Week7
•  “Midterm”examinclassnextThursday,March24
•  Eveningsessionsthisweekarepythondataanalysispackageorientedin
supportofLab3writeupsandansweringPrelab4quesGons.
–  GiventheinterrupGonfortheexamthenoGonalduedatewillbeMarch26.
•  Dayassignment4willbeavailableshortly(andin-partintendedfor
midtermexampreparaGon).
•  Lab4(makingbeauGfulthree-colorcalibratedimageswiththeFan
MountainRRRT)willbeoutearlynextweek.
–  ObservinghappenstheweekaRermidterm.
•  APOobservingGmehasbeensecuredforthefinalassignment.“A-half”
ontheeveningofMay6.
•  Topicsthroughthemidterm:
–
–
–
–
PhotondetecGon/Imagingdevices
PoissonstaGsGcs/noise/background
Determiningdetector“gain”withPoissonstaGsGcs
Astronomicalphotometryandfilters
•  Aperturevs.PSFfitphotometry
QuanGfyingLight:PhotonDetecGon
•  ThreemethodsforconverGngphotonsinto“data”
1.  DirectelectromagneGcdetecGon
•  ElectromagneGcwavesdrivecurrentsinanelectricalconductor.Amplifiers
enabledirectmeasurementofamplitude(signal)vs.frequencyof
oscillaGon.
àRadio…savethatmethodforadifferentclass
2.  PhotoncounGng(conversionofphotonsintofreeelectronsinfreespaceor
withinanotherwiseelectrically“insulaGng”solidmakingitmoreconducGve)
•  Thephotoelectriceffectdescribestheabilityforaphotontoliberatean
electronfromametalifthephotoncarriesenoughenergytoovercomethe
potenGalbarrierbindingtheelectrontothemetal.
–  DirectevidenceforthequanGzaGonofphotonenergy.
•  Similarbehaviorcanoccurinthesolidstate.
3.  Integratedphotonresponse
•  AbulkmaterialrespondstothephotonenergydepositedperunitGme.
–  IncidentradiaGonheatsa“brick”
–  Thealteredtemperatureleadstoachangein“brick”properGes–e.g.changed
electricalconducGvity.
Making“Free”ElectronswithPhotons
•  Afreedelectronisadetectableelectron(viavoltageorcurrent)
–  anelectroncanbefreeinspace--photoelectriceffect
–  oritcanbe''free''withinacrystalla`ce--solidstatedetecGon
The Photoelectric Effect
•  Metals are characterized by a work function that determines the
energy difference between the highest energy state for an electron
within the metal and the energy of an electron in free space.
•  A photon with energy in excess of this work function will liberate a
free, detectable, electron -- the photoelectric effect
.
Making“Free”ElectronswithPhotons
•  Afreedelectronisadetectableelectron(viavoltageorcurrent)
–  anelectroncanbefreeinspace--photoelectriceffect
–  oritcanbe''free''withinacrystalla`ce--solidstatedetecGon
The Photoelectric Effect
•  Metals are characterized by a work function which determines the
energy difference between the highest energy state for an electron
within the metal and the energy of an electron in free space.
•  A photon with energy in excess of this work function will liberate a
free, detectable electron -- the photoelectric effect.
•  Warmmetalswillemitfreeelectrons,thosewiththermalenergyinexcessofthe
material'sworkfuncGon
•  GivenaBoltzmanndistribuGonforthethermalelectrons,thehighenergy
tailwithenergyofafewkTwillbeasourceoffree(usuallyundesirable)
electronsifafew*kTexceedstheworkfuncGonàthermionicemission.
Maxwell-BoltzmannDistribuGon
•  Thermionicemissionandatmosphericescapebothdependonthe
fewkTtailoftheMaxwell-BoltzmannDistribuGon.
ThePhotoelectricEffect
•  PhotomulGpliersarebasedonthecascade
amplificaGonofindividualelectronsliberated
bythephotoelectriceffect
•  WorkfuncGonsformetalsaretypicallyafew
electronvolts
–  1eV=1240nm
WorkFuncGonsofMetals
•  Typicallyalloysorceramicsareusedtomake
photocathodeswithmoreinteresGngwork
funcGons.
http://hyperphysics.phy-astr.gsu.edu/hbase/tables/photoelec.html
PhotomulGplierShortcomings
●
●
●
●
PoorwavelengthcoverageduetolargeworkfuncGonofmaterials
(limitedtovisibleoperaGngwavelengthwithsomeexcepGons)
Poorquantumefficiency(<20%conversionofphotonstoelectrons)
Thermallyemihedelectrons(knownasdarkcurrent)
Largesingle-detectorarea
Onebigadvantage→fastphotoncounGng
Onebigdisadvantageàonetube=onemeasurement
SolidStateDetecGon:Metalsvs.Insulators
•  AtT=0K,theclassicalworldcontainsonlyconductorsandinsulators.
•  Amaterial’sproperGesdependonhowatomicenergylevelsfillout
degenerateenergystatesasinteratomicdistancedecrease.
•  Materialswithgapsareinsulators.
SolidStateDetecGon:Semiconductors
•  Materialswithsmall(<2eV)gapsaretechnicallyinsulators,butatroom
temperatureelectronsatthetopofthe“Fermisea”getkickedintothe
“conducGonband”makingthemweakconductors–semiconductors.
SolidStateDetecGon:Semiconductors
•  NotonlycanthermalexcitaGonyieldconducGonbandelectrons,but
photonscanalsokickelectronsupintotheconducGonband–analogous
tothephotoelectriceffect.
SolidStateDetecGon:Semiconductors
•  Technicallytheelectronisnotsomuch“free”inasemiconductorasitis
“borrowed”.
•  PhotonexcitaGoncreatesanelectronandacorresponding“hole”both
areconducGve.
–  Iftheyfindoneanothertheyrecombine.
–  Aslongastheyarekeptseparatetheycanbedetected.
•  Asacurrentiftheychangetheresistanceofthematerial.
•  Asavoltageiftheyarecollectedonacapacitor.
SemiconductorDetectors:Bandgaps
•  PhotoexcitaGononlyoccursifhν>bandgapenergy.
•  Differentmaterialshavedifferent“cutoff”wavelengths.
SemiconductorDetectors:Bandgaps
•  PhotoexcitaGononlyoccursifhν>bandgapenergy.
•  Differentmaterialshavedifferent“cutoff”wavelengths.
Cryogenics
•  SincedarkcurrentistheresultofthermalexcitaGon,coolthe
detectorsothatkT<<bandgapenergy.
Longer wavelength = smaller bandgap =
lower operating temperature.
ImagingDevices
•  Becausethesolidstatedetectormaterialsarecrystalline(e.g.
silicon)thesamecrystalgrowthtechniquesusedtomakeintegrated
electroniccircuitscanbeappliedtodetectorsthemselves.
–  EnablestheconstrucGonofprecisionstructuresonthesubmicronscale
containingbothelectronicsanddetectors–Arrays!
CCDArchitecture
Test
open shutter
closed shutter
Note that bad things can happen when
buckets overflow (saturation).
CCDvs.CMOS
•  CCD’sdragchargetoadesGnaGonamplifier.
–  Good:thefewamplifiersonthechipcanbeengineeredtobeverysensiGve.
–  Bad:chargecanbelostandsmearedalongtheway,each“buckepull”hasa
longjourney,alsoreadouttakesalongGme
•  CMOSarrays“x:y”addresseachpixel.Thechargestays“local”
–  Good:fastreadout,non-destrucGvereadout(youcan“peek”atthe
accumulaGngimagewithoutdestroyingit).
–  Bad:millionsofamplifiers,buttodaytheirsensiGvityiscomparabletoor
beherthanCCD’s.
“Sandwich”InfraredArrays
http://gruppo3.ca.infn.it/usai/cmsimple3_0/images/PixelAssembly.png
•  Silicon is a terrific material because it not only makes
great detectors, but it is the basis of nearly all integrated
circuit electronics. Silicon CCD arrays can be “grown”.
•  Infrared detector material (e.g. InSb) must be attached to
silicon integrated circuits, typically through mechanical
means
•  metallic bumps of elemental indium here
http://www.flipchips.com/tutorial10.html
WhatDoYouActuallyMeasure?
Photons make electrons, but electronics of some
sort must convert that signal into a detectable
voltage.
Electrons →
Voltage
Analog to Digital
Converter (ADC)
Digital “counts”
proportional to the
voltage
For example
5V might correspond
to 65536 counts
WhatDoYouActuallyMeasure?
Photons make electrons, but electronics of some
sort must convert that signal into a detectable
voltage.
Electrons →
Voltage
Analog to Digital
Converter (ADC)
actual voltage
counts = 65536*
5V
Digital “counts”
proportional to the
voltage
For example
5V might correspond
to 65536 counts
WhereDoTheVoltsComeFrom?
Circuitry converts collected electrons into
electronically quantified information.
Electrons →
Voltage
Drive a photon-produced current
through a resistor (Ohm's Law).
Collect electrons in a (very small)
capacitor, “C”.
Analog to Digital
Converter (ADC)
Digital “counts”
proportional to the
voltage
AnalysisintheFrequencyDomain
•  AnyGmeseriessignalcanbereconstructedfromthesumofa
conGnuumofsinewavesofdifferentfrequenciesandphases.
•  The“FourierTransform”providesameansofcalculaGngthe
frequencyspectrumdecomposiGonofaGme-domainsignal.
•  |S(f)|2representsthe“powerspectrum”ofthesignal–theamount
ofpowerintheGmeseriesateveryfrequency.
AnImage!
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PoissonStaGsGcs
•  TheuncertaintyinameasurementinacounGngexperiment
(detecGngphotonsinthiscase)isequaltothesquarerootofthe
numberofcounts.
–  QuanGzaGonoflightasphotonsmakesastronomicaldetecGonacounGng
experiment
–  EvenwithaperfectdetecGonsystemwithnonoiseandnointerferinglight
frombackground,ifyoudetect100photonsfromastar,themeasurementis
uncertainby10photons,or10%.
Uncertainty = counts
PoissonStaGsGcs
•  TheuncertaintyinameasurementinacounGngexperiment
(detecGngphotonsinthiscase)isequaltothesquarerootofthe
numberofcounts.
–  QuanGzaGonoflightasphotonsmakesastronomicaldetecGonacounGng
experiment
–  EvenwithaperfectdetecGonsystemwithnonoiseandnointerferinglight
frombackground,ifyoudetect100photonsfromastar,themeasurementis
uncertainby10photons,or10%.
–  Youcan'tmeasureastartoaprecisionof1%unGlyouhavedetected10,000
photonsfromthatstar.
–  ComplicaGngthisfactisthatdetecGonsystemsaren'tperfectandthereare
contaminaGngsourcesoflightsuchastheglowofthesky(andglowofthe
telescopeinthethermalinfrared)
•  NottomenGonextraneoussourcesofnoise(detector“readnoise”in
parGcular)thatmasqueradesasaddiGonalunwantedcounts.
SignaltoNoiseRaGo
•  TradiGonally,astronomersliketoexpressthequalityofthe
detecGonofastarorspectrallineintermsoftheraGoofsignalto
noise(signal-to-noiseraGoorSNR).
–  Insimplesttermstakethenumberofsignalcountsanddividebythe
uncertainty.
–  S/N=10isameasurementwith10%precision
•  100electronsgetsyouthereifthereisnosourceofcontaminaGnglight.
–  S/N=100isameasurementwith1%precision
•  10,000electronswithoutcontaminaGon.
•  Ingeneral,ifthestaristheonlysourceofcounts,N:
AccounGngforBackgroundContaminaGon
•  Sourcesofbackgroundaddtothedetectedphotons.
–  TheseunwantedcountsthusaddaddiGonalPoissonnoise.
–  Reducingthesebackgroundsimprovesignal-to-noise
•  sharperimages(landingonfewerbackground-containingpixels)
•  selecGngfilterbandpassestoavoidskyglowandmaximizesignal
•  coolingtelescopesusedinthethermalinfrared
•  IfNisthenumberofcountsfromthestarandBisthenumberof
countsfromthebackground.
•  Considerastarwhichcoversfourpixels,eachcontaining
contaminaGngbackground,vs.astarthatcoversonlyonepixel.
–  Same“N”but4Gmeslowerbackground,B,inthesecondcase.IfBislarge
comparedwithNsensiGvityisimproved.
“ReadNoise”fromaPoissonPerspecGve
•  Theactofmeasuringthecounts,inaCCDpixelforexample,canbe
(usuallyis)inherentlynoisy.
–  Thisnoisetendstoberandom/Gaussian(i.e.thevaluebeingdrawnfroma
GaussiandistribuGonofprobability)
–  Itisthereforecharacterizedbythe“width”ofthedistribuGon,typicallyusing
theroot-mean-squared,RMS,value,whichforpureGaussiandistributed
noiseisthe“σ”ofthedistribuGon.
–  RecallthatthePoissonnoiseforanactual“count”ofNelectronsissqrt(N).
–  Althoughreadnoise,characterizedbyanRMSuncertainty,“RN”,isnot
Poissonnoise,onecanpretendthatthenoiseRNiscausedbythecollecGon
ofRN2counts.
ReadNoiseandSNR
●
Ifsourcephotonsaretheonlysourceofnoise,recall
N
SNR =
N
●
Inthepresenceofbackgroundtheunwantedbackgroundphotonsaddtothe
Poissonnoise.
●
SNR =
N
N+B
ReadnoiseactsasanaddiGonalsourceofunwantedbackground.Readnoiseis
characterizedastheRMSfluctuaGon(inunitsofelectrons)inthemeasurement
(readout)ofadetector.Toconvertthereadnoiseintotheequivalentnumber
ofelectronsthatwouldcausethatnoiseonehastosquarereadnoise.
SNR =
N = source/star electrons
B= background electrons
N
N + B + RN 2
RN= read noise in RMS electrons
CCD“Gain”
•  AsnotedmulGpleGmes,thenumbersassociatedwitheachpixelina
digitalimagearenotnecessarilyactualcountsofcollectedelectrons.
•  Firstanaside….
–  Note“electrons”intheabovesentenceasopposedto“photons”.What
counts,nopunintended,isthethingsthatactuallygetdetected/countedin
theend–theelectrons.
–  Forthesamephotonfluxlevelinafixed,say10second,integraGon,the
Poissonnoiseislowerforalowquantumefficiencydetectorcomparedwitha
highquantumefficiencydetectorbecausephotonsproducefewerelectrons.
•  BUTthehighquantumefficientdetectorwillmakethedetecGonata
highersignaltonoiseraGo,whichiswhatcounts
•  Ifthoselasttwosentencesmakesenseyou“getit”.
Recall….WhereDoTheVoltsComeFrom?
Circuitry converts collected electrons into
electronically quantified information.
Electrons →
Voltage
Drive a photon-produced current
through a resistor (Ohm's Law).
Collect electrons in a (very small)
capacitor, “C”.
Analog to Digital
Converter (ADC)
Digital “counts”
proportional to the
voltage
CCD“Gain”
•  Electronic“gain”(a.k.a.amplificaGon)accountsforthedifference
betweenmeasureddigitalcountsandcollectedelectrons.
–  10electronsmayendupontheoutputcapacitor,buttheanalogtodigital
convertermayreadthese10electronsas4digitalcounts.
•  Inthisexamplethe“gain”is2.5electronsperanalogtodigitalunit:
2.5e-/ADU
•  PoissonnoiseprovidesatooltodeterminethisCCDgain.
–  Considerasystemwithagainof100e-/ADUthatmakesmulGple
measurementsofasignalof10,000counts.
–  Giventhegain1,000,000electronswerecollectedineachmeasurement.
–  ThePoissonnoiseresulGngfromthosemillioncollectedelectronsis1000
electrons,butsincethegainissuchthatittake100electronstomakeoneADU
countthemeasuredRMSnoiseinthecountswillbe1000/100=10ADU.
–  So,inthissituaGonyouhaveasignalof10,000countsresulGnginanRMS
noiseof10counts–clearlynotPoisson,butacluetothegain.
StaGsGcallyEsGmaGngCCDGain
•  Ifthegainwereunknownintheexampleonthepreviouspageone
couldreverseengineerthevalueundertheassumpGonthatthenoise
wasPoisson.
–  YouilluminateyourCCDuniformlyandmakeabunchofmeasurementsofthe
scene,eachoneilluminatedtoameanlevelof10,000ADUcounts.
•  Atthispointyouhavenoideahowmanyelectrons10,000ADUcounts
represents.
–  GiventhatyouhaveanumberofexposuresyoupunchtheexactADUvalueof
agivenpixelineachoftheframesintoyourcalculatorandfindthestandard
deviaGon.
•  YourcalculatorspitsoutthatthestandarddeviaGonis10ADU,soclearly
notPoisson(itwouldhavebeen100ADUifitwasPoisson).
–  Youcannowask(inequaGonformbelow)whatdoesthegain,g,havetobein
ordertomakethemeasurementsagreewithPoissonstaGsGcs.
σ observed =
g * ADU average
g
σ observed =
Number of collected electrons
gain
StaGsGcallyEsGmaGngCCDGain
•  Ifthegainwereunknownintheexampleonthepreviouspageone
couldreverseengineerthevalueundertheassumpGonthatthenoise
wasPoisson.
–  YouilluminateyourCCDuniformlyandmakeabunchofmeasurementsofthe
scene,eachoneilluminatedtoameanlevelof10,000ADUcounts.
•  Atthispointyouhavenoideahowmanyelectrons10,000ADUcounts
represents.
–  GiventhatyouhaveanumberofexposuresyoupunchtheexactADUvalueof
agivenpixelineachoftheframesintoyourcalculatorandfindthestandard
deviaGon.
•  YourcalculatorspitsoutthatthestandarddeviaGonis10ADU,soclearly
notPoisson(itwouldhavebeen100ADUifitwasPoisson).
–  Youcannowask(inequaGonformbelow)whatdoesthegain,g,havetobein
ordertomakethemeasurementsagreewithPoissonstaGsGcs.
σ observed =
g * ADU average
g
σ observed =
Number of collected electrons
gain
ADU avg
g =
σ2
WhyDoYouNeedtoKnowtheGain??
•  Assigningaproperuncertaintytothemeasurementofastar’sfluxis
possiblymoreimportantthanmeasuringthefluxitself.
–  Ameasurementismeaninglessifitdoesnothaveareliablyassignedsta;s;cal
significance.
–  Forastellarfluxmeasurementextractedfromasingleimageframeproper
quanGficaGonofthePoissonnoiseistheonlymeansofassigningan
appropriateuncertainty.
CCDQuantumResponse
•  Technicallysilicondetectorssensealllightshortwardof1.05µm.
•  Justhowefficientlyvs.wavelengthdependsondetectorstructure.
–  Insimplestterms,lightmustpenetratetoandinteractinaregionwhereit
canproduceelectron-holepairsthatulGmatelysurvivetoyieldacollected
electron.
•  Electrodes may absorb photons on the
way in (short wavelengths).
•  Photons may penetrate too far before
being absorbed (long wavelengths).
CCDQuantumEfficiencyvs.Wavelength
•  TheacGve,photon-detecGnglayerinaCCDlies
withabout10micronsofthesiliconsurface
wherethereadoutstructuresaregrown
(brownatright).
•  Typicallylightshinesonthislayerthroughthe
gatestructuresusedtoshufflethecharge.
–  Thesestructuresaretransparentatlonger
wavelengthsbutbecomeopaqueintheblueand
ultraviolet.
–  SimpleCCDarchitectureshavepoorblue/UV
response.
http://hamamatsu.magnet.fsu.edu/articles/quantumefficiency.html
ImprovingBlueResponsevia“Thinning”
•  BacksideilluminatedCCD’stakeadvantageofmechanicalthinning
oftheoriginalsiliconsubstrateonwhichthedeviceisgrownto
permitilluminaGonfromthesideoppositeelectrodes.
Fluorescent coatings that convert ultraviolet photons to longer
wavelength photons can enhance ultraviolet quantum efficiency.
http://hamamatsu.magnet.fsu.edu/articles/quantumefficiency.html
OpGmizingCCDInfraredResponse
•  DetecGnginfraredphotonsrequiresathicker“acGve”layerinthe
CCD.Aspecialclassof“deepdepleGon”devicesopGmizequantum
efficiencyfortheinfrared.
F = front illuminated
B = back illuminated (thinned)
DD = deep depletion
Non-IdealDetectorBehavior
Non-IdealDetectorBehavior
Image Calibration!
How do we made a frame not only beautiful, but quantifiable.???
StellarPhotometry
•  Why?PrecisionstellarphotometryisthegatewaytoobservaGonal
astrophysics.
HR Diagram in Omega Centauri
StellarPhotometry
•  Why?PrecisionstellarphotometryisthegatewaytoobservaGonal
astrophysics.
HR Diagram in Omega Centauri
StellarPhotometry
•  Why?PrecisionstellarphotometryisthegatewaytoobservaGonal
astrophysics.
•  Time variability in pulsating stars
(top) and eclipsing binaries
(bottom).
•  Variable stars are key
“standard candles”
calibrated by amplitude and
period measurements.
•  Eclipsing binaries permit
direct measurement of
stellar dimensions and
masses, putting stellar
models to the test.
StellarPhotometry
•  Why?PrecisionstellarphotometryisthegatewaytoobservaGonal
astrophysics.
Planetary Transits
StellarPhotometry
•  Why?PrecisionstellarphotometryisthegatewaytoobservaGonal
astrophysics.
Planetary Transits…. with precision
StellarPhotometry
•  Why?PrecisionstellarphotometryisthegatewaytoobservaGonal
astrophysics.
Asteroid Light Curves