sub-pixel characterization for
Transcript of sub-pixel characterization for
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/[email protected]/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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RFGen
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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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100Aquicktestofphotometricnonlinearityistheappearanceofa2nd harmonic.WhentakingAtemporalFFT.
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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A(i,j)isthesumofthetwoGaussiansVis(i,j)=2*sqrt(G1*G2)/(G1+G2)
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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