sub-pixelcharacterizationforµasAstrometrywithLUVOIR

M.Shao,AndapplicationtoprecisionRVmeasurements.

PixelPositionto10-5pixCentroidingto10-4pixelsNyquistsampling12mtelescopeSampling(2.5pix/(l/D))Singleshot0.41uas#dither120Singleepoch0.07uas

JetPropLab,Pasadena,California©2017CaliforniaInstituteofTechnology.Governmentsponsorshipacknowledged

Outline

• Sciencecases– Exoplanets– Cosmology(darkmatter,directdistanceto10’sofmegaparsec?)

• Random(photnoise)andsystematicerrorsinastrometry• Calibrationofsystematicerrors– Detectorerrors(manytypesofdetectorerrors)– Opticaldistortion,(intheopticaldesignvsbeamwalkonimperfectoptics)

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ExoplanetScience• WhataccuracyisneededtodetectanExoplanet?

– SNR=6isneededforafalsealarmprob<1%– SNR=signal/noisewheresignalisamplitudeofthereflexmotion.Noise=

0.07uas/sqrt(#hrsobserved)– Assumingtotal#obs>>10,spreadover>(1orbitperiodor1year)

• Iftherearemultipleplanetsorbitingthestarthe#ofobservationshastobe>5+N_plan*6.

• HowmanyExo-Earthscanbefound?– HowmanyhoursofLUVOIRtime(notincludingslew)wouldittaketo

surveytheeasiest(nearby)100starsforanEXO-Earth(1Mearth,1AUscaledtoStar’sluminosity)?Answer150hrsnotincludingslewtime.

– WesortedtheHipparcoscatalogforallFGKstars<30pc.(doublestarswhereaHZorbitwasnotstablewereremoved)Wefound384stars.Itwouldtake~1500hrs orLUVOIRintegrationtimetosearchallofthem.

• Howcanastrometryhelpadirectimagingprogram?– Directdetectionneedstoimagethestarmultipletimesbeforeitseesthe

exo-EarthoutsidetheIWA.Thenmultipledetectionstoknowtheplanethasa~1yrorbit(HZ).

– Astrometrycaninformthedirectdetectionprogramwhich90%ofstarsdonothaveanEarth-likeplanet.

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Extra-galacticParallaxes• Atechniqueusedinradio

VLBIastrometrycanbeusedintheoptical

• AnumberofOstarscanbemonitored,bothwithpropermotionandradialvelocitytomeasurethedistancetothegalaxy.– PropermotionofalltheOstarsaredoneatonce.

Motion~100km/sec@50MPcis0.4uas/year~2uasover5years

DirectdistancemeasurementtoVirgo

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Darkmatter,exoplanets(inthatorder)isthesciencerationaleforTHEIA(ESA)astrometrymissionconcept,usingupixeldetectorcalibration.Multipleground/labsearchesfordarkmatterhave“null”results.Colddarkmatterhasbeenverysuccessfulatexplainingthe“soapbubble”geometryofgalaxyclusters,butnotverysuccessfulongalacticscaledistances.µasastrometryisemergingasaleadingcandidatetoexploredarkmatter.

SolarSystemScience• DoesplanetX(9)exist?(AseveralEarthmassobjectat

200AUexertsasignificantperturbationontheplanetsintheoutersolarsystem>>1uas.(35uasin1year)– Theproblemwithastrometryofplanetsisthecenteroflightvscenterofmassoffset.Thecenterofmassmovesinahighlypredictableway.Thecenteroflightnotsomuch.

– Thesolutionistolookat0.1~1.0km(orsmaller)moonsoftheseplanets.Theyorbitthecenterofmassoftheplanet.• Theseobjectsarefaint,hencetheneedforhighsensitivityalongwithhighastrometricaccuracy.

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GettingtoSubuasAstrometry

• Theeasypartcomeswithalarge~12maperture.– (Notea10mapertureonlylooses20%fromthesystematicerrorpointofview,8mis1.5Xlessaccurate)

• Withlargeapertures,photonnoiseisnotanissue(photonnoiseofrefstarsdominatesoverthetargetstar)

• Twomajorsourcesofinstrumental/systematicerror– Detector– Optics– (everythingthatcomesbetweenphotonsfromthestarsandbitsinthecomputer)

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Random/SystematicErrors• Randomerrors,primarilyphotonnoise(anddetectorreadnoise)For

exoplanetscience,primarilyfromrefstars.• Systematic(instrumental)errors

– Detectorimperfections• Photometricerrors(non-lin,ghosts,non-unisubpixQE)• Geometricerrors(pixelsarenotregularlyspaced)

– Opticsimperfections(calledopticaldistortion)• Mostfamiliarwithpin-cushiondistortion.ButaTMAtelescopeevenifmanufacturedperfectlytopicometerlevelswillhavedistortion,(butpredictable).

• Beamwalk.(thestarlightfootprintonopticsotherthantheprimaryisdifferentfordifferentstars,thisbeamwalkcoupledtoimperfectlyfiguredopticsproducesopticsdistortionerrors.

• Weattempttocalibrateallinstrumentalbiases.Thecalibrationwillnotbeperfect,butweassumethecalibrationerrorsare“random”anddecreaseassqrt(N)fordifferentmeasurements(atleastforsmallN<1000).Ifwechangethepointingofthetelescopebyafewarcsec,wewillsampleadifferentinstrumentalerror(bothopticalanddetector)

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ExoPlanetAstrometryErrBudget

Targetstar7magRefstars13~18magDia12mSampling2.4pix/(l/D)120dithersin1hr

DetectorErr1e-4pixOpticaldistortion1e-4pixFOV~0.06degAveragesky(forrefstars)~20stars<18mag

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LightSourceforDetectorCalibration

• Whataretheimportantpropertiesofthelightsourceforcalibratingdetectors?

• Dimensionalprecision(x,y)• Photometricprecision

• Whatsourceisclosesttoperfection?• Singlemodeopticalfiber.

WavefrontfromfiberGaussianamplitudesphericalwavefrontfrom2fibersformfringes

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WavefrontfromaSingleModeFiber• Thewavefrontfromasinglemodefiberis

theclosestthingtoaperfectspheremadebyHumans.

• Anyerrorisintheflatnessoftheglass.• Take2inchopticlambda/20p-vsurface.

Andpowerspectrum– ~1/f2.5– Ona4umscalethesurfacecan

potentiallybeflatto~10-5l• Interferencebetweentwospherical

wavefrontsproducehyperbolicfringes(thatvisuallylooklikestraightfringes)

• TheintensitydistributionisideallyaGaussian.InrealityalsoveryclosetoaGaussian.DeviationsfromaGaussianareduetophasetoamplitudeconversion.

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4umcore

Detectorundertest

4um4cm()

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FringesfromTwoFibers• Therearemultiplewaysto“movethefringesacrossthedetector”• OnecommontechniqueistouseAOMfrequencyshifters.

– ThesedevicesshiftthefreqofthelaserlightbyanamountbyXhz,theRFsignaldrivingtheAOM

– TheaccuracyofthefreqshiftofthelaserlightisthefreqaccuracyoftheRFsource.

AOM’sAsfreqshifters

AOMdrivenby2RFSources40.000,000MHz

40.000,003MHz

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Fringesfrom2Fibers• Thedimensionalaccuracyofthe

fringes(acrossthewholedetector)isdirectlyrelatedtothewavefrontqualityfromthefibers.

• Thefringesarecausedto“move”eitherwithanAOMorstretchingthefiber.WithanAOMthemotionisaslinearasthepurityoftheRFsourcedrivingtheAOM.

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WhatareWeMeasuring?

• Thefringeisanearperfectsinusoidinspace(x,y)andintime(t)

• Flux(I,j,t)=A*Vis*sin(kx*X+ky*Y+w*t+f)– Kx,ky spatialfreqoffringe– w istemporalfreqoffringe– f isthepixelpositioninthedirection

offringemotion.

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ThedetectoronlyoccupiesasmallpartoftheGaussianbeamfromthefiber

A(I,j)isthesumofthetwoGaussiansVis(I,j)=2*sqrt(G1*G2)/(G1+G2)

ProjectingPointSourcePSFs• Apointsourcediffractsoffthefocusingoptictoproducean

airyspotonthedetector.

Fiberbundle(smf)

Limiting(diffracting)aperture(actuallyamirror)

Thewavefrontfromthefiberisnearperfect.(geometricpoint)Thereisonly1optic thatreimagesthefibertothedetector

Thatopticisnotperfectl/100,theairyspotisnotexactlytheBesselfunction(squared).Butsincealltheimagesusethesamepartofthesamefocusingoptic,allthePSFsareidentical.

GhostImagesWenoticedghostimagesinoursetup.Atfirstwelookedforstraylightreflections(eggwindowonthedetector)

Butwhenwelookedathowtheghostimagesmovedrelativetotherealimages,werealizedthattheseghostsweretheresultofelectricalxtalkbetweenthe4readampsonthechip.

OursetupatJPLandourcolleague’ssetupinGrenobleusedthesameE2Vchipbuttotallydifferentreadoutelectronics.Butsawsimilarghosts.

ChipRotated90degWrtmovie

PhotometricLinearityCalibration

• Foreachpixel’soutput,thelaserfringesareanearperfectsinusoidintime.ThephaseofthesinusoidisasgoodastheRFgeneratordrivingtheAOM.

• Adeviationofaperfectsinewaveisameasureofthenon-linearityofthedetector.

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CCDsdon’thave(much)persistence.Butwithfiberilluminationwecanchangethetemporalfreqwithoutaffectingthefringeamplitude.Achangeinamplitudewithfreqisasignofpersistence.

InternalFringesfromLaserIllumination• WithCCDs,atlong

wavelengths,thedetectorsaresemi-transparent.

• Aflatfieldmeasurementinlaserlight(especiallyatlongl)willexhibit“fringing”thatisabsentinawhitelightflatfieldatthesamewavelength.

• Thesolutionistouseatunablelaser,andrepeatthedetectorcalibrationmeasurementsacrossenoughdifferentwavelengthstoaveragethiseffectaway.

780nm6%bw

ImagefoundviaGooglesearch

PhotometricErrorsfromGhosts• Imageswerelowpassfiltered,andupsampled(to16pix/(l/D)

– Imageistaken~4pixels/(l/D)– Sourceiswhitelight~5%bandwidth– Ghostimages~10-3 fromelectricalXtalkonchip

• Veryhighwavefrontqualityintestsetup.(visuallysee8th diffractionring)

• Parametersfitted• X,Ycenterofimage• Asemi-majoraxis• Bsemi-minoraxis• q angleofsemi-majoraxis• DC

Log 1

0scale

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ImageShape

• Thefocusingopticwasanoffaxisparabola.Thecircularaperturewasslightlyoffaxis,resultinginaslightlyellipticalPSF.

• Butbothfiberimageshadexactlythesamepupilaperture,andthetwoPSFs,andshouldthereforehavealmostthesameellipticity.

Multifiberbundle

FibersreimagedonCCD

Thisexercisedidnotusethemeasuredpixeloffseterrors.Theimagesweremovedacross3pixels,thesigmarepresentthepixelationerrorinmeasuringellipticity. 19

PixelsGeometryErrors

• Thefringeisanearperfectsinusoidinspace(x,y)andintime(t)

• Flux(i,j,t)=A(1+*Vis*sin(kx*X+ky*Y+w*t+f))– Kx,ky spatialfreqoffringe– w istemporalfreqoffringe– f isthepixelpositioninthedirectionof

fringemotion.

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Dynm

Thecolorscaleisinnanometersthebiggestoffsetisthe700nmslipbetweentheleft½andright½ofthechip.

Dxnm

Randomx,yerr40~50nm

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TheSystematicPixelShiftinE2V39

• ThereisaanabruptYpixelshiftasonemovesacrossXinthedetector

• Sizeofshiftis~700nm• Ontopofthatthereare

30~50nmrandompixelpositionerrorsateverypixel

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ProjectingPointSourcePSFs• Apointsourcediffractsoffthefocusingoptictoproducean

airyspotonthedetector.

Fiberbundle(smf)

Limiting(diffracting)aperture(actuallyamirror)

Thewavefrontfromthefiberisnearperfect.(geometricpoint)Thereisonly1optic thatreimagesthefibertothedetector

Thatopticisnotperfectl/100,theairyspotisnotexactlytheBesselfunction(squared).Butsincealltheimagesusethesamepartofthesamefocusingoptic,allthePSFsarenearlyidentical.

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AccurateAstrometryNeedsanAccurateOpticalPSF

OriginalPSF(specifiedathighresolution)Bothimageshavethesameinformationcontent

PixelatedPSF(Nyquistsampled)>2pixelsperl/D

ForaNyquistsampledimages,onecanshiftthepixelatedimageby3.1416pixelswithoutanycomputationalerror.onecangeneratetheoriginalhighresolutionPSFfromthepixelatedPSFwithouterror.

Possiblewithaperfectdetectororaperfectlycalibrateddetector.

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Centroidingat10-5 l/D• OneoftheerrorsintraditionalCCDastrometryisalackof

knowledgeofthetrueopticalPSF.– ButthetrueopticalPSFcanbemeasuredwithNyquistsampled

images(applyingcorrectionswithsubpixelcalibration).

Achievedaverageerrorof9e-6l/D

Wetookthe3airyspotsandmovethemacross3pixelsofaCCD. Totalof30positions.TheseparationbetweenA,Bwasconstantto1.2e-4pixelsateachofthe10positions.Afteraveraging10positions,theseparationagreedto~10-5 l/D,4e-5pixels.

PSFoversampled4pix/(l/D)

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OpticalDistortion• Alltelescopeshavedistortion,fromthe

design.(pincushionshown)– Butthedistortionfromthedesignis

“known”• Butdistortioncanalsoarisefromoptics

misalignmentandbeamwalk.• Lightfromallstarshittheprimarymirror.

Butdifferentstarsusedifferentpartsofthesecondary(tertiaryetc.)optics.

• Imperfectionsinthefabricationoralignmentoftheopticswillchangedistortionfromthe“design”.

• SimulationsofaTMA(1.5m)telescopewithstateoftheartoptics,showedthatdistortionatthe1uaslevelimpliedneedtocalibrateevery~15arcsec.Distortioncanbemodeledto~1uasovera4arcminFOVwith~200terms.ForLUVOIR,ahighernumberoftermsmaybeneeded.

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OpticalDistortionStabilityandCalibration

• Opticaldistortionexistsevenforatelescopewhosesurfacesareperfect.• HSTisinahostilethermalenvironment(Sunlight,nighttime)future

observatorieswillbeGEO/L2orbitsmanyordersofmagnitudemorethermallystable.

• Calibratedistortionbyditheringonadensestarfield(globularother)– What’simportantisthedistortiondoesn’tchangebetweenmorethan

errorsfromdetectorimperfections.• Comparisonwithcoronagraph.

– Astrometryto1e-4pixels=>stabilityat~5x10-5 l– Coronagraphy(1e-10)=>correctionto~3x10-6 l

• Goodthermaldesign,ChoosecalibrationfieldandtargetfieldtoonlyrequiresrotationalongtheSunvector.(sosolarilluminationofthespacecraftisconstant)

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MaintainingStability

• Stableopticalsystemforastrometry

• Keypoints– Alignmentstability– Opticalfigureof

secondary/tertiaryoptics– (paradoxicallystabilityofthe

primaryisnotcritical,changeinfigureappearsacrossthewholeFOV)

• OperateopticsneartheirZeroCTEtemperature.

• Opticalmetrologytomeasure/maintainalignmentatnmlevels.

Opticsstableto10-4 l,~60pmCTE~10-8/Ka2mopticisstable60pmwhenthetempisstableto3mK.(butuniformexpansionof60pmisnotaproblem)Thermalgradientsstable~10mK.

ThislevelofstabilityisNOTSufficientforcoronagraphy

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Summary• Therearetwo(andonly2)typesofinstrumentalerrors.

– Detectorerrors(almostreadyat~1e-4pixels)– Opticaldistortionerrors.(notdemonstratedinthelabyet,but

simplecalculationsonthermalstabilityimplythisisdoablewhenthetelescopeisinHEO/GEO/L2)

• Majorimpactonexoplanetscienceandcosmologyandsolarsystemdynamics(planetX)

• Onorbitmetrology ispartofthebaselinedesignoftheLUVOIRHighdefinitioncamera.(alongwithNyquistsamplingofthePSFto~400nm.)

• DetectorcalibrationisalsoimportantforprecisionRVspectrometersthatareaimingtogetbelow10~20cm/sec.

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