AGA5802Spectroscopy:gra4ng,filters,arcs

•  Gra$ngs•  Filters(blockingorderfilters)•  Dichroics(doublespectrophaps)•  Lineardispersionofthespectrum

•  Basicdesignofspectrographs•  Wavelengthcalibra$onlamps(arcs)

•  Grisms

Bibliography:ToMeasuretheSky,Kitchin,Lenaandothers

Prof.JorgeMeléndez1

Dispersionbyadiffrac4ongra4ng(redededifração)

2

Type--------Capacity---Trackpitchhowmanypermm(1mm=103µm)?CD--------------0.7Gb---1.6μmà103um/1,6um=625lines/mmDVD------------4.7GB---0.74μmà103um/0,74um=1351lines/mmBlu-rayDisc---25GB----0.32μmà103um/0,74um=3125lines/mm

DiffracKongraKng

3

WhilelightMicroscopicpictureofpartofadifracKongraMngof1180lines/mm©Gray,StellarPhotospheres,3rded.,Fig.3.2(p.55)

+ -

α

d

SpectrumformedbydiffracKongraKng

4hTps://opentextbc.ca/physicstestbook2/chapter/mulKple-slit-diffracKon/

graK

ng

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GraKngequaKon

dsinθ=mλ

Light

Linesareformed(construcKveinterference):

m=0,±1,±2,…

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αθ

d

dsinθ

θ

dsinα

α

θαα

d

GraKngequaKon:dsinθ+dsinα =mλm=0,±1,±2,…

GraKng

AngulardispersionofagraKng

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d(sinα+ sinθ)=mλsinθ = mλ/d � sinα

DifferenKaKngthegraKngequaKon:

-  cosθchangesonlyslowlywithλàdispersionofthegraKngdoesnotchangemuchwithwavelength

-  Dispersioncanbeincreasedathigherorders

d

ResoluKonRofthegraKngR=Nm

N:numberoflinesacrossthegraKngm:order

Example:graKng500linesmm-1inagraKngoflength=10mm,atsecondorder:R=500x10x2=104

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Thishighresolvingpowerisactuallylimitedbytheslitwidthofthespectrograph,thereforeitisrarelyachievedinpracKce.

AngularoverlapofgraKngorders

9©ToMeasuretheSky

sinθ = mλ/d � sinα

θ

λ1 = 2λ2 = 3λ3 = ... = mλm λm = λ1 /m

Freespectralrange

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λ1 = 2λ2 = 3λ3 = ... = mλm Forex.,wewouldhavethesameangleθfor:

λ1=8000Åλ2=4000Åλ3=2666Å

…λm=λ1/m

λm+1=λ1/(m+1)

order0

(m+1)λm+1=mλm

sinθ = mλ/d � sinα

DiffracKongraKng

MinimumλtoavoidcontaminaKonoftheorderm,byorderm+1

PracKcalcoverageofanorder

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Formaximumλ=λmaxatorderm,the

minimumλissetbythenextorderλm+1:

DiffracKongraKng

order0

Forexample,forλmax=9000Åat1storder,wewillhavecontaminaKonforλ = 4500 Åofthe2ndorder.Wemustintroduceafiltertoblockλ < 4500 Å,sothatwecanobservein4500-9000Å.

sinθ = mλ/d � sinα

Orderblockingfilters

12Examplesfrom1.5-mR-CSpectrograph:hTp://www.cKo.noao.edu/spectrographs/60spec/filters.html

100Tran

smission

(%)

Wavelength(A)

4000

Blocks Transmits

6000 8000 100003000 5000 7000 9000

80

60

40

20 Transmits

Blocks

Orderblockingfilters

13hTp://www.as.utexas.edu/mcdonald/faciliKes/2.7m/lcs.html

99%

90%

50%

10%

1%

Tran

smissão

Wavelength(nm)20030040050060070080090010001100

0,1%

Blocks Transmits

Redblockingfilters

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BlocksTransmits

hTp://www.noao.edu/kpno/manuals/l2mspect/

Freespectralrange(ΔλFSR)

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Thefreespectralrange(FSR)isthecoverageinλthatisnotblocked

order0

Forexample,forλmax=900nmat1storderwewouldhaveΔλFSR = 450nmàwecanobserveintherange450-900nm

Lambdaminimum:

DiffracKongraKng

BlazedgraKngs(redescomblazing)

16©Kitchin

DisadvantageofflatgraKngs:muchlightislostatorder0andotherorders.IngraKngswithblazingthefacetofeachrulinghasanangle,concentraKngmostofthelightinagivenwavelength

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BlazedgraKngsBestKlttoconcentratealllightinagivenλ:

©ToMeasuretheSky

Inthebook�ToMeasuretheSky�isα,butiswrong

sinθ+sinα=mλ/dGraKngequaKon:

sin(ε � β)+sin(β + ε)=mλ/d

sin(ε)=mλ/2dcos(β)

Blazewavelengthλb:

Blazing’sefficiency

Theefficiencyismaximumatblazewavelengthλb,withtheefficiencydecreasingto50%at:• λmin=2/3λb• λmax=3/2λbExample,λb=6000Åàwecancoverwithefficiency>50%(maxefficiency):4000–9000Å.

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Example

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Diffraction Gratings available for LCS

grating number lines/mm blaze

(Å)effective blaze (Å)

dispersion λ/ one-pixel Δλ

(TI1 CCD)

40 300 4200 3900 55041 300 7500 6000 550 42 300 10000 9200 55043 600 4000 3700 1100 44 600 7500 6900 1100 45 600 10000 9200 110046 1200 4000 3700 2200 47 1200 6000 5500 2200 48 1200 7500 6900 2200

Gratings are blazed for use in first order.

hTp://www.as.utexas.edu/mcdonald/faciliKes/2.7m/lcs.html

Importantpoints1.  Duetoblazing,thegraKngisopKmizedforaparKcular

regionofthespectrum(althoughyoucanuseseveralgraKngs,ofcourse).

2.  Duetoorderoverlapping,thespectralcoverageislimited3.  Differentelements(e.g.CCD)couldbeopKmizedfora

givenspectralregion

IscomplicatedtocoveralltheopKcalspectrum(300-1000nm)withonly1spectrograph

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�Doublespectrograph��J

Doublespectrograph(2arms)

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DoublespectrographforthePalomartelescope(5meters).REDsidecovers550-1000nmBLUEsideisop4mizedfor300-550nm

Dichroic:dichroicreflecKngcoaKngononesurface&anKreflecKoncoaKngontheopposingsurface

22hTps://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3313

Substrate:UVfusedsilica

ThorLabs:LongpassDichroicMirrors/BeamspliTers:650nmCutoffWavelength

23hTps://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3313

Dichroic:lightintodifferentλàdoublespectrograph

reflect&transmitlight

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Example:PalomarDoubleSpectrograph

300040005000600070008000900010000Wavelength(A)

Tran

smifan

ce(%

)

100

80

60

40

20

0

Reflects Transmits

GraKngsforthePalomardoublespectrograph

1stOrder UsefulRange(Å) RedCamera BlueCamera

lines/mm Blaze(Å) (toblaze1/2-intensity)

Dispersion(Å/mm)

Dispersion(Å/mm)

158[a] 7560 5000-11300 2011st[c] 1352nd[d]300[b] 3990 2700-6000 - 1401st316[a] 7150 4800-10700 1021st -600[b] 3780 2500-5700 - 711st600[a] 9500 6300-14300 541st -1200[b] 4700 3100-7100 - 361st1200 7100 4700-10700 271st 361st1200 9400 6300-14100 261st 351st

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(F)GRATINGSPECS(lines/mm,blaze,dispersion)

NOTE:"UsefulRange"givesthewavelengthlimitsatwhichdiffractedintensitydropsto1/2ofitspeakvalue(2/3and3/2oftheblazewavelength,byacommonruleofthumb).[a]silvercoaKng...canbeusedonlylongwardof3500Å.[b]canbeusedonlyinbluespectrograph.[c]firstorder.[d]secondorder.

R~1,000to10,000

Lineardispersionofthespectrum(validforbothprisms&graKngs)

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Angulardispersionofprism AngulardispersionofgraKng

Lineardispersiondx/dλ

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CCD

Lineardispersion

Exampleforprism(α=60O)

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Typicalvaluefordθ/dλ=1,39x107Om-1

Computedθfordλ=1Å

dθ=1,39x107Om-1x10-10mdθ=1,39x10-3O=5arcsec

LineardispersiononCCD?

Lineardispersiondx/dλ

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dθ/dλ=1,39x107Om-1

CCD Lineardispersion:

1degree=0,0174radiansàdθ/dλ=2,426x105radiansm-1

dx/dλ = f2 dθ/dλ=0,5mx2,426x105radiansm-1=1,21x105

dx=dλx1,21x105= 1,21x105x2Å=2,42x105x10-4µmdx=24µm.Ifpixelis12µmà2pixels

Exampleforf2=50cmEs4matedxindλ=2Å.Howmany12-µmpixels?

Typicalvaluefordθ/dλ=1,39x107Om-1

Reciprocallineardispersionp(platefactor)

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CCDLineardispersion:

p=dλ/dx= 2Å/24x10-3mmp=83Å/mm

Inlastexampledλ=2Ådx=24µm=24x10-6m=24x10-3mm

Reciprocallineardispersion:

f2

Highdispersion(highresoluKon)andlowdispersion(lowresoluKon)spectroscopyhighdispersion(spectroscopy)means:Largelineardispersionorsmallplatefactorforex.:p~5Å/mmlowdispersion(spectroscopy)means:Lowlineardispersion,i.e.largeplatefactor,porex.:p~100Å/mm

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Largeorsmallplatefactorisnotusedanymore.OnlymenKonedhereforcompleteness.

Basicdesignofspectrographs

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ProperKesofthebasicspectrograph

33©ToMeasuretheSky

Dcol

SlitWidth:wsDtel,ftel:aperture&effecKvefocaldistanceofthetelescope

Dtelftel

Angularsizeoftheslitonthesky

34©ToMeasuretheSky

Dcol

Theangularsizeoftheslitontheskyis:

Dtelftel

SlitWidth:ws

wscouldalsobethediameterofthefiber

Howtodefinethecollimator’sfocalraKof/#?

35©ToMeasuretheSky

Dcol

Dtelftel

Slitwidth(ordiameterofthefiber):ws

TheopKmaldesignmustsaKsfy:

Forfibers:

ThefibermaydegradethefocaldistanceofthetransmiTedbean,thereforetherelaKonincludesafactorgf,whichcouldbe<1,dependingontheextension&qualityofthefiber

Whatisthesizeoftheslit(orfiber)onthedetector?•  Withoutthedisperser:

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Forexample:Ifws=0,04mm,fcam=10cm,fcol=40cm

àw0=¼ws=0,01mm

However,thedisperserintroducesa(anamorphic)magnificaKonfactorran

Whatisthesizeoftheslitorfiberonthedetector(w0)?

37©ToMeasuretheSky

Dcol

Dtelftel

ran=cosα/cosθ=DCOL/DCAM

Whatisthesizeoftheslitorfiberonthedetector(w0)usingtheanglesubtendedbytheslitonthesky?

38©ToMeasuretheSky

Dcol

Dtelftel

Angleoftheslitonthesky:

Weknow

ran=DCOL/DCAM

ResoluKonδλ0ofthespectrograph

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©ToMeasuretheSky

Dcol

Dtelftel

Using:

δλ0=w0p

ran=DCOL/DCAM

Otherforms:

ResolvingpowerR(=λ/δλ0)ofthespectrograph

40©ToMeasuretheSky

Dcol

Dtelftel

Ideallytheangleoftheslitontheskyshouldbe<seeing:However,ifseeingislowerthanàuseforR

Actually,wecanhavedifferentslitsizes

TheresoluKondoesnotchangeifweusethespectrographatothertelescope,becauseitdepends

onlyonproperKesofthespectrograph

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Resolvingpowerdependsonthefocaldistanceofthespectrograph’scollimatorfCOL,theslitwidthws,anddispersionofthegraKngdθ/dλ

R = λdλ

=λ fCOLranws

dθdλ

Canweuseaspectrographdesignedforadifferenttelescope?

42

PHOENIXINFRAREDHIGH-RESOLUTIONSPECTROGRAPHAtthe2.1mthe4pixelslitis1.4arcsecwide.Atthe4mitis0.7arcsecwidehTp://www.noao.edu/kpno/phoenix/

Yes,IFthefocalraKoissimilarbetweenthespectrographandtelescopes

ThePhoenixinfraredspectrographhasf/15,andhasbeenusedatthe2.1m&4mKiTPeaktelescopes(bothf/15)andatthe8mGemini(f/16).However,theangularsizeoftheslitchangeswiththefocaldistanceofthetelescope:

ResoluKonvs.slitwidthws

•  EXAMPLEwithPHOENIXspectrograph,slitsavailable:2pixel(54µm),3pixel(81µm),and4pixel(107µm)

•  ws=4pixelsondetectoràR=50000

•  ws=2pixelsondetectoràshouldbeR=100000,butduetoproblemsintheopKcsitisactuallyR=75000

•  ws=3pixelsondetectoràshouldbeR=75000,butitisactuallyR=63000

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PhoenixspectrographatKiTPeak(2m&4m)

ResoluKonvs.slitwidthws

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Deckname Length(") Width(")Resolu4on(calculated)

Resolu4on(measured*)

Resolu4on(measured+)

B1 3.5 0.574 72,000 67,000 66,400B2 7.0 0.574 72,000 67,000 66,400B3 14.0 0.574 72,000 67,000 66,400B4 28.0 0.574 72,000 67,000 66,400B5 3.5 0.861 48,000 49,000 50,000C1 7.0 0.861 48,000 49,000 50,000C2 14.0 0.861 48,000 49,000 50,000C3 28.0 0.861 48,000 49,000 50,000C4 3.5 1.148 36,000 37,000 37,500C5 7.0 1.148 36,000 37,000 37,500D1 14.0 1.148 36,000 37,000 37,500D2 28.0 1.148 36,000 37,000 37,500D3 7.0 1.722 24,000 24,000 24,700D4 14.0 1.722 24,000 24,000 24,700D5 0.119 0.179 pinholeE1 1.0 0.400 103,000 84,000 86,600E2 3.0 0.400 103,000 84,000 86,600E3 5.0 0.400 103,000 84,000 86,600E4 7.0 0.400 103,000 84,000 86,600E5 1.0 0.800 51,000 52,000 52,000

*UsingUVcross-disperser.Averageof5Th/Arlinesnear4100A.+UsingRedcross-disperser.Averageof4Th/Arlinesnear5240A.

HIRESspectrographon10mKecktelescope

ResoluKo

nvs.slitwidth

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UVESspectrographon8mVLTtelescope

hTp://www.eso.org/sci/faciliKes/paranal/instruments/uves/doc/

UVESredarm

UVESbluearm

ResoluKonvs.slitwidthws-CoudéOPD

46

CalibraKonlamps(a.k.a.arcs)(tocalibratewavelength)

47hTp://mthamilton.ucolick.org/techdocs/instruments/nickel_spect/arcSpectra/Pixelnumber

λ=5852,49Å

λ=7245,17Å

λ=8495,36Å

NEONarc(observedwitha600lines/mmgrism)

020040080010001200

Flux

SOARGoodmanHgAr

48

λ=3650,146Å

λ=8667,944Å

λ=6965,431Å

λ=5460,735Å

HgArarc600l/mm

Goodman/SOAR

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Grism=GraKng+Prism

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ThedeviaKonofthelightbeambytheprismiscompensatedbythedeviaKonduetothegraKngàlightpassesstraightthrough

Theinstrumentcouldserveasanimager,removingthegrismfromtheopKcalpath

Grisms

CCD

Cameralens

Collimator

hTp://mthamilton.ucolick.org/techdocs/instruments/nickel_spect/hw_overview/

51EFOSC2@ESONTT

52.�@ISaviane

53

PunchingEFOSC2MOSPlates

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X-Shooter@ESOVLT

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FuncKonaldiagramofX-shooter.ThelightpathrunsfromthetoptotheboTomofthefigure.EachelementisdescribedinSect.2.

59

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Fig.4.ThecombinedefficiencyofthetwodichroicbeamspliTers.Inblue:reflecKononthefirstdichroic;inorange:transmissionthroughthefirstdichroicandreflecKonontheseconddichroic;inred:transmissionthroughbothdichroics.

61

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However,asGeministaff,wehavenovestedinterestinbuildinganinstrument,soourchiefpurposeistoencouragefurtherdebateandout-of-the-boxthinking.

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Slidesfrom2017

•  GraKngequaKonfollowingthebook“ToMeasuretheSky”

66

Construc4veinterferenceinreflec4ongra4ngs

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Whenexi4ngthegra4ng,theop4calàpathofraysX&YdifferbyΔτ=AB–CD=σsinα � σsinρ àΔτ=σsinα + σsinθ

σsinα+σ sinθ=mλ

α

σθ

αρ

ρ = 360 � θ

α

α

ρρ

AB=σsinαCD=σsinρ

X Y

Construc4veinterferencewhenΔτ=m λ , m=0,±1,±2,…

Gra4ngequa4on:

©ToMeasuretheSky

68

σ  sinα+σ sinθ=mλ

orderm=0,±1,±2,…

Gra4ngequa4on:

©ToMeasuretheSky

AlightbulbofaflashlightseenthroughatransmissiongraKng,showingthreediffractedorders.Theorderm=0correspondstoadirecttransmissionoflightthroughthegraKng.InthefirstposiKveorder(m=+1),colorswithincreasingwavelengths(frombluetored)arediffractedatincreasingangles.

Construc4veinterferenceintransmissiongra4ngs