimageplane,withatiltofthewaveplateof0.4°.

343Analysisoftheeffectofinstrumentalpolarizationonthepolarimeter(DeliverableB2)Thepolarimeteriscomposedofarotatinghalfwaveplatefollowedbyapolarizerservingasananalyzer.Forcalibrationpurposes,asecondpolarizercanbeplacedinfrontofthehalfwaveplate.3.1PerfectpolarizerinacollimatedbeamIfweuseJonesmatricestosimulatetheopticalcomponentsofthepolarimeter,wethendefine:ri0-Thepolarizeras:P=Equation1Thehalfwaveplateas:HWP=100-1Equation2AnelementMrotatedbytheangle0aroundthezaxis:M'=/?(—8)MR⑼rcose)sin0)where:R=,、,、一sin®)cos®)Equation3wecanthendemonstratethatarotatedpolarizedcanberepresentedby:1000p,_cos2(^)cos®)sin®)cos(-8)sin(-e)-sin(-^)cos(-6)IFcos(8)sin®)J[-sin(6)cose)cose)sin(8)sinEquation4andthatarotatedhalfwaveplatecanberepresentedby:HWPf=/?(-=cos(-6)sin(-^)T10Tcos(^)sin®)-sin(-^)cos(-0]0-1-sin®)cos®)Equation5cos(2e)sin(xsin(26)-cosiWeassumethatthetwopolarizershavethesameattenuationcoefficientA,andthatthehalfwaveplatehaveanattenuationcoefficientB.Thosecoefficientsrepresentthebulkabsorptioninthematerial.Wesupposealsothattheanalyzerpolarizerhasitsopticalaxisrotatedaroundtheopticalaxis(z-axis)byananglearelativetoamechanicalreference,andthatthecalibrationpolarizeraxisisrotatedbyanangleY,relativetothesamemechanicalreference.ThehalfwaveplatehasitsaxisrotatedbyanangleBrelativetothemechanicalreference.3.1.1CalibrationmodeM=A2BR(-a)PR(a)R(-6)R(-0)HWPR⑻力PR(力M=A2Bcos2acosasinacos(-0)sin(-^)Tcos(2yff)cosasinasin2a-sin(-0)cos(-利|[sin(23)MA2Bcos2acosasina「cos(2夕+20)sin(2/?+23)1cosasinasin2asin(24+26)-cos(2/?+26)Jsin(2/7)Tcos®)sin®)cos2ycos/siny一cos(2⑶」[一sin®)cos®)cosysinysin2ycos2ycosysinycosysinysin2yM=A2Bcos(a+y-2；S-26>1义乂/JEquation6|_sin(a)cos(y)sin(a)cos(7)Jwherea,petyareconstants.

35Theremainingintensityafterthepolarimeterincalibrationmodeis:j,「/J)/八Jcos(aXcos(r)J.+sin(y)/^)where*,=M=A~8cos(a+/-24一26),v(x(\Equation7j|_J2J]sin(a)(cos(y)4+sin(以/?)_andwecanconcludethat:I=A4B2cos2(a+y-2/一2^)(cos2%J,+sin2+cosysin八J；J?+J,))Equation8WecanverifythatthemodelinZemaxisvalidwithasimplecase,wheretheinputbeamislinearlypolarized(Ji=1,J2=0),andwhereA=B=1anda=P=Y=0.Themeasuredintensityshouldbeequalto/=cos2(20)andweeffectivelyobtainthisresultwithZemax:□OLIBPOTZDNMODE,~~LJNCOCPQLOCISBTIQN07THEINPUTFOLnf^TMT尺£S.ZHXCONPIGUGRTIDN1□匚1thatisacircularlypolarizedinputbeam(Ji=1/V2,J2=i/V2),andFigure34-Polarimeterincalibrationmode,linearlypolarizedinputbeamWealsotriedanothersimplecase,whereA=B=1anda=p=Y=O.Themeasuredintensityshouldbeequalto/=ycos2(2^)andweeffectivelyobtainthisresultwithZemaxfor0=[O,9O]degrees.

36aCLtJdzQINHW山doiicellje0J日日PPPPiMETGRJDNSLIOPRC-E5tOLLQpnTiQN-oiRCULnpPOLn^isnrroiT^itTieinpui000000000MEORPRJ20缶JFQLHRIMTRESIMPLE.ZMXCDNCIGUPPTinN1CJ匚1Figure34-Polarimeterincalibrationmode,circularlypolarizedinputbeamWetriedthecasewhereoneoftheopticalelementsaxispresentsanoffsetrelativetotheotherelements.Wetiltedthecalibrationpolarizerby5degreesalongtheopticalaxis.TheintensityresultssimulatedbyZemaxmeettheanalyticintensityequationandthecurvesfromZemaxareperfectlysuperimposedontheanalyticalcurves.Alsuau-p号Esuall1.6666666666Polarimeterincalibrationmode(circularlypolarizedinputbeam)halfwaveplaterotationangle(deg)calibrationpolarizerOdeg(Zemax)1/2*cosA2(2*theta)calibrationpolarizer5degtiltz(Zemax)1/2*cosA2(5deg-2*theta)Figure35-ComparisonofanalyticequationsandZemaxsimulationfortiltedelements3.1.2OperationmodeInthesamewaywederivedthematrixrepresentingthepolarimeterinthecalibrationmode,wecanderivethematrixrepresentingitintheoperationmode,wherethecalibrationpolarizerisnotpresent.Inthatmode,thebeamgoesthroughtherotatinghalfwaveplateandthroughtheanalyzerpolarizer.

37ThepolarimeterisrepresentedbythematrixMasfollows:M=ABR(-a)PR(a)R(-e)R(-0)HWPR⑻R(6)M_abc°s2acosasincos(-8)sin(-^)Jcos(2；S)sin(2yff)Tcos(^)sine)]cosasinasin2aj|_-sin(-0)cos(-8)Jsin(2夕)-cos(2夕)]-sin®)cos(^)J■,…cos2acosasinaTcos(2夕+20)sin(2夕+29)1M=AB、/八、/-\cosasinasin，a」[sin(26+26)-co$(2力+28)ifwesubstitute(20+26)by(p:cos(a)cos(a-(p)sin(a)cos(a-(/))—cos(a)sin(a-(p)-sin(a)cos(a-cp)Equation9whereaandpareconstants.Theremainingintensityafterthepolarimeterincalibrationmodeis:wherecos(a)cos(6r-(p)J।_cos(6r)sin(6r-(p)J2sin(a)cos(a-(p)J}-sin(a)sin(a-(p)J2Equation10andwecanconcludethat:/=A2BPJKIM尺STfTE0MnCOFAPfCflllDN/fixCDNCIGUPHTIDNJQP1\co^(a-(p)JJy+sin2(a-^)/2*J2--sin(2(a-^))(j,*j2+Equation11WecanverifythatthemodelinZemaxisvalidwiththesametwosimplecasesasinthecalibrationmode.Ifa=p=v=0andA=B=1,themeasuredintensityisequaltoI=cos2(-97)=cos2(2^)withalinearlypolarizedinputbeam:QLLCL□DERaT匚ONMODE」l■匚N匚口RL"PGLARIZZ匚口INPUTREAMFigure37-Idealpolarimeterinoperationmode,linearlypolarizedinputbeam,1Themeasuredintensityisequalto/=—withacircularlypolarizedinputbeam:2

38i0.90.70.50.3日：2Q10Q0b]B0(>qDttM£T£Q£ONSUP匚口C匚二。口匚口口THONMACi匚，C工RCLJLatJLV口口一口住工2匚口UNCUT口匚DMf=QJ=RIM旺SITRfnDOEOP£Rfll]DN.ZHXCDNCIGUQOTTON10二1Figure37-Idealpolarimeterinoperationmode,circularlypolarizedinputbeam3.2RealpolarizerinacollimatedbeamTherealpolarizerisnotperfectandexhibitsanextinctionratioofapproximately100.Theparametersforthepolarizerare:PowerTransmissionReference:SCUBA-2PolarimeterPolarizerSpecificationsSC2/POL/SRE/007Version1.0,November182004.:EFieldperpendiculartowires:>0.95EFieldparalleltowires:0.01Anon-idealpolarizercanberepresentedby:,-wherea=J0.95,b=Jo.01andA=.-=/yla2+b2L°牙^a2+b2V0^6Equation12andthesamepolarizerrotatedbyanangle0canberepresentedby:=sin(-6)]1「a0][cos®)sin®)-sin(-6)cos(-H)J.2+/o/?J[sin(^)cos®)

39〃=，acos"e）+bsin2⑻（a-/?）sin（28）（a-b）sin（20）asin2（0）+bcos2（0）3.2.1CalibrationmodeWesupposethatthehalfwaveplateisrepresentedby:「1o]HWP=B0-1Thewholepolarimeterinthecalibrationmodecanberepresentedby:M=0）HWPR⑻R⑼PB42cos（24一26）ahsin（2/?-2^）M-a2+b-["sin（2/?-26）-b2cos（2/一2。）Equation13Equation14B2毋，*4+b4J2*J2）cos2（2^-2^）+a2b2（j/jI+J2*J2）sin2（2/J-2^）landI=—<../~>（a2+b2）[+（a3。一加筋*（+J2*/Jcos（2p-26）sin（2（3-20）Equation15Iftheinputbeamislinearlypolarized:d2I=-7—^■匕4COS2（2〃—26）+/b2sin2（2/—2。）｝Equation16\a2+b2）§22.（〃2+川2｛（/+//）cos2（24一26）+2〃方sin2（24一2。）｝Equation17Iftheinputbeamiscircularlypolarized:IfB=1,a=a/0.95,b=VO.OI,theresultsobtainedbyZemaxmeettheanalyticalsolution:

40ndEId7口NHW山d口Ndl-lluNnu.LI(yUJ£«ZJ]日日3t>0pqoqMCTCGCONSLU3匚口C匚J0CnLlQQQFIONMODE.LlNC^PLYPDLnOIZCDINDUTQCRN利用小litRiecranisaiR⑶中门0皿「军用狂，值CDNPIGUPOTI0N1。二1Figure39-Realpolarimeterincalibrationmode,linearlypolarizedinputbeam££ZUNHd出口NDSNnu-二弟5Z电]b0ac>BPPRAMCTEP5ONSURPRCE弓9B?h5MI321B0B233332C'QLJSQflFEEJNMODEuCL«CULqPLVPQlPOIZ^OINPUTTUEPPQL22GJ砥nifRmit砥FdfS&ajR（Limnoinurfrwin.zncCaNPIDUGOTIDN」（□匚JFigure40-Realpolarimeterincalibrationmode,circularlypolarizedinputbeamIftheanalyseraxishasanoffsetofaandthecalibrationpolarizeraxishasanoffsetof丫relativetoareferencemechanicalaxis:M=R（-a）PR（a）R（-0）R（-B）HWPR（B）R（O}R{-y）PR⑺

41;y）+"sinQco《a+力;/+a加in°sin（a+y）cos/。？cosacos/-/?2sinasiny）—aZ?sin［sin（a+y）cos^（a2cosasiny-/?2sinacos;a2+h2cos^t72sinacosy+Z72cosasiny）+absin/co（a+y）cos^（tz2sinasiny-/72cosacos;wheiw=（0-a-y）and0=（2夕一明andB2cos2^（（a4cos2y+Z?4sin2八J；J、+（《""sin?cos24-+sin2（pa2b2\J^Jl+J2*A）+cossin^（cos（2/）（6z3Z?-ah^j'J2+J2\/1）-sin（2y）（6zyb-airJ2-））（a4-/?4）cosysin/（j,J,+J2*J2））Equation18Equation193.2.2OperationmodeThewholepolarimeterintheoperationmodecanberepresentedby:M=PR（—8）R（-0）HWPR（夕）R®）B「qcos（2夕一2。）asin（2/-2。）Equation20二——y/a2+b2bsin（2/?-28）-bcos（2夕-2。）andi_B2［（a2cos2（24一28）+/sin2（2/—28））j；j1+（a2cos2（24一2夕）+小足2（2"-（。-+62）［+6-/?2）cos（2夕一28）sin（2〃一2^）（J,*J2+j/jJEquation21B2Iftheinputbeamislinearlypolarized:｛/cos（2'-2e）（cos（2,-2e）+sin（2'-2^））+b2sin2（2/7-23）｛sin（2/3-20）-cos（2/5-2^））｝Equation22

42IfB=1,a=a/0.95,b=<0.01,theresultsobtainedbyZemaxmeettheanalyticalsolution:1B0PORAMETERJUNSURPOCGJae>0]B013b口PHRAMEZTCPJUNSUQI-PCCSq口7-tbL0rm2n000000000B□P£OPTIONMOOR.LENEPPL\DaLPOLZEDINPUTQCPMTWU口DDLU2(2)BGFLiRmwmKrtiRsajRtuuinBikinprmai.iiKCQNFIGURnTIDN1QP1Figure41-Realpolarimeterinoperationmode,linearlypolarizedinputbeamIftheinputbeamiscircularlypolarized:Equation23QPERaTIQNMODE,CIPrCULOGLYPOLPPIZCQINPUTQ£ONmum>QLU2QQ5rilRmKfilRFlIRRMR隙ill门以N>rHJffldt.ZlKCaNPIGUPPTION3QI-1Figure42-Realpolarimeterincalibrationmode,circularlypolarizedinputbeam

43Iftheanalyseraxishasanoffsetofarelativetoareferencemechanicalaxis:M=M—a)PR(a)R(—e)R(—0)HWPRR(。)BcoM〃co/a+bsin。a)+sin幽-b)cosasinasin^cos2a+fesin2a)-cos^(t7-fe)cosasinaa2+/?2sin^(tzsin2a+bcos?a)+cos^(tz-h)cosasina-cos^(asin2a+bco^a)+sin0(a-/?)cos6rsinawherW=(2/一羽Equation24and/=叱(a2+b2)2Q2cos2(a-0)+〃2sinYa-。)}/[J】+(tz2sin2(a-0)+Z?2cos2(a-^)1/2.72-(a2-b2)cos(a-0)sin(a-0)(J)*J2+(/)Equation253.3RealwaveplateandrealmirrorsurfaceseffectonthepolarizationstateAt0°incidentangle,relativeamplitudeofthereflectedlight,asaproportionoftheincidentlight,isgivenby:(1-pY/R=wherep=—wheren^landn2=3.07.11+pJn2Thevalueforn2istherefractiveindexofsapphireat300Kand580pm(or517.5GHz).ThisvaluecomesfromalistorpublishedvaluesandwasprovidedbyUniversitedeMontreal.Fromtherefractiveindex,wecanderivethereflectanceR=25.87%andthetransmittanceT=1-R=74.13%foranuncoatedinterfaceair/sapphire.ThosevalueswillbeupdatedifmoreaccuratedataontherefractiveindexandthenatureoftheA/Rcoatingofthehalfwaveplatematerialbecomesavailable.TRANSMISSIONUS.RNGLEWEDAPRJ32005THERE13NOCOATINGONSURFACE9INCIDENTMEDIA：RIRSUBSTRATE:SAPPHIRE_O_300KWAVELENGTH：H50,0000MKKUaanDlRIinRDlMUaCONFZCURPTION1DF1Figure43-Transmissionattheinterfaceair-sapphireatdifferentincidenceanglesThecurvesabovearethetransmissionfortheSandPpolarizationstates,andAistheaveragetransmissionofbothpolarizationstates.

44TRHNSM工SS工CJNUS.RNGLEWEDAPR132005THERE13NOCOATINGONSURFACE号INCIDENTMEDIA：SAPPHIRE_O_300KSUBSTRATE：RIRWAVELENGTH：H50,0000MKKlimanDlRIinRDlMUaCONFZCURPTION1DF1Figure43-Transmissionattheinterfacesapphire-airatdifferentincidenceanglesCardiffUniversityprovidedtransmissioncoefficientsforthewholewaveplateincludingA/Rcoatings.T=0.828atawavelengthof450pmand0.947at850pm.WehavenotincludedthisdataintheZemaxfilesinceanewmaterialwillbeusedforthewaveplate.Thefilewillbeupdatedwiththenewmaterialdatawhenitbecomesavailable.ThereflectanceofthemirrorsintheZemaxfileis94.60%at0°incidentangleandvarieswiththeincidentangleasinFigure45below.Thiscurvedoesnotrepresentthereality.REFLECTIONUS.ANGLEUEDAPR132D05THEREISNOCOATINGONSURFACE3INCIDENTMEDIA:RIRSUBSTRATE：MIRRORWAVELENGTH：H50.B00BSC2_POL_OPT_004.ZMXCONF工CURATHOZ1DF13Figure44-Reflectionatumirror,,surfacevs.angleofincidence

45REFLECT工ONVS.ANGLEUEDMRYH2005COATINGJCMTONSURFACE75INCIDENTMEDIA:MIRRORSUBSTRATE:MIRRORWAVELENGTH：H50,B00B0.994778000.102062AdditionaldatarelativetothetelescopemirrorsreflectioncoefficientwasaddedintheZemaxcoatingcatalogtorepresentmoreaccuratelytheJCMTmirrors.Thereflectancethenbecomes99.24%,andthereflectivitydifferencebetweentheSandPpolarizationisonlyof0.54%atanincidenceangleof450.SC2_POL_OPT_00M.ZMXCONFIGURATION1DF3Figure43-ReflectionatJCMTmirrorsurfacevs.angleofincidenceTheJCMTmirrorsareAl-Alloy6061-T651,andtheconstantsnandk(providedbyUKATC)are103and208respectively,at32micronswavelength.Thiswasextrapolatedto450and850micronswavelengthtogivethereflectivityshowninFigure46.Toobtainthatresult,thefollowinginformationwasaddedtotheZemaxcoatingcatalog:MATEJCMTcoating450103-208517.5103-208850103-208COATJCMTJCMTcoating0.043.4RealpolarimeterwiththetelescopeandtheSCUBA-2cameraTheparametersusedinZemaxtodefinethepolarizerare:Imperfectpolarizer:p=1「廊Vo^96[0asdefinedinpreviousparagraphs.Imperfecthalfwaveplate:Flol.HWP=50]whereB=T=0.7413isthetransmittanceforanuncoatedair/sapphireinterfaceThishalfwaveplatemodelwillbeupdatedwhenthenewmaterialrefractiveindexandA/Rcoatingdatabecomesavailable.

46LinearlyPolarized(alongtheX-axis)inputbeam:Thebeamintens计yinfrontofthepolarimeteris:EDOU町DZEULDNDIlDNnLII比iuza.miB0.50.136(30180PARAMETER5ONSURFACEH7SC2-POL_OPT_00H.ZMXCONFHCURATHOZ1DF3SDU-r口Na:区lu(L口NDHlDNnu.himwe0180360PARAMETER5ONSURFACEH79B7t5M32100QQ0a000SCUBA27.8X7.8ARCMINFIELD.850MICRONSWEDMRYM2005Afterthepolarimeterinoperationmode,thebeamintensityvarieswiththehalfwaveplaterotationangle:SCUBA27.8X7.8ARCMINFIELD,350MICRONSWEDMRYH20D5SC2_POL_OPT_00H.ZMXCONFIGURATION2DF3

47Atthedetector,theresultingintensityis,withtherotationifthehalfwaveplate:180360PARAMETER5ONSURFACE17SCUBA27.8X7.8ARCMINFIELD,950MICRONSWEDMRYM20D5SC2_POL_OPT_00M.ZMXCONFrCURRTION2DF3IftheinputbeamislinearlyPolarizedbutalongtheY-axis:Infrontofthepolarimeter,wehavethefollowingbeamintensity:ia.9a.B0.73.50.1PARAMETERSONSURFACEM7EDOUroZOHHDZDLlIuiuESC2-POL_OPT_00H.ZMXCOZFHCUMTHQZ2DF：3SCUBA27.8X7.8ARCMINFIELD.950MICRONSWEDMRYM2005

48Afterthepolarimeterinoperationmode,theintensityvarieswiththehalfwaveplaterotationangleasfollows:EDOU口NHMluL。NDHlDNnL1I比UJZ0180360PARAMETERSONSURFACE47SCUBA27.8X7.8ARCMINFIELD.3SDMICRONSWEDMRYH2005SC2_POL_OPT_00M.ZMXCONFICURRTJON2DF3Atthedetector,theresultingintensitybecomes:EDOUIDONy区luLDNDIluNnIL1IMWZSCUBA27.8X7.8ARCMINFIELD.950MICRONSWEDMRYM20D5SC2_POL_OPT_00M.ZMX8ZF工CURATHON2OF33.4ImpactofthepolarimeterontwoorthogonalpolarizationstatesFollowingisthepolarizationstateofthebeamatthedetector,overthepupil,forthecentralfield,fortwoorthogonalpolarizationstatesattheapertureofthetelescope.Wecomparedthetelescopeandcameraalone,andthewholeinstrumentwiththepolarimeterinoperationmode.3.4.1Telescopeandcamera

49INPUT:PDLHRIZRTIC1NPUPIISCUBR27.8X7,BARCMINFIELD.950MICROIFigure48-EffectoftheJCMTandSCUBA-2cameraaloneonabeamlinearlypolarizedat+45°relativetotheXaxis\lMPDLHRWT工ONPUPILMRPSCUBA27,8X7,BARCMINFIELD.950MICRONS-FRIMAY62005FIELDPQSJ0.0000.0,0000DECWAVELENGTH：H50.BOOBIX：1,00。TY：0.000PX：0.D0QPY：0,B00SC2_POL_OPT.00M.ZMXSURFACE7BTRANSMISSION；66,2MB0XCONFICURPTION1DF3Figure47-EffectoftheJCMTandSCUBA-2cameraaloneonabeamlinearlypolarizedalongtheXaxis(paralleltotheanalyzeraxis)FRIMRY62005\iFIELDPQSJ0,00呵0,BBO0DEC\IWAVELENGTH：H50,B00B\I

50IX：D.707TY：D,7D7PX：0.DBQPY：0,BO&SC2^SURFACE7BTRHNSM工S3工ON；65.I了今QK、c6n《

51IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIMIIIIIIIIinputiIIII!IIIIIIIIr-|IIIIMIIIIIIIIIIIIIIIIIIIII।NIIIIPOLARIZATIONPUPILMAPSCUBA27,8X7,BARCMINFIELD.950MICRONSFRIMRY6Z0B5FIELDPQSsB.QDDQ.0.0000DECWAVELENGTH：H50.0000IX：B.Q0DTY：1.ODOPX：0,B00PY：0,B00SURFACE7BTRANSMISSION；.1BB9XSC2_POL_OPT_00M.ZMXCONFICURPTION1DF3Figure49-EffectoftheJCMTandSCUBA-2cameraaloneonabeamlinearlypolarizedalongtheYaxis(perpendiculartotheanalyzeraxis)Ifwehaveanunpolarizedbeamatthetelescopeaperture,thebeamatthedetectorwillbe1.65%polarized.Ifwehavealinearpolarizationat+45°andamagnitudeof1atthetelescopeaperture,weobtainaslightlyellipticpolarizationstateatthedetector.ThephasebetweenExandEyis1.83°.Thosevaluesareforthecentralfield.ThepolarizationpupilmapanalysisofZemaxwasusedtoobtainthetelescopeandcameraMuellermatrix(averagedoverthepupil).WederivedtheMuellermatrixforeachfieldandpositioninthepupilknowingtheinputandoutputpolarizationstateofabeam.Anaveragedmatrixoverthepupilwasthenobtained.Field#1:(0,0)-0.6496280.010605-0.0000250.0000000.0106130.649609-0.000208-0.000003-0.0000220.0002080.6491930.020900().(X)0()01-0.000003-0.0206950.649203Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:1.65%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.83°Field#2:(0.0625,0.0625)-0.6324960.005989-0.0023660.000169'0.0()58850.6321540.0182130.002243-0.002582-0.0181740.631892—0.0174830.000075-0.0027560.0174240.632193Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:1.19%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.56°Field#3:(0.0652,-0.0652)

520.0076540.0011010.6312420.0227520.6318090.0122110.007665-O.OOO1350.0122350.631706-0.000808-0.003797-0.0003350.003759-0.0227530.631189Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:2.36%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:2.12°Field#4:(-0.0652,0.0652)■0.6323100.0060690.0059610.002704-O.(XX)()750.6319620.0175730.0027280.002480-0.0176100.6316980.017428-0.000172-0.002229-0.0174830.632006Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:1.21%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.61°Field#5:(-0,0652,-0.0652)-0.6319600.0124810.012437-0.0079130.0001320.631851-0.0004770.()03779-0.007878O.(X)O1760.6313860.0227750.000338-0.()03785-0.0227680.631331Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:2.42%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:2.02°Field#6:(0,0.0652)*0.6410380.0098780.000033-0.00000f0.0098760.641017-0.0000990.0000130.0000360.0001000.640688-0.0180080.000000-0.0000090.0180160.640700Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:1.55%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.61°Field#7:(0,-0.0652)'0.6396950.0154900.015486-0.0(X)032-0.0000010.639684-0.000158-0.000002-0.0000280.0001580.6390640.023436O.OOO(MX)-0.000003-0.0234350.639054Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:2.47%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:2.10°

53Field#8:(0.0652,0)■0.6401320.0070890.0070810.002694-O.(XX)O250.639993-0.008762-0.0033100.002810-0.0000740.()088870.0030260.639659-0.0200820.020()510.639740Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:1.34%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.81°Field#9:(-0.0652,0)-0.6403030.007132-0.0027430.0000710.007114-0.0()26340.0000240.6401640.0076050.003289-0.0077290.6398290.020062-0.003039-0.0200870.639911Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:1.35%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.78°3.5.2TelescopeandcamerawithpolarimeterinoperationmodeINPUT：FtLHRIZHTIQNPUPILHRFSCUBR27,8X7,BARCMINFIELD.9SDMICRONSFRIMRY62005fteldpas>B.aeena.0.0000decWRVELENGTH：450,01308IX：1.000TY：B.0B0PX：0,BB0PY：0.B00SC2_POL_OPT_00H.ZMXSURFACE7BTRHNSMTSSTON；36,0633“COZECUMTHOZ2OF3Figure50-Effectofthepolarimeterinoperationmodeonabeamlinearlypolarizedalongtheanalyzeraxis

54INPUTIPDLARIZRTIQNPUPILMAPSCUBA27,8X7,BARCMINFIELD.950MICRONSFRIMRY6Z005FIELDPQS：0.0000.0.BBQ0DECWAVELENGTH：H50.0000IX：B.Q0DTY：1,ODOPX：O.B00PY：0,B0QSURFACE7BTRANSMISSION；0,M669XSC2_POL_OPT_00M.ZMXCONFICURPTION2DF3Figure50-EffectofthepolarimeterinoperationmodeonabeamlinearlypolarizedperpendiculartotheanalyzeraxisThepolarizationpupilmapanalysisofZemaxcanbeusedtoobtainthetelescopeandcameraMuellermatrix(averagedoverthepupil).Asanexample,wederivedtheMuellermatrixforeachfieldandpositioninthepupilknowingtheinputandoutputpolarizationstateofabeam.ToderivetheMuellermatrix,weusedfourknownpolarizationstatesfortheinputbeam:outQout7EBFCGD'HQ.nwhere:Q“,11or1or10or10JKLMa.0010NPRsLkJ%000]andwhere:h=intensitytransmittedwithalinearlypolarized(horizontal)inputbeam;l2=intensitytransmittedwithalinearlypolarized(vertical)inputbeam;l3=intensitytransmittedwithalinearlypolarized(diagonal,+45°)inputbeam;l4=intensitytransmittedwithacircularlypolarized(right)inputbeam.AStokesvectorisdefinedas:[/QUV]=Lj+(Ev)22(纥X4)cosA夕2⑸⑸sinandwecanobtainEx,Ey,themagnitude〜andthephase△夕oftheoutputbeamforeachfieldandpupilposition,fromthepolarizationpupilmapanalysisfromZemax.

55ABCD~\'rA+B^therefore:e,q=—EJFKGLHMi0二E+FJ+K*._2（生乂々）sin△夕匚NPRS]0N+P_，一,但二+⑹；-~ABCD~'i-A-Band:%=阈；-⑹;28sm=EJFKGLHM01E-FJ-KM一_2闾1约）…也NPRS[o-N-P7J一伍,〉：+,,）；r7BCD~TA+C'and:23=6；飞工2〈七）3（纥）3cos=EJFKGLHM01E+GJ+L一匕一NPRS0N+R7J7BCD'ri--A+D'and:心6；弋\：EFGH0E+Hq2（⑷非，户s«4JKLM0J+M一匕一_2(£v)4(£v)4sinA^4_NPRS[l_-N+S_2l2但源但心魔如卜极邑弘玛小鹏如｝WecanthencomputealltheelementsoftheMuellermatrixoftheinstrument:

56*{2〈E)(4，cosA/}一{2(幻2(4)2cos△%}1\=2L=2(E，3(eJ38s△小々M=2(E)/E)48s3-JN={2{E)(E)sin八0杆匕低)9)sin4％}一1D_1〈E)DsinA^,)-也幻2(J)2sinA。』l-2R=2(Ex)3{Ey)^n^-NS=2Cm-NAnaveragedmatrixoverthepupilcanthenbeobtainedforeachfield,forthewholeinstrument(theJCMT+SCUBA-2camera+polarimeter)inoperationmode,andwiththehalfwaveplateat0°and45°.Withthehalfwaveplateat0°:Field#1:(0,0)-0.1820080.1773660.000040-0.00000f0.1771770.1794040.000036-0.000001-0.000024-0.(X)0017-0.0337280.0010750.0000000.000000-0.001169-0.036323_Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.99%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:3.68°Field#2:(0.0625,0.0625)-0.1779000.1704300.1705380.0270900.0000510.1688400.0325460.0002090.0305290.035337-0.026690-0.000963-0.000064-0.0001910.000883-0.035685Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.96%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:0.99°Field#3:(0.0652,-0.0652)0.1784630.1720500.025902-0.0002370.1720160.1716160.030885-0.0000560.0262590.031177-0.028699-0.(X)0076-0.0003040.001195-0.001345-0.035538Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.99%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.39°

57Field#4:(-0.0652,0.0652)■0.1778770.1704480.170469-0.027019-0.0000530.168809-0.032426-0.()00210-0.030284-0.035063-0.026681-0.0009620.0000620.()001880.000881-0.035679Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.96%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:-5.59°Field#5:(-0.0652,-0.0652)-0.1788720.1721650.172097-0.026189O.(X)()2280.171697-0.0311390.000047-0.026085-0.031043-0.028676-0.0013430.0000690.0002960.001196-0.035543Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:98.00%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:-2.85°Field#6:(0,0.0652)-0.1785960.1737690.173400-0.000330-0.0000020.175366-0.0003970.000002一0.00028()-0.000355-0.032856-0.001002O.(XX)O280.0000310.000918-0.036063Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.94%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:-1.95°Field#7:(0,-0.0652)■0.1791820.1746430.174656-0.000014-0.0000020.176992-0.000004-0.()000020.0000540.000052-0.033685-0.001337-0.000003-0.000(M)30.001239-0.035872Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.97%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:2.49°Field#8:(0.0652,0)'0.1810370.1741820.1742030.026419-0.0000990.1732820.0316150.0000690.0282710.033115-0.028192-0.0()1158-0.000072-0.0002470.001033-0.035920Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:98.01%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.18°

58Field#9:(-0.0652,0)■0.1810530.1742380.174174-0.0265230.0000950.173295-0.031687一0.000073-0.028077-0.032933-0.028199-0.0011570.0000680.0002430.001033-0.035927Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:98.01%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:1.06°Withthehalfwaveplateat450:Field#1:(0,0)-0.177792-0.173025-0.0000330.0000010.172913-0.000024().(XX)()()0-0.1751810.000017O.OOOO(X)-0.0000350.033731-0.0()05740.0000()1-0.000503-0.036337Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.89%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:2.34°Field#2:(0.0625,0.0625)-0.174062-0.167038-0.0278420.000008-0.166657-0.165611-0.0327970.0000870.026649-0.0318880.027303-0.0004200.0000520.0(X)028-0.0(K)506-0.035695Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.87%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:0.56°Field#3:(0.0652,-0.0652)-0.174096-0.1671240.1677770.024754-0.000235-0.166920-0.0300570.000302-0.027485-0.0323450.028414-0.0005540.0001420.000172-0.000525-0.035558Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.89%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:0.60°Field#4:(-0.0652,0.0652)-0.174044-0.1670580.166593-0.026577-0.000055-0.1655840.031768-0.0000260.0276090.0325350.027297-0.000505-0.0000()7-O.OOOO85-0.000417-0.035689Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.87%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:0.21

59Field#5:(-0.0652,-0.0652)-0.174082-0.1670340.167587-0.0263610.000240-0.1665900.031911-0.0003010.0272450.0321480.028401-0.000557-0.000132-0.0(X)166-0.000526-0.035563Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.89%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:-0.92°Field#6:(0,0.0652)-0.175941-0.1712300.000248-0.0()00270.170744-0.1729850.000325-0.000029-0.0010360.0012090.033045-0.000421-0.0()00030.000011-0.000503-0.036073Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.87%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:2.22°Field#7:(0,-0.0652)-0.175568-0.1707730.171023-0.000018-0.000002-0.1732220.0000040.000001-0.000070-0.0000680.033561-0.0005940.0000()30.000003-0.000537-0.035892Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.89%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:3.03°Field#8:(0.0652,0)-0.175893-0.168941-0.0274770.000071'0.169094-0.168263-0.0323550.(XX)1270.025464-0.0307120.028322-0.000494-0.00()0960.000173-0.000554-0.035934Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.89%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:0.61Field#9:(-0.0652,0)-0.175921-0.1690110.169078-0.168291-0.0255700.0307840.027277-0.0000670.032168-0.0()01230.028329-0.0004940.0(X)092-(1(X)0169-0.000555-0.035941Polarizationofadepolarizedbeamfromthetelescopeaperturetothedetector:97.89%PhasebetweenExandEyatthedetector,foradiagonallinearlypolarizedinputbeam:-0.18°