Week9
•  DayAssignment4dueApril5(extended)
–  Because….WatchoutforthatMoon
•  Lab4sourceselecDonandpre-labworkineveningsessionsthis
week.
–  April1,2,and3aretargetdatesforgoingtoFanMountain.
–  Pre-lab4isavailable(andfun).Prelab4willbeconductedenDrelyinthe
Tue/Wedeveningsessions.
•  Lab3noDonalduedateisApril1.
–  NoteyouhavetosharereducDonsofyourpersonalobservaDonsusing
python/SEPandpostedonthesharedGoogledoc
•  Onthehorizon
–  Lab5–spectroscopy
–  Finalproject–competeforAPOobservingDme…anduseit.
•  Topics
–  CCD’swartsandall
–  SourceextracDon(aperturevs.PSFphotometry)
–  ImagecalibraDon
Non-IdealDetectorBehavior
CCDTerminologyReminders
•  ChargeTransferEfficiency–ThefracDonofchargethatsurvivesthe
transferfromonewelltoanother.
–  Ina2048x2048deviceasinglechargepacketcangettransferredupto4096
Dmes.
–  IftheCTEis0.9999nearly1/3ofthechargewillbelostbeforeitgetstothe
output(=0.99994096)-atleastforthemostdistantpixel
–  CTEcanbedifferentmovingchargeindifferentdirecDons
CTE
•  Residualchargecanbe“trapped”andreleasedinsubsequentreadouts.
http://www.stsci.edu/instruments/wfpc2/Wfpc2_hand/HTML/W2_43.html
CCDTerminologyReminders
•  ChargeTransferEfficiency–ThefracDonofchargethatsurvivesthe
transferfromonewelltoanother.
–  Ina2048x2048deviceasinglechargepacketcangettransferredupto4096
Dmes.
–  IftheCTEis0.9999nearly1/3ofthechargewillbelostbeforeitgetstothe
output(=0.99994096)-atleastforthemostdistantpixel
–  CTEcanbedifferentmovingchargeindifferentdirecDons
•  PixeldwellDme
–  Chargehastobeshieedandthentheoutputamplifierhastosegletoa
stablevalue.
•  TypicaldwellDmesaretensofmicroseconds
•  ReadoutDmesforastronomicalCCD’scanbeminutes.
•  ReadoutDme=dwellDme*numberofpixels
–  DwellDmecanbereducedattheexpenseofincreasingreadnoise.
–  ReadoutDmecanalsobereducedbyhavingmulDpleamplifiers.
SaturaDon •  ACCDpixelhasalimitedcapacitytocollectelectronsbefore
overflowingthepotenDalwell.
–  CCDsaturaDonisspecifiedintermsof“well-depth”inelectrons.
–  OverflowofCCDwellscanleadtoimagefeatureslike“blooming”
SaturaDon •  ACCDpixelhasalimitedcapacitytocollectelectronsbefore
overflowingthepotenDalwell.
–  CCDsaturaDonisspecifiedintermsof“well-depth”inelectrons.
–  OverflowofCCDwellscanleadtoimagefeatureslike“blooming”
SaturaDon •  ACCDpixelhasalimitedcapacitytocollectelectronsbefore
overflowingthepotenDalwell.
–  CCDsaturaDonisspecifiedintermsof“well-depth”inelectrons.
–  OverflowofCCDwellscanleadtoimagefeatureslike“blooming”
Linearity
•  ACCDoutputamplifierisacapacitorandconvertsstoredcharge(Q)
toavoltage(V)àV=Q/C
–  Theoutputvoltage,intheory,shouldbelinearlyrelatedtoaccumulated
charge.
–  InrealitythestoredchargechangestheeffecDvegeometry,andthusthe
capacitance,ofthecapacitorandtheoutputdeviatesfromthelineartrendas
theaccumulatechargeapproachesfullwell.
Reality
Ideal
CosmicRays
•  CCDpixelsareexcellentdetectorsofanythingthatcreateselectronholepairs.
–  Asidefromvisiblephotons,energeDcparDclesproduce“ionizaDons”
proporDonaltotheirenergyandthusmanydetectableelectronsperevent.
–  FortunatelycosmicrayeventshavePSF’sunlikethoseofstars–oeenlimited
toasinglepixel.
CosmicRays
•  CCDpixelsareexcellentdetectorsofanythingthatcreateselectronholepairs.
–  Asidefromvisiblephotons,energeDcparDclesproduce“ionizaDons”
proporDonaltotheirenergyandthusmanydetectableelectronsperevent.
–  FortunatelycosmicrayeventshavePSF’sunlikethoseofstars–oeenlimited
toasinglepixel.
https://www.youtube.com/watch?v=IF0-wpXBulk
CosmicRayRemoval
•  Cosmicraysaresparselydistributed.InmulDpleexposuresonthe
sametargetcosmicrayhitswillunlikelyilluminatethesamepixel.
•  MedianfilteringortrimmedaveragingcanlargelymiDgatethe
effectsofcosmicrays(andotherbadlybehavedpixels).
SkyBackground:Medianvs.Mean
•  ThemedianstaDsDc(themiddlevalueinasortedlistofnumbers)is
agoodesDmateofthemeanand,inalargesample,largelyimmune
toafewsevereoutliers.
TrimmedAverage
•  DeterminethestandarddeviaDonoftheensemble,rejectvalues
morethanNsigmafromthemean,iterate(becausetheoutlierswill
iniDallyinflatetheesDmateofthestandarddeviaDon).
DarkCurrent
•  Sinceelectron-holepairscanbecreatedbythermalexcitaDon
(exacerbatedbycrystaldefects/impuriDes)thesethermalelectrons
areanaddiDonalsourcebackground.
–  Darkcurrentcanbemeasuredwiththearrayshugeredfromthesky.
–  Sincedarkcurrentistemperaturedependent,astabledetectortemperature
isimportanttowell-calibratedobservaDons.
•  Ifthedarkcurrentis“brighter”thantheskybackgroundthen
observaDonalsensiDvitysuffers.
Hot/BadPixels
•  InfraredarraystendtohavemorecosmeDcdefectsthatCCDs.
–  Individualpixelscansufferfromhighdarkcurrentduetolocaldefects.
–  Individualpixelscanhaveexcessivelyloworzeroquantumefficiency.
–  CCD’shavetheirproblemsaswellsuchasbadcolumns.
Dithering
•  Shieingthetargetonthe
arraypermitsthefiltering
ofbadpixelsviaa
median/trimmedaverage
sinceabadpixelwilllikely
landonceonagiven
locaDononthesky.
Bias
•  ACCDplusitselectronicsusuallyproducesarepeatablepagernwhen
readoutwithzerointegraDonDmeandnolightfallingonthedevice.
–  This“bias”ispresumedtobeanunderlyingpagernforeveryexposureandis
subtractedoutaspartofstandardimageprocessing.
http://www.stsci.edu/hst/acs/documents/handbooks/currentDHB/acs_Ch43.html
Shugers
•  Sincereadoutdragsascene(oratleastitscharge)acrossaCCDthe
CCDmustbeblockedfromreceivinglightduringthereadout.
•  IntheabsenceofashugertheimageontheCCDwouldbestreaked.
–  Streakedstars,bytheway,havetheiruses….
Shugers
•  Sincereadoutdragsascene(oratleastitscharge)acrossaCCDthe
CCDmustbeblockedfromreceivinglightduringthereadout.
–  ImplemenDngashugercanbetricky,astheshugermustcover/revealthe
arraysothateverypixelhasequalexposureDme.
–  ImageprocessingmayincludeaknownshugercorrecDonforexposureDmevs.
posiDononthearray–shugersdon’tnecessarilyhavetobeperfect.
FrameTransferCCD’s
•  Providingalight-shieldedchargestorageareamakesshugerless
CCDreadout
–  Andmaximizesefficiencybyreadingoutthepreviousresultwhilethenext
imageisexposing).
http://www.andor.com/learning-academy/ccd-sensor-architectures-architectures-commonly-used-for-high-performance-cameras
MatchingPixelScaletoImageInformaDon
•  Seeing/diffracDondictatestheminimumextentofpointsource
images–typicallyclosetoaGaussianPSF.
•  Pixelshaveafinitesize,welldefinedforaparDcularCCDarray,and
typicallyoforder10micrometers
•  OpDcspermitconversionoftelescopefocallengthtoavaluethat
matchesthePSFwelltothepixelsampling.
•  TheNyquistTheoremprovidesguidancetothecoarsestreasonable
sampling.
–  ThesamplingtheoremappliestoreconstrucDonofimageswithfidelity.
–  IfyouareonlyinterestedinthefluxofasourceandnotitsposiDonorshape
youcangetawaywithyourstarbeingsmallerthanapixel.
ImagesasaConvoluDonof“Reality”andaPSF
•  PSF=PointSpreadFuncDon=Thefocalplaneresponseofa
telescope/opDcalsystemtoatargetthatisatruepointsource.
–  TypicallystarsproduceexcellentrepresentaDonsofthesystem’sPSF
–  PSF’scanbevariableacrossthefieldofviewofanimagerorinDmewith
changingfocus,forexample.
Don’tForgettoAddNoiseandDetectorIdiosyncrasies
TheNyquistTheorem
•  IfyouaresamplingaDmedomainsignal,yoursamplingfrequency
determinesthesignalfrequenciestowhichyouhaveaccess.
•  The“NyquistFrequency”istwicethehighestfrequencyyoudesire
tosamplereliably.
–  DetecDngthe400Hzcomponentofasignalrequiressamplingatatleast
800Hz.
–  Ifsamplingat800Hz,frequenciesabove400Hzwillbe“aliased”toother
(lower)frequencies.
SpaDalFrequency
•  ImagefeaturescanbedescribedintermsofspaDalfrequency–the
rateofoscillaDonbetweenbrightanddark.
–  Consider,forexample,“linespermillimeter”or“dotsperinch”
–  ImagesarecomposedofsuperposiDonofdifferentspaDalfrequencieswith
differentphases(andindependentxandyamplitudesforagivenfrequency)
–  FourierTransformsyieldthespaDalfrequencycomponentsofanimage.
NyquistSamplingofanImage
•  JustlikesamplingaDmedomainsignal,twosamplesperspaDal
scaleofinterestrepresentaminimumsamplingofanimage.
•  One pixel per PSF
undersamples an image
•  Two pixels per PSF marginally
samples an image.
News
•  Lab4islooming(Sundayislookinggood)andguideisposted
–  Everyoneshouldhave
•  beenthroughprelab4.
•  dividedintogroups.
•  thoughtabouttarget,filters,and“science”objecDves.
•  sharedtargetswithothergroupsandcoursestaff.
•  readtheRRRTmanual.
•  bethinkingaboutPizza.
•  FinishthoseDayAssignment4observaDons,theMooniswaning.
–  DeadlinepushedouttoApril5togiveDme.
•  Lab3deadlineshie?
IdenDfyingtheDominantNoiseSource
ReadNoisevs.PoissonNoise
100
10
Ifsource+background<<
read_noise2,thenthenoise
equalsthereadnoise
regardlessofcounts.
1
1
10
100
Counts = source + background
Noise = source + background + read_noise 2
1000
10000
Assume gain=1 (top set of
curves) here in order to
make these equations
strictly correct.
ReadNoisevs.PoissonNoise
100
10
ReadnoisedominatesunDl
source+backgroundis
comparabletoread_noise2
1
1
10
100
Counts = source + background
Noise = source + background + read_noise 2
1000
10000
ReadNoisevs.PoissonNoise
100
10
Ifsource+background>>
read_noise2thenthenoiseis
dominatedbysqrt(noise
+background)–purePoisson.
1
1
10
100
1000
10000
If source+background >>
Counts = source + background
Noise = source + background + read_noise 2
MeasuringtheReadNoise
100
10
Ifsource+background<<
read_noise2,thenthenoise
equalsthereadnoise
regardlessofcounts.
1
1
10
100
Counts = source + background
Noise = source + background + read_noise 2
1000
10000
In the “low count” regime
(low being small compared
to RN2) you directly
measure the read noise (in
ADU units) when you
measure the frame to
frame RMS jitter in a pixel.
MeasuringtheGain
100
10
Ifsource+background>>
read_noise2thenthenoiseis
dominatedbysqrt(noise
+background)–purePoisson.
1
1
10
100
Counts = source + background
Noise = source + background + read_noise 2
1000
10000
In the high count regime the
statistics are all Poisson
(noise equal to the square root
of the number of electrons), so
measurements out here can
determine the gain of the
system.
FlatField
•  Supposeyoupointyourtelescopeataperfectlyuniformsceneand
see…
FlatField
•  Whatareyouseeing:
–  PixeltopixelresponsevariaDon.
–  GeneralilluminaDon–vignerng,
non-uniformtransmission.
–  DustontheopDcsinvariousdegrees
ofdefocus.
•  Whatareyouhoping:
–  ThispagernisstableandrepresentaDve
ofarray/pixelresponsetoincoming
starlight.
•  Stable…Dmescalesofhours?Days?
•  RepresentaDve...Didtheflatfield
illuminaDonmimicthepathofstarlight
throughthetelescope.
–  Dividingaskyimagewiththispagernwill
correctfortheseresponsevariaDonsand
restorea“flat”imageofthescenewhere
relaDvefluxesofstarsarequanDtaDvely
meaningful.
FlatFielding
÷
Science Frame
=
Flat Field
Calibrated Result
FlatFieldDataAcquisiDon
•  Inordertomeasureat“flatfield”onemust
–  Uniformlyilluminatethearray
–  CollectenoughphotonssothatthePoissonnoiseisinsignificant.
•  Dosowhileremaininginthelinearregimeofthedetector(don’tpushtoocloseto
saturaDon).
•  Howtouniformlyilluminatethearray?
–  Pointataflatfieldscreen.
•  Easiersaidthanimplemented
–  Observethetwilightsky
•  Watchoutforscageredlightfrominsidethedomeandtelescopestructure(lessof
aproblemwitha“wellbaffled”telescope.
•  UsedifferenDalskysubtracDon(takeframesasitgetsdarkerforexample)totake
outotherarrayidiosyncraciessuchasbiaspagern.
–  Frame_at_7:00pm-Frame_at_7:05pm=flatwithbiasremoved.
–  Useairglowtocreateaflatfieldfrom“science”data.
•  MedianfilterstarsoutofmulDpleditheredframes.
•  Problems:Starscars,illuminaDonisnarrowband(causes“fringing”),theairglowis
notuniform....Don’tdoit!
FringingDuetoNarrowbandIlluminaDon
•  AnalogoustoNewton’sRings,narrowbandlight(spectralline
illuminaDon)cancreateinterferencepagernsgiventhewavelengthscalestructuresinarraypixels.
http://faculty.virginia.edu/skrutskie/airglow/airglow.html
FlatFieldScreens
•  Thescreenisgrosslyoutoffocus(whichisgood)butsDllmustbe
uniformlyilluminatedwithcare.
ImageCalibraDon:What’sinaFrame?
•  AdigitalimagecontainsasuperposiDonofmanythings:source
photons,underlyingpagern(bias),darkcurrent,noise,background.
Source
Background
Dark
Bias
Read Noise
ImageCalibraDon:What’sinaFrame?
•  AdigitalimagecontainsasuperposiDonofmanythings:source
photons,underlyingpagern(bias),darkcurrent,noise,background.
–  Someofthesecomponentsarescaledbythepixelresponse(i.e.scaledbythe
flatfield).Somearenot.
Source
Background
Dark
Bias
Read Noise
What's in a Frame?
l
A digital image contains a superposition of many things: source
photons, underlying pattern, dark current, noise,
-
Some of these components contribute to Poisson noise. Some do
not.
Source
Background
Dark
Bias
Read Noise
What's in a Frame?
l
A digital image contains a superposition of many things:
source photons, underlying pattern, dark current, noise,
-
Some of these components contribute to Poisson noise. Some
do not.
Source
Background
Dark
Bias
Read Noise
Contributes to the noise as “fake”
Poisson noise equivalent counts = RN2
That is, if RN2 photons were collected
they would produce noise
sqrt(RN2) = RN
Quick and Dirty Image Calibration –
Background Subtraction
l
Assuming the flat field of the device is pretty flat – a simple
subtraction can remove some of the most offensive image
properties.
Source
Background
Dark
Bias
Read
Noise
Noise
Dark
Bias
Read
Noise
Noise
minus
Background
equals
Source
Zero: but
background poisson
noise * sqrt(2)
Zero: but
dark poisson
noise * sqrt(2)
Read Noise *
Noise
sqrt(2)
Quick and Dirty Image Calibration –
Background Subtraction
l
Assuming the flat field of the device is pretty flat – a simple
subtraction can remove some of the most offensive image
properties.
Frame 1
Source
Background
Dark
Bias
Read
Noise
Noise
Dark
Bias
Read
Noise
Noise
minus
Frame 2
Background
equals
Source
Zero: but
background poisson
noise * sqrt(2)
Zero: but
dark poisson
noise * sqrt(2)
Read Noise *
Noise
sqrt(2)
ideally zero
That is, a clean picture of the source with ~1.4 times the noise of a
typical frame.