Photometry & Digital Images - NOAO · 2010. 8. 5. · Photometry & Digital Images A. Saha Tuesday,...

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.


IdealvsPossible


Whatismeasured?


WemeasureaquanAtywhichdependsonexAncAonandeffecAvebandpass:

StandardizaAon•  Absolutestandards–  Inphysicalunits,e.g.ergscm‐2s‐1Hz‐1

•  RelaAvestandards–  Intermsofareferencestandardstar(or`basket’ofstars)

•  SourcesofUncertainty– Transmissionthroughatmosphere– Systemresponse:fromtopoftelescopetoresponsedata

– Timedependenceinabove


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?


Λ

TheEffectsofSystem`DriX’


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.


Flatfields

•  Flatfieldsmappixelvaluetosurfacebrightnessonallimagescales,iffFFsourceprovidesuniformilluminaAon

•  `UniformIlluminaAon’==Constantintensityintegralatallrelevantincidentanglesattelescopepupil.HardtoperfectinpracAce,forwidefields.

•  DomeflatsvsSkyFlats@twilightvsdarkskyflats

•  FFcorrecAoncorrectsforsurfacebrightness:whenthereisgeometricaldistorAon,theydonotrestoreintegratedfluxes!



MiAgaAonforPointSourcePhotometry

RecAfyImagesoeachpixelprojectsequalsolidangleonskybyresampling.

OR

ApplyacorrecAontoimageforpixelarea,i.e.dividebyrespecAvepixelarea.9(usefulwhenimagesareunder‐sampled)

NoiseDomains


CaseB(readnoisedominated)e.g.100electronRDNineverypixel

CaseCBackgrounddominated:Addanother10^6electronskybackgroundineverypixel

Ifallthelightwerein1pixel,thenCaseBSNR~175,andCaseCSNR~37!!

Needfor`AlltheLight’

•  Notallimageshavethesameseeing–soneedallthelighttocomparebrightnessindifferentexposuresorevenonsameexposureifvaryingPSF.

•  Brightstarsarelessvulnerabletototallight•  EventotallightneedssurrogateinpracAce:PSFvs.scayeredlightwings

•  Butmeasuring`allthelight’isproblemaAcforfaintstars…..


OpAmalS/Nvs‘All’thelight


ThingstoConsider

•  PSFvariesfromexposuretoexposure•  Totallightgoesto`infinity’– HowtokeepfracAonmeasuredconstacrossallimages?Orhowlargemusttheaperturebe?

– Seeingvsscayering•  Largeaperturesarebadforfaintstars– RelaAveordifferenAalphotometry– Renormalizetolargeapertures(ifPSFconstant)usingcorrecAonsderivedfrombrightstars


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 )


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


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.


Pointstoponder:

•  WhatifPSFusedisnotaperfectmatchtotruePSF?

•  WhatifPSFisnotconstantacrosstheimage?•  HowbesttodetermineIB?•  WhatifIB isnotflatacrossPSFarea?Thecrowdedfieldproblem

•  WhatifposiAonsx0,y0areindependentlyknown?

•  Notethatpixelsaretreatedasindependent–arepixelvaluesreallyuncorrelated?


ImperfectPSF

•  ImperfecAonsinmodelsPSFwrtrealonegenerates`extra’residualsinfit– Tozerothorder:

•  makingsameerroronallobjects•  degradesfitquality,andoveresAmateserrors•  poor`subtracAon’offiyedobjects–affectscrowdedfieldphotometry

– Subtlerissues:•  SinceS/NvsrisfuncAonofbrightness,caninducenon‐lineariAeswithbrightness,butseentoworkfineinpracAceunlessmis‐matchisquitesevere.


PSFnotconstantacrossimage

•  CanhappeninpracAce,e.g.:– especiallyinwidefieldimagers,duetofield‐flayeningerrors

–  inadapAveopAcs,duetoscaleofiso‐planaAcpatches

•  KeytomiAgaAonisthat`aperture’integratedbrightnessshouldnotvary,so– mapaperturecorrecAonasfuncAonofposiAononFOV•  EasierforwidefieldimagersthanforAO,becausemethodhingesonavailabilityofhighSNRobjects


CrowdedFields

•  IB underobjectAisaffectedbyPSFofneighboringobjectB.BaffectedbyC,etc.&soon.

•  IB isnotconstantunderPSF•  MiAgaAonstrategies:– DAOPHOTway:clusterfitallobjectswithchainofinfluence

– DoPHOTway:iteraAvelyfitobjects–brighteronesfirst


IC1613(C‐band)ImagevsResidual


IC1613(C‐band)ImagevsModel


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.


DON’TPANIC,butholdontotowel!

1.  Observestandards–  OFTEN–  Coverrangeofcolorsandairmasses

2.  Getadequateflatfields(andfringeframes)soasnottoaddnoise

3.  CheckSkycondiAons–  OFTEN–  Watchforcon‐trails

4.  Getbiasframesthroughoutthenight5.  Makeuseofcloudy/shutAme–  VerifyshuyercorrecAons–  Verifylinearity


Photometry & Digital Images - NOAO · 2010. 8. 5. · Photometry & Digital Images A. Saha Tuesday,...

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