vlt-tre-esp-13520-9202 fpcs test report v1obspepe/repository/vlt-tre-esp-13520-9202_fpcs… · test...

Name Date Signature

Name Date Signature

Name Date Signature

ESPRESSO

Fabry-PérotCalibrator

TestReport

VLT-TRE-ESP-13520-9202,Issue1

May4th,2016

Prepared F.Pepe 4/05/2016

Approved F.Zerbi

Released F.Pepe

CentrodeAstrofísicadaUniversidadedoPorto

UniversidadedeLisboa,SIM/IDL&LOLS

INAF,OsservatorioAstronomicodiTrieste

INAF,OsservatorioAstronomicodiBrera

ObservatoryoftheUniversityofGeneva

VLT-TRE-ESP-13520-9202,Issue 3/23

ChangeRecord

Issue/Rev. Date Section/Pageaffected Reason/Remarks

1 04/05/2016 All PreparedinviewofSub-systemacceptance


TableofContentsChapter1. Introduction..............................................................................................................................................7

1.1ScopeoftheDocument......................................................................................................................................7

1.2Documents..............................................................................................................................................................7

1.2.1 ApplicableDocuments................................................................................................................................................................7

1.2.2 ReferenceDocuments..................................................................................................................................................................7

1.3AcronymsandAbbreviations..........................................................................................................................7

1.3.1 Acronyms..........................................................................................................................................................................................7

Chapter2. VerificationMatrix.................................................................................................................................9

Chapter3. PerformanceVerification..................................................................................................................10

3.1Wavelengthcoverageandenergydistribution.....................................................................................10

3.2SystemTransmittance.....................................................................................................................................12

3.3TransmittanceUniformity..............................................................................................................................13

3.4TransmittanceVariations...............................................................................................................................13

3.5FinesseandSpectralResolution..................................................................................................................13

3.6Etalonspacing......................................................................................................................................................14

3.7PhotonNoise........................................................................................................................................................14

3.8FluxHomogeneity..............................................................................................................................................16

3.9LineWidth.............................................................................................................................................................16

3.10LineSeparation.................................................................................................................................................17

3.11Short-TermRepeatability............................................................................................................................17

3.12Long-TermRepeatabilityandLine-ShapeStability..........................................................................19

3.13LocalWavelengthAccuracy........................................................................................................................20

Chapter4. Conclusions.............................................................................................................................................23

ListofFiguresFigure1:Top:RawHARPSframeoftheFPCspectrumilluminatingbothfibers.Bottom:For

comparison,aframeisshowninwhichoneofthefiberwasilluminatedwiththethoriumlamp.NotetherichnessoftheFPCspectrumcomparedtothatofthethorium.......................11

6/23 ESPRESSOProject

Figure2:Left:TransmissionspectrumoftheFabry-Pérotetalonaveragedofabroadband(>>thanatypicalFSRoftheetalon).Right:fluxatthepeakofatransmissionlineoftheFPwhenilluminatedbytheXe-lampcomparedtothetungstenlamp.MeasurementshavebeencarriedoutwithHARPS..........................................................................................................................12

Figure3:DirectmeasurementoftheFPtransmittancewhenvaryingtheopticallengthofthegapbyvaryingthepressureinsidetheFPC..............................................................................................14

Figure4:FluxoftheLDLSlampthough-outthespectralrangeofESPRESSO....................................15

Figure5:Fundamental(photon-noiselimited)precisionobtainedonasingleFPspectrum.Theresultsfromthethoriumlampareshownforcomparison................................................................16

Figure6:Relativedriftmeasurementsover7hourstotesttheshort-termperformancesoftheFPC...............................................................................................................................................................................18

Figure7:Absolutedriftmeasurementsover7hourstotesttheshort-termperformancesoftheFPC...............................................................................................................................................................................19

Figure8:Driftmeasurementsover180daystotestthelong-termperformancesoftheFPC.....20

Figure9:DispersionlawoftheFPC(expressedineffectiveetalongap)recordedovertwoseasonsseparatedbymorethanoneyear.Left:fullwavelengthrangeofHARPS.Right:Zoomoverasingleorder...................................................................................................................................22

Figure10:Dispersionvariation(expressedindifferenceofeffectiveetalongap)betweentwoseasonsseparatedbyoneyearasafunctionofwavelength.Left:fullwavelengthrangeofHARPS.Right:Zoomoverasingleorder...................................................................................................22

Figure11:Effectiveetalongap2D(λ)asafunctionofwavelengthandisdifferencefromthenominalvalueof14.6mm.................................................................................................................................21

ListofTablesTable1:FPCRequirementsandVerificationMatrix.........................................................................................9


Chapter1. Introduction

1.1ScopeoftheDocumentThis document describes the tests on the Fabry-Pérot Calibrator (FPC) performed in order todemonstratecompliancewithsub-systemrequirements.ForthedetaileddesigndescriptionwerefertoRD-2.

1.2DocumentsTheapplicableandreferencedocumentsarelistedbelow:

1.2.1 ApplicableDocumentsAD-1 ESPRESSOStatementofWork VLT-SOW-ESO-13520-5059 1 01.02.2011AD-2 ESPRESSOTechnicalSpecifications VLT-SPE-ESO-13520-4633 3 01.02.2011

1.2.2 ReferenceDocumentsRD-1 Fabry-PérotCalibratorFinalDesign

DescriptionandPerformancesAnalysis

VLT-TRE-ESP-13520-0154 2 04.05.2016

RD-2 Fabry-PérotCalibratorProductTree VLT-LIS-ESP-13520-9201 1 04.05.2016

1.3AcronymsandAbbreviations

1.3.1 AcronymsAD ApplicableDocumentAIV Assembly,IntegrationandVerificationCCL CombinedCoudéLaboratory(oftheVLT)CIDL ConfigurationItemsDataListCTE CoefficientofThermalExpansionE-ELT EuropeanExtremelyLargeTelescopeESO EuropeanSouthernObservatoryESPRESSO EchelleSpectrographforRockyExoplanetsandStableSpectroscopicObservationsFDR FinalDesignReviewFP Fabry-Pérot(etalon)FPC Fabry-PérotCalibratorFWHM Full-WidthatHalfMaximumHW HardwareICD InterfaceControlDocumentICS InstrumentControlSoftwareISO InternationalOrganisationforStandardisationIP InstrumentalProfile


LDLS Laser-DrivenLightSourceLFC Laser-FrequencyCombLRU Line-ReplaceableUnitMTBF MeanTimeBetweenFailuresN/A NotApplicablePAC ProvisionalAcceptanceChilePAE ProvisionalAcceptanceEuropePDR PreliminaryDesignReviewPI PrincipalInvestigatorPLC ProgrammableLogicControllerPM ProjectManagerQA QualityAssuranceRAMS ReliabilityAvailabilityMaintainabilitySafetyRD ReferenceDocumentRfW RequestforWaiverRV RadialVelocitySOW StatementOfWorkSW SoftwareTBC ToBeConfirmedTBD ToBeDefined/ToBeDevelopedThAr Thorium-Argon(lamp)ULE Ultra-LowExpansion(material)UPS UninterruptedPowerSupplyUT UnitTelescope(8.2metertelescopeatParanal)VLT VeryLargeTelescopeVM VerificationMatrixWBS WorkBreakdownStructureWP WorkPackage


Chapter2. VerificationMatrixInthefollowingTable1werecallthesubsystemrequirementsfortheFPCdefinedinRD-2andproposeaverificationmethod.

Table1:FPCRequirementsandVerificationMatrix

Item Requirement VerificationDATSI+Comment

Wavelengthcoverage 380–780nm S:HARPS-N,T:AtsystemlevelwithESPRESSO

Systemtransmittance >10%Inthewavelengthrange

T:Atvariouswavelength,inlab.

Transmittanceuniformity Tmax/Tmin<2Inthewavelengthrange

T:Atvariouswavelength,inlab..

Transmittancevariations dT/dλ <2%pernm S:HARPS-N,T:AtsystemlevelwithESPRESSO

EtalontotalFinesse 10<FE<12Inthewavelengthrange

T:HeNelaser,Pressurescaninlab.

Etalonspacing D=7.6mm±0.0005mm D,T:ManufacturerofEtalon

Photonnoise <5cm/sGlobalprecisionachievedinasingleexposure

S:HARPS-N,T:AtsystemlevelwithESPRESSO

Fluxhomogeneity Fmax/Fmin<5Inthewavelengthrange

S:HARPS-N,T:AtsystemlevelwithESPRESSO

Linewidth δλ <2/3ofspectralelementAspectralelementisthewavelengthdividedbythespectralresolution

T:HeNelaser,Pressurescaninlab

Lineseparation Δλ = 2-7xspectralelement T:HeNelaser,Pressurescaninlab

Short-termrepeatability dλ/dt<210-10λ (0.07m/s) Over12hours

S:HARPS,T:AtsystemlevelwithESPRESSO

Long-termrepeatabilityandline-shapestability

dλ/dt<210-10λ (0.07m/s) Over20years(goal)


Localwavelengthaccuracy λ-λ0< 3x10-8 λ(10m/s)ForanyFPClinewithrespecttotheoretical



Chapter3. PerformanceVerificationInthefollowingweshallpresenttheresultsobtainedwithESPRESSO’sFPC.Someparameterscouldnotbeverifiedinlaboratoryduetotheabsenceofahighlystablehigh-resolutionspectrograph.InthosecasestheperformancesisdemonstratedbysimilaritywiththeperformancesoftheHARPSandHARPS-NFabry-Pérots.ItmustbepointedoutthatESPRESSOFPCdesignisanexactcopyofHARPS-N’sFabry-Pérotsystem.

3.1WavelengthcoverageandenergydistributionThehigh-resolutionspectrumoftheFPCsystemoftheHARPSspectrographisshowninFigure1.Onlyapartoftherawframeisshown,asthewholeimagewouldbetoolargeandthevariouslineswouldnotberesolvedindividually.OnecanseethespectraofthetwofibersbothilluminatedbytheFPCsystemspectrum.Thewavelengthincreasesfromlefttorightandfrombottomtotop,directionoverwhichthespectrumissplitoverseveralechelleorders.ThelargegapinthecenteroftheimageisduetoaphysicalgapintheCCDmosaiccomposedoftwoCCDs.Forcomparisonaframeisshowninwhichoneofthefiberwasilluminatedwiththethoriumlamp.NotetherichnessoftheFPspectrumcomparedtothatofthethorium!


Figure1:Top:RawHARPSframeoftheFPCspectrumilluminatingbothfibers.Bottom:Forcomparison,aframeisshowninwhichoneof thefiberwas illuminatedwiththethoriumlamp.Notetherichnessof theFPCspectrumcomparedtothatofthethorium.

TheaveragetransmissionoftheFPCsystemhasbeenmeasuredusingalow-resolutionspectrograph.Thereferencespectrumwasrecordedbyinjectingthelightofatungstenlampintoa200µmfiber,inturnconnectedtoa600µmfiberinjectingthelightintothespectrometer.TheFPCspectrumwasthenrecordedbyseparatingthetwofibersectionandconnectingthe200µmfibertothe200µminputfiberportoftheFPCandthe600µmfibertothe600µmfiberoutputportoftheFPC.ThetransmittancespectrumwasdeterminedbydevidingtheFPCspectrumbythereferencespectrumafterhavingsubtractedthedarkspectra.

500 1000 1500 2000 2500 3000


Figure2:Left:TransmissionspectrumoftheFabry-Pérotetalonaveragedofabroadband(>>thanatypicalFSRoftheetalon).Right:fluxatthepeakofatransmissionlineoftheFPwhenilluminatedbytheXe-lampcomparedtothetungstenlamp.MeasurementshavebeencarriedoutwithHARPS.

TheresultingtransmissionspectrumisshownbythebluelineinFigure2.Thespectrumshowshoweveronlyan‘average’transmittanceoftheFPCgiventhelowresolutionofthespectrograph,whichcannotresolveindividualFPClines.InordertodeterminethetransmissionatpeakthisvaluehastobemultipliedbytheFinesseoftheetalon.Aswewillseelater,thefinessemeasuredis12.27.Theresultingpeak-transmittanceisshownbytheredcurve.

Althoughthebluepartofthespectrumisaffectedbysomemeasurementnoise,mainlyshotnoise,itcanbeclearlyseenthattheFPCcoversthewholespectralrangeofESPRESSO.ThisisalsobythespectrarecordedwithHARPS-N,ofwhichtheFPChasbeeninoperationformorethan3years.

3.2SystemTransmittanceAsseeninFigure2thesystemtransmittancelieseverywherebetween22%and40%,andisthussignificantlylargerthantherequiredminimumT>10%.AnindependentverificationoftheabsolutetransmittancehasbeenmadebyfeedingtheFPCwithanHeNelaserandrepeatingthereferenceandFPCmeasurementdescribedabovewhileusingaradiometer.InordertoobtainpeaktransmittancetobecomparedwiththereadcurveinFigure2,wehavescannedthepressureinsidetheFPCtoobtainmaximumtransmittance.Theresult,indicatedbythereddiamondat632.8nm,isperfectlyinlinewiththetransmissionspectrum.

0

5

10

15

20

25

30

35

40

45

50

380 430 480 530 580 630 680 730 780

Tran

smi(an

ce[%

]

Wavelength[nm]

AverageFPCtransmi9ance

PeakFPCtransmi9ance

HeNemeasurementatpeak


3.3TransmittanceUniformityThemaximumtransmittanceTmaxisreachedattheveryblueendofthespectrumandisabout40%,whileTminisabout22%.ThereforthetransmittanceuniformityTmax/Tmin=1.82<2justinlinewiththespecifiedrequirement.

3.4TransmittanceVariationsThemaximumtransmittancevariationdT/dλisobservedbetween380and400nmdroppingfrom40%to25%within20nm.Wecomputethenarelativefluxvariationoftheorder37%,whichproducesaslopeofdT/dλ =1.85%/nm.

3.5FinesseandSpectralResolutionThefinesseF=Δλ/δλ(distanceoftwoneighboringlinesdividedbythelinewidthofaline)oftheFPetalonhasbeenmeasuredinlaboratorybyscanningtheetalon’seffectivegap.Thescanningwasachievedbyvaryingthepressureinsidethevacuumvesselandconsequentlybetweenthetwomirrorsoftheetalon.Thus,aneffectiveopticalpathdifference(OPD)isintroducedandthetransmittedwavelengthchanged.AcommercialHeNelaserofλ=632.8nmwasusedforthelinescanningmeasurement.

Figure3showsthetransmittedlaserfluxasafunctionofeffectiveopticalgapvariationascomputedassumingalinearrelationshipbetweenpressureandrefractiveindexofair.TheredcurvecorrespondstotheAiryfunctionwhichtheoreticallydescribesthetransmittancefunctionoftheFPetalonwithasingleeffectivefinesseFE.ThemeasuredFEisinourcasesimplytheratiobetweentheFWHMofasinglepeakdividedbythedistancebetweentwoneighboringpeaks,orcanbedeterminedbyfittinganAiryfunctionwithFEasoneofthefreeparameters.InbothcasesweontainafinesseFE=12.27.Thisvaluecorrespondsexactlytothedesignedandthusexpectedvalue,andisthereforperfectlycompliantwiththeminimumrequirementofFE=12.27.Althoughisliesslightlyoutsidethehigherendonthespecifiedrange,wehavetomentionthata)themeasurementofthefinessecanbeaffectedbysmallmeasurementerrorsandb)thehigherfinesseonlyimpactsthefluxdeliveredbytheFPC,wemaybereducedbyacoupleofpercents.WeconsiderthereforetheFPCtobefullycompliantwiththefinesserequirement.


Figure3:DirectmeasurementoftheFPtransmittancewhenvaryingtheopticallengthofthegapbyvaryingthepressureinsidetheFPC

3.6EtalonspacingTheetalonhasbeenmanufacturedbyICOStothedesignedgapof7.6mmwithinbetterthanafringeofthemeasuringinterferometer,whichisexpectedtobeD=7.6mm± 0.0003mm.AfinalmeasurementwillbedoneduringsystemverificationsoftheESPRESSOspectrographbyrecordingandfittingtheentireFPCspectrum.ByanalogywiththeHARPSFPC(seeSection3.13)wecanhoweverstatethatthegapDlieswithin0.3µmP-Vofthespecifiedvalue.

3.7PhotonNoiseTheabilityofdeterminingthepositionofaspectrumontheCCD(linepositionexpressedinpixel)andassociateitwithagivenwavelengthdependsonthewidthandtheintensityoftheline.Ingeneralonecansaythatthefundamentallyattainableprecisionisproportionaltothesquarerootofthenumberoflinesinthespectraldomainandtheirintensity,andinverselyproportionaltotheirwidth.InHARPS,theformulaedescribedbyBouchy&Pepe(2001)areemployedtomeasurethefundamental(photon-noiselimited)precisioncontentofaspectrum.

Figure4showsthefluxproducedbytheLDLSlampwithinitsthenominal230µmfiberilluminatingtheFPC.Theemissionisextremelyflatandvariesfrom40µW/nmto50µW/nm


fromtheredtotheblueendodthespectralrangeofESPRESSO.Let’sassumetheworstcase,i.e.intheblue,wherethephotons‘weigh’moreandtheinstrumenttransmittanceislower.At380nmweobtainaphotonfluxofabout10!"photons/s/nmoutofthelampfiber.Let’sconsidernowapessimistisPFCtransmittanceof10%,atransmittanceofthecalibrationunitof50%,anétenduematchingefficiencyof10%,andaspectrographefficiencyof10%,weobtainafluxonthedetectoroftheorderof5 ∙ 10!" ph s!! nm!!.ThelinewidthofaFabry-Pérotlineisgivenbyitsresolution𝑅!" = 𝐹! ∙𝑚 = 12.3 ∙ 40′000 ≈ 500′000,wheremistheordernumberoftheFPClineat380nm.Innm,thelinewidthisthus𝑤!" = 𝜆 𝑅!" =0.00076nm.Weexpectthereforeaphotonfluxofabout3.8 ∙ 10! ph s!!perspectrallineoftheFPC.FromHARPSwecanestimatethattheRVprecisiondeliveredbyasinglelineofabout10!photo-electronsisoftheorderof1ms-1.Byanalogywecanthereforeextrapolatethatinanexposureof10secondstheRV-precisionperlineisoftheorderof5cms-1withtheFPCofESPRESSO.IfweconsiderthattheESPRESSOspectrumcontainsoftheorderof20’000FPClines,thenweendupwithapotentialglobalprecisionof0.04cms-1ina10-secondsexposure,whichmeansthatwehaveafluxmarginoftheorderofafactor10’000withrespecttothespecifiedrequirement.

Figure4:FluxoftheLDLSlampthough-outthespectralrangeofESPRESSO

Itisimportanttonotethat,inHARPS-N,weobtain5cms-1globalRVprecisionina20-secondsexposure,afterhavingattenuatedtheLDLSfluxbyafactorof300.Figure5showstheattainableprecisionusingtheFPCsystemasafunctionofthesquarerootoftherelativefluxmeasuredonthedetector.ThefluxwasvariedeitherbychangingthevariableND-filterinfrontofthecalibrationlamporbyvaryingtheexposuretime.Forcomparison,alsotheresultsobtainedwiththehollowcathodethoriumlampareshown.Inbothcasesitcouldbedemonstratedthattherelationshipisperfectlylinearasexpectedfrompurephotonnoise,andthataprecisionofabout2cms-1canbeattainedonasinglespectrum.


Figure5:Fundamental(photon-noiselimited)precisionobtainedonasingleFPspectrum.Theresultsfromthethoriumlampareshownforcomparison.

Asmentionedabove,thefluxlevelcanbevariedeitherbyincreasingthelightintensityortheexposuretime.InthepresentHARPS-Nsystemthethoriumlampistunedinawaysuchtobalancelifetimeandflux.Inanexposureof20s,whichisthe(minimum)nominalexposuretimeforawavelength-calibrationexposure,theattainedprecisionlevelisoftheorderof2cms-1.Notonlythisdirectlydemonstratedthattherequiredphoton-noiseprecisionisachievedalreadywithHARPS-Nandasimilarsystem,butalsovalidatedtheperformandetheoreticalcomputations,whichareperfectlycompliantwiththeHARPS-Nmeasurement,ifweconsiderthatthecouplingefficiencyoftheHARPS-NFPChasnotbeenoptimizedinthesamewayasforESPRESSO,andthatthecalibrationandscientificfibersofHARPS-NareconsiderablylongerthatthoseofESPRESSO.

Inpractice,andinordertonotsaturatetheESPRESSOdetector,wewillhavetointroducefixedNDfilterattheoutputofthelamp.ThelocationisalreadyforeseewiththefilterboxbetweentheLDLSlampandtheVacuumTank.ThefilterdensitywillbeadaptedduringsystemtestsofESPRESSO.

3.8FluxHomogeneityGiventheflatspectralpoweroftheLDLSandtheflatspectraltransmissionoftheFPC,themaindriverforfluxinhomogeneitiesistheenergyofthephotonsacrossthespectrum.Sincethephotonenergyincreasesbyafactorof2fromtheredtotheblueendofthespectralrange,andthatboththespectralpoweroftheLDLSandthetransmittanceoftheFPCbothincreasetowardstheblue,wedonotexpectfluxinhomogeneitieslargethanafactorof2,thusperfectlywiththespecifiedmaximumfluxvariationFmax/Fmin=2<5.

3.9LineWidthThelinewidthofaFabry-Pérotlineisgivenbyitsresolution𝑅!" = 𝐹! ∙𝑚 = 12.3 ∙ 40′000 ≈500′000,wheremistheordernumberoftheFPClineat380nm.ThelinewidthoftheFPCisthus𝑤!" = 𝜆 𝑅!" =0.00076nm.ThesizeofthespectralelementofESPRESSOisgivenbythe


spectralresolutionRofthespectrograph,whichisabout𝑅 = 140′000initsstandardHRmode.Therefore,thewidth𝑤!" ofthespectralelementis𝑤!" = 𝜆 𝑅,whichisabout0.0027nmintheextremeblueand0.0056nmintheextremeredpartofthespectrum.Therefore,intheworstcase(blue),theFPClinewidthis𝒘𝑭𝑷 < 𝟎.𝟑 ∙𝒘𝑺𝑬.TheFPCisthusnotonlycompliantwiththeline-widthrequirementfortheHRmode,butalsowiththeUHRmodeofESPRESSO.InnocasetheFPClinesareresolvedbythespectrograph.

3.10LineSeparationThelineseparation∆𝜆ofFabry-Pérotlinesisgivenbytheformula∆𝜆 = 𝜆! (2𝐷).Thisvalueisminimumittheextremeblue,whereitvalueis∆𝜆! = 0.00475 nmandmaximuminthered,whereitsvalueis∆𝜆! = 0.02 nm.TheratiobetweenthelineseparationandthewidthofthespectralelementofESPRESSOliesthereforebetween∆𝝀𝑩 𝒘𝑺𝑬 = 𝟏.𝟕𝟔and∆𝝀𝑹 𝒘𝑺𝑬 = 𝟕.𝟒.Althoughthesevaluesareslightlynon-compliantwithrespecttothespecifiedvaluesonbothsends,itmustbenoted,thatitwasalreadytheoreticallynotpossibletocomplywiththemeverywhereinthewidespectralrangeofESPRESSO(morethanafactorof4duetothespectralwidth!).

3.11Short-TermRepeatabilityThefollowingsectionsarebasedonmeasurementsandtestsperformedontheHARPSFPC,sincethecorrespondingparameterscanonlybedeterminedusingahighlystablyhigh-resolutionspectrograph.ThetestswillberepeatedfortheESPRESSOFPConeESPRESSOisfullyfunctionalandstable.

InordertousetheFPCinastandardwayonHARPS,theDRS(pipeline)hadtobeadaptedandsomefunctionalityadded.Inparticular,onehadtoaddthepossibilityoftreatingframesusingtheFPConfiberBforbothcalibrationandscientific(target)exposures.Therecognitionandthecorrecthandlingofthevariouscaseshadtobeimplemented.Also,forthemeasurementofthedrift,severalnewalgorithmshavebeentestedandimplemented.

ItisimportanttonotethatthesedevelopmentshavebeenalsousedforthesimultaneousdevelopmentoftheLFCbyESOandMPQ,sincetheLFCaswellhadtobetestedonHARPS.ThespectraoftheLFCandtheFPCareactuallyqualitativelyidentical,andthesamedatareductioncanbeusedinbothcases.TheseconceptshavebeenfullyintegratedintheESPRESSOpipelineandapplyinanidenticalwayfortheLaser-FrequencyCombandtheFabry-Pérot.

Wehavetestedtheshort-termstabilitybyperforminglongseriesofThAr-FPexposures(ThAronfiberA,FPConfiberB)andbycomputingtherespectivedriftsindependently.Figure6showsthedriftfromoneexposuretotheotherascomputedbytheThArlampandtheFPC,aswellasthedifferenceofbothtoremovepossibleinstrumentaldrifts.

FortheThAraloneweobtainadispersionofabout0.19ms-1rmswhichshouldbecomparedtoabout0.09ms-1purephoton-noiseerror.FortheFPCweobtain0.176ms-1rmsdispersion,tobecomparedto0.06ms-1photonnoise.Forthedifferenceofboth,weendupwithaphotonnoiseof0.11ms-1andameasureddispersionof0.14ms-1.Thedispersionofthedirrenceiswellbelowthesquarerootofthequadraticsumoftheindividualdriftmeasurementsof0.26ms-1,demonstratingthatbothsourcestracka‘real’instrumental’drift.Ontheotherhand,thedifferencebetweenthephotonnoiseandthemeasureddispersionleavesroomfora0.08ms-1additionaldispersion,whichisnot‘seen’byatleastoneofthefibers(orbettersources).


Figure6:Relativedriftmeasurementsover7hourstotesttheshort-termperformancesoftheFPC

TheplotinFigure7showsthesamedata,butthistimeinabsoluteterms,i.e.itindicatestheabsolutedriftforFPandTHwithrespecttotheveryfirstexposureoftheseries.ItshouldberemarkedthatingeneraltheFPandtheTHfollowthesame‘high-frequency’behavior,trackingrealinstrumentaldrifts.Thisisdemonstratedbythefactthatthedispersionofthedifferenceiswellbelowthedispersionoftheindividualmeasurements.Ontheotherhand,theplotshowsalsothatonecanhavedifferentialdriftsoftheorderof0.9ms-1P-Vor0.23ms-1rmsifnorecalibrationisperformedduringeverynight.Again,thisisaworstcaselimitifweassumethatthedifferentialdriftbetweenTHandFPisfullyduetotheFP.Asitwillbedemonstratedinthefollowing,theshort-termstabilityoftheFPCiswellwithinspecs.


Figure7:Absolutedriftmeasurementsover7hourstotesttheshort-termperformancesoftheFPC

3.12Long-TermRepeatabilityandLine-ShapeStabilityTheline-shapestabilitycannotbemeasuredseparatelyfromthephotocentermeasurementanditisthereforemeasuredasapartofthelong-termrepeatability.Thelong-termstabilitywastestedinasimilarwayastheshort-termstabilityusingHARPS@ESOdata.Framesweretakeninroutineoperationalmosteveryday.Theideawastomonitorpossiblelong-termdriftsoftheFPCwithrespecttotheThArcalibrationlamp.

Figure8showstheresults.Overthe6monthsofoperationsin2012,theFPCslowlydriftedbyatotalof11.6ms-1,assumingthattheThArlamphasnointernaldrift.ThemeasureddriftismostlyduetothefactthatthepressureintheFPCincreasesslightlywithtime,sinceitisnotcontinuouslypumped.Thissequenceshowsneverthelessinaclearandimpressivewaythatthelong-termdriftoftheFPCisofabout0.063ms-1perdayinaverage.Duringanobservingnight,betweenthecalibrationandthescientificexposures,weshouldnotexpectadriftlargerthan0.05ms-1,ifthedailycalibrationsaredoneatthebeginningofthenight.


Figure8:Driftmeasurementsover180daystotestthelong-termperformancesoftheFPC

3.13LocalWavelengthAccuracyForthetheoreticalFabry-Pérotthewavelength(orfrequency)ofagiventransmittedpeak(order)misfullydeterminedbyasingleparameter:thegapD.Thecorrespondingformulaisλm=2D/m.Providedthatweknowtheetalon’sgap,wecan,fromthisformula,directlydeterminethewavelengthofagivenlinebyknowingitordernumber.Inpractice,however,onedoesnotknowtheabsoluteordernumberoftheline,butonlyarelativenumberingbyassumingthatthepeaksmusthavecontinuouslyincreasinganddiscreteordervalues.Wehavethereforereversedtheproblembyusingthespectrographscalibrationdeliveredbythethoriumsourceandusedittoassignawavelengthtoeachtransmissionpeak.Usingthiswavelengthandassumingagapof2D=14.6mmfortheFPCofHARPS,wehavebeenabletodeterminedirectlytheordernumberofeachtransmittancepeakappearingintheFPspectrum.

WedidnotexpectthegapDtobeexactlythetheoreticalvalues,nortobeconstantasafunctionofwavelengthduetothevaryingeffectiveopticaldepthofthedielectricmirrorcoatings.Indeed,thecomputedordernumberswerenotallperfectlydiscrete.Nevertheless,thedifferencetothediscretecontinuousnumberisalwaysbelow0.25.Fromthiswecanconcludethatbyroundingtheobtainedordernumbertotheclosestintegervalueweunambiguouslyidentifytherealordernumber.Usingthisfact,wehavethenusedthesocomputeddiscreteordernumberandthewavelengthassignedfromthethoriumcalibrationtodeterminetheeffectivegapD=D(λ)oftheetalon.TheresultisshowninFigure9.Notethemechanicalgapoftheetalonisof7.3mmandthatinthefiguretheopticalpathdifference2Disactuallyshown.


Figure9:Effectiveetalongap2D(λ)asafunctionofwavelengthandisdifferencefromthenominalvalueof14.6mm

Itappearsthatthe‘manufactured’mechanicalgapofD=7.3mmisfullycompliantwiththemeasuredopticalpathdifferenceof2D=14.6mmwithinaquarterofwavelength,whichconfirmsthattheordernumberingcanbeassignedunambiguouslybyassumingthetheoreticalgapvalue.IfawrongvalueDhadbeenassumed,theD(λ)wouldshowaslopeofatleastonewavelengthovertheplottedspectralrange.

Nevertheless,D(λ)seemstovarysignificantly.Themeasuredchangescorrespondtoabout10-5or,expressedinradialvelocities,oftheorderof3kms-1.WeassumeherethatD(λ)isconstantintimeandthatthusthepresentedfactdoesnothaveanyimpactonabilityoftheFPsystemtotrackinstrumentdrifts.However,wealsoconcludeinordertousetheFPCsystemforabsolutewavelengthcalibrationstobetterthat10-5,D(λ)oftheFabry-Pérotmustbecalibratedbyanothermean(e.g.laserfrequencycomborthoriumlamp).

AlthoughD(λ)seemswelldeterminedwehavetoremarkthatshort-scalepatternswithamplitudeoftheorderof50ms-1havebeenrecordedinD(λ).AtfirstglancethepattersseemstobelinkedtotheFPsystemitself(thepatternisthesamewhencomparingwavelengthspresentintwodifferentorders),andshouldbecalibrated..

WeconcludeherethattheFPetalonbehavesasexpectedintermsofspectralperformances.Theetalongaphasbeenmanufactured(andmeasured)withanamazingaccuracy.WeconfirmthattheeffectivegapD(λ)varieswithwavelength.However,wewillseelaterthatthisgapD(λ)remainsconstantwithtimeandcanbethuscalibrateddowntophotonnoiseprecision.

Theeffectiveetalongapvariesasafunctionofwavelengthduetothefactthatthepenetrationdepthinthecoatingdependsonthewavelength.ByusingtheThArcalibrationoftheFPframes.Wehaverepeatedthismeasurementinordertoverifywhethertheetaloncharacteristic,inparticularthecoatings,remainconstantwithtime.Figure10showstheeffectivegap(twicethephysicalgap)asafunctionofwavelength.ThetwocurvesandtherespectivezoomshowameasurementtakenwiththecontinuumlasersourceofHARPSin2011andanotherin2012morethanoneyearlater.Bothplotsshowthatthetwocurvefolloweachothertoalargedegree.Theabsolutevariationof0.3µmcorrespondstoa‘velocity’of6kms-1.Thedifferencebetweenthetwocurveismuchsmallerandbasicallyanoffset.Itismainlyduetoapressurechangeinthe


FPCsystemwhichinfluencestheeffectivegapoftheetalon.Small‘coherent’variationscanbeseenonshortscale.Theycorrespondtoabout0.003nmor60ms-1.

Figure10:DispersionlawoftheFPC(expressedineffectiveetalongap)recordedovertwoseasonsseparatedbymorethanoneyear.Left:fullwavelengthrangeofHARPS.Right:Zoomoverasingleorder.

Figure11showsthedifferenceindispersionbetweenthetwoseasonsseparatedbymorethanoneyear.Thevariationisexpressedintermsofeffectiveetalongapvariation.Asitcanbeseen,thevariationisconstantwithwavelength.Thegeneraloffsetof0.65nm(=13.4ms-1)canbeexplainedbythedifferencesinpressureinsidetheetalondewarbetweenthetwomeasurements.Itinterestingtonotethatthetwocurvesshowthesamelow-frequencybehavior,confirmingthatthecoatingscharacteristicsremainunchangedtothelevelgivenbythemeasurementnoiseofeachsingleline.Itshouldbenotedthatthedifferenceofthedispersionsremovesthe‘coherent’wigglesseenintheabsolutedispersioncurveshowninthepreviousfigure.Theremainingdifferenceoftypical±1nmorabout±20ms-1isprobablysimplydueto‘photonnoise’whendeterminingthelinepositionononesingleframe.Indeed,abackoftheenvelopeestimationofthecentroiderrorobtainedonalineof5000electrons/extractedpixel,atypicalvaluefortheHARPSFPCframes,leadstoanerrorof20ms-1.OntheHARPS-NFPCthefluxisaboutafactorof6higher,suchthatwecanexpectthattheFPClinesaredeterminedwithaprecisionofabout2.5timesbetter,i.e.toatypicalprecisionof8ms-1.

Figure11:Dispersionvariation(expressedindifferenceofeffectiveetalongap)betweentwoseasonsseparatedbyoneyearasafunctionofwavelength.Left:fullwavelengthrangeofHARPS.Right:Zoomoverasingleorder.


Chapter4. ConclusionsWehavedescribedtheexceptionalperformancesoftheESPRESSOFPCand,togetherwiththeexperienceacquiredontheHARPSFPC,wehavedemonstratedthattheFPCisindeedavaluablefallbacksolutionfortheLFCundertwoaspects:

1. Itisabletoprovideadriftmeasurement(simultaneousreference)wellwithintherequiredphotonicprecisionandshort-termstability.

2. Ifcombinedwithexternalabsolutereference,itcanbeusedtocharacterizetheCCDandprovidewavelengthcalibration.Theglobalaccuracywillbegivenbytheexternalsource.Thelocalaccuracyisgivenbytheabilityofcalibrationthegroup-delaydispersionoftheFabry-Pérot.TestonHARPSshowthatthedispersionlawisreproduciblewithin1/30’000’000oftheFabry-Pérotthickness,whichcorrespondstoanequivalentlocalrepeatabilityof10ms-1.

3.