Upload
others
View
9
Download
0
Embed Size (px)
Citation preview
Photometry&DigitalImages
A. Saha
Tuesday,August3,2010 1GeminiDataReducAonWorkshop
Scopeofthistalk
• Emphasisonprinciples,notprescripAon• Whatisphotometry?
– PhysicalvsReferenAalmeasures&standardizaAon– DifferenAalvssystemicneeds
• Digitaldataandwhattobeawareof– WhatobservaAonalmaterialoneneeds– Imageprocessingsteps
• Aperturemeasures&opAmizingSNR• PSFfiPng
– AperturecorrecAons– WhenPSFsvary– Crowdedfields– Remainingconcerns
• Discussionrestrictedtopointsources,butprinciplesapplytoall
Tuesday,August3,2010 GeminiDataReducAonWorkshop 2
NeedforPhotometry
• “Low”dispersionSEDs– Colorsofobjects‐>Temp,gravity,abundance,redshiX
• RelaAveBrightnessofobjects– CMDs,distancemeasurement,exAncAon,etc.
• Timevariabilityofsourcebrightness– Stellarmasses,Distances,PulsaAon,etc,etc.
Tuesday,August3,2010 GeminiDataReducAonWorkshop 3
IdealvsPossible
Tuesday,August3,2010 GeminiDataReducAonWorkshop 4
Whatismeasured?
Tuesday,August3,2010 GeminiDataReducAonWorkshop 5
WemeasureaquanAtywhichdependsonexAncAonandeffecAvebandpass:
StandardizaAon• Absolutestandards– Inphysicalunits,e.g.ergscm‐2s‐1Hz‐1
• RelaAvestandards– Intermsofareferencestandardstar(or`basket’ofstars)
• SourcesofUncertainty– Transmissionthroughatmosphere– Systemresponse:fromtopoftelescopetoresponsedata
– Timedependenceinabove
Tuesday,August3,2010 GeminiDataReducAonWorkshop 6
CommonFormalism
• MeasurestandardstarsatdifferentairmassesX,andindifferentpassbands,B&V,say.
b=P+B+αX+β(B‐V)+γ(B‐V)2
v=Q+V+ζX+η(B‐V)+θ(B‐V)2Solvecoeffs,andapplyto“unknowns”
(recallthatthesearemagnitudes,orlogsofintensity)
Whythe`colorterms’?
IslineardependenceonXok?
Tuesday,August3,2010 GeminiDataReducAonWorkshop 7
Λ
TheEffectsofSystem`DriX’
Tuesday,August3,2010 GeminiDataReducAonWorkshop 8
OtherMusictoKeepYouAwake
• Device/SystemLinearity?• CTEorlackthere‐of,anditseffects• GeometricalProjecAonofSkyonDetector• DetectorNoiseCharacterisAcs• SystemOddiAes–e.g.cross‐talk• ShuyerPerformance–Amingerrors,shading• VignePng• ScayeredlightandmiAgaAon• FlatFieldingandFringing• ‘Pupil’GhostsTuesday,August3,2010 GeminiDataReducAonWorkshop 9
Pre‐ProcessingImages• SourceSignalondetectorismodulatedbydeviceresponse
andarAfacts,andaccompaniedbynoise.
• Rawimagesmustbeprocessedtoremoveinstrumentsignatures– Biases,flats(pixeltopixelvariaAons),geometricaldistorAons,fixed
payerns,darkcurrent
• Noiseshouldbetrackedtoenable:– OpAmaldataextracAon
– EsAmateuncertainAes
• Pre‐processingsteps(whichmiAgatesystemaAcerrors)canaddrandomnoise.Stepsshouldbedesignedtoaddminimalnoise.
Tuesday,August3,2010 GeminiDataReducAonWorkshop 10
Flatfields
• Flatfieldsmappixelvaluetosurfacebrightnessonallimagescales,iffFFsourceprovidesuniformilluminaAon
• `UniformIlluminaAon’==Constantintensityintegralatallrelevantincidentanglesattelescopepupil.HardtoperfectinpracAce,forwidefields.
• DomeflatsvsSkyFlats@twilightvsdarkskyflats
• FFcorrecAoncorrectsforsurfacebrightness:whenthereisgeometricaldistorAon,theydonotrestoreintegratedfluxes!
Tuesday,August3,2010 GeminiDataReducAonWorkshop 11
Tuesday,August3,2010 GeminiDataReducAonWorkshop 12
MiAgaAonforPointSourcePhotometry
RecAfyImagesoeachpixelprojectsequalsolidangleonskybyresampling.
OR
ApplyacorrecAontoimageforpixelarea,i.e.dividebyrespecAvepixelarea.9(usefulwhenimagesareunder‐sampled)
NoiseDomains
Tuesday,August3,2010 GeminiDataReducAonWorkshop 13
CaseB(readnoisedominated)e.g.100electronRDNineverypixel
CaseCBackgrounddominated:Addanother10^6electronskybackgroundineverypixel
Ifallthelightwerein1pixel,thenCaseBSNR~175,andCaseCSNR~37!!
Tuesday,August3,2010 GeminiDataReducAonWorkshop 14
Needfor`AlltheLight’
• Notallimageshavethesameseeing–soneedallthelighttocomparebrightnessindifferentexposuresorevenonsameexposureifvaryingPSF.
• Brightstarsarelessvulnerabletototallight• EventotallightneedssurrogateinpracAce:PSFvs.scayeredlightwings
• Butmeasuring`allthelight’isproblemaAcforfaintstars…..
Tuesday,August3,2010 GeminiDataReducAonWorkshop 15
OpAmalS/Nvs‘All’thelight
Tuesday,August3,2010 GeminiDataReducAonWorkshop 16
ThingstoConsider
• PSFvariesfromexposuretoexposure• Totallightgoesto`infinity’– HowtokeepfracAonmeasuredconstacrossallimages?Orhowlargemusttheaperturebe?
– Seeingvsscayering• Largeaperturesarebadforfaintstars– RelaAveordifferenAalphotometry– Renormalizetolargeapertures(ifPSFconstant)usingcorrecAonsderivedfrombrightstars
Tuesday,August3,2010 GeminiDataReducAonWorkshop 17
PSFfiPng
I(x,y) = I0 f( x‐x0 , y‐y0 ) + IB(x,y)
(PSF)
IfIB(x,y) = IBis flatovertheextentofthePSF,and
Iffisknown,andI(x,y)aregiven,wecansolvefor
x0 , y0 , IB , I0 ( linear in IB , I0 ; non‐linear in x0 , y0 )
Tuesday,August3,2010 GeminiDataReducAonWorkshop 18
CharacterisAcsofaPSFfit
• APSFisamodelderivedfrombrightstarswhereSNRisnotaconcern
• APSFfitisamaximumlikelihood,ormostprobablecharacterizaAonofapointsourceimage,iffiPngisdoneconformingtoSNRofindividualpixels:I0 is thus the best possible measure of a point source intensity in the sense of op>mal S/N.
• IfPSFisconstantacrosstheimage,thenI0 isbestrelaAvephotometryonagivenimage
• ErrorscanbeesAmatedfromfitresidualsTuesday,August3,2010 GeminiDataReducAonWorkshop 19
Tuesday,August3,2010 GeminiDataReducAonWorkshop 20
Tuesday,August3,2010 GeminiDataReducAonWorkshop 21
IfChi‐squareIunexplainablyhigh,thenitmayindicatethatadoptedmodelisnotcorrect.Non‐stellarobject?
AbasisforclassificaAonbasedonimagemorphologyIsmodelforCRbeyerthanforpointsource?Ismodelfor“galaxy”beyerthaneither?
Is2‐starmodelbest?etc.
The‘ApertureCorrecAon’• PSFfiyedI0 ,doesnotrepresentallofthelight,andsocannotbecomparedacrossimagesunless:– I0 isusedinwithintegraloff( x‐x0 , y‐y0 )
– Meaningful only if PSF is known exactly » Not straighIorward in prac>ce
– I0 isusedwithasurrogatefootprintinlieuoftheintegraloff( x‐x0 , y‐y0 ),
AND theresultisnormalizedtothetruetotalintensityviaobjectswithhighSNR,i.e.theaperturecorrecAon.
Tuesday,August3,2010 GeminiDataReducAonWorkshop 22
Pointstoponder:
• WhatifPSFusedisnotaperfectmatchtotruePSF?
• WhatifPSFisnotconstantacrosstheimage?• HowbesttodetermineIB?• WhatifIB isnotflatacrossPSFarea?Thecrowdedfieldproblem
• WhatifposiAonsx0,y0areindependentlyknown?
• Notethatpixelsaretreatedasindependent–arepixelvaluesreallyuncorrelated?
Tuesday,August3,2010 GeminiDataReducAonWorkshop 23
ImperfectPSF
• ImperfecAonsinmodelsPSFwrtrealonegenerates`extra’residualsinfit– Tozerothorder:
• makingsameerroronallobjects• degradesfitquality,andoveresAmateserrors• poor`subtracAon’offiyedobjects–affectscrowdedfieldphotometry
– Subtlerissues:• SinceS/NvsrisfuncAonofbrightness,caninducenon‐lineariAeswithbrightness,butseentoworkfineinpracAceunlessmis‐matchisquitesevere.
Tuesday,August3,2010 GeminiDataReducAonWorkshop 24
PSFnotconstantacrossimage
• CanhappeninpracAce,e.g.:– especiallyinwidefieldimagers,duetofield‐flayeningerrors
– inadapAveopAcs,duetoscaleofiso‐planaAcpatches
• KeytomiAgaAonisthat`aperture’integratedbrightnessshouldnotvary,so– mapaperturecorrecAonasfuncAonofposiAononFOV• EasierforwidefieldimagersthanforAO,becausemethodhingesonavailabilityofhighSNRobjects
Tuesday,August3,2010 GeminiDataReducAonWorkshop 25
CrowdedFields
• IB underobjectAisaffectedbyPSFofneighboringobjectB.BaffectedbyC,etc.&soon.
• IB isnotconstantunderPSF• MiAgaAonstrategies:– DAOPHOTway:clusterfitallobjectswithchainofinfluence
– DoPHOTway:iteraAvelyfitobjects–brighteronesfirst
Tuesday,August3,2010 GeminiDataReducAonWorkshop 26
IC1613(C‐band)ImagevsResidual
Tuesday,August3,2010 GeminiDataReducAonWorkshop 27
IC1613(C‐band)ImagevsModel
Tuesday,August3,2010 GeminiDataReducAonWorkshop 28
Pre‐knownPosiAonsFixed
I(x,y) = I0 f( x‐x0 , y‐y0 ) + IB(x,y)
(PSF)
• Ifx0andy0 aresomehowknown,thenthePSFfitislinear– Faster, easier, and smaller correla>ons in params.
Tuesday,August3,2010 GeminiDataReducAonWorkshop 29
Tuesday,August3,2010 GeminiDataReducAonWorkshop 30
DON’TPANIC,butholdontotowel!
1. Observestandards– OFTEN– Coverrangeofcolorsandairmasses
2. Getadequateflatfields(andfringeframes)soasnottoaddnoise
3. CheckSkycondiAons– OFTEN– Watchforcon‐trails
4. Getbiasframesthroughoutthenight5. Makeuseofcloudy/shutAme– VerifyshuyercorrecAons– Verifylinearity
Tuesday,August3,2010 GeminiDataReducAonWorkshop 31
Tuesday,August3,2010 GeminiDataReducAonWorkshop 32