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AGA5802Spectroscopy:gra4ng,filters,arcs
• Gra$ngs• Filters(blockingorderfilters)• Dichroics(doublespectrophaps)• Lineardispersionofthespectrum
• Basicdesignofspectrographs• Wavelengthcalibra$onlamps(arcs)
• Grisms
Bibliography:ToMeasuretheSky,Kitchin,Lenaandothers
Prof.JorgeMeléndez1
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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
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DiffracKongraKng
3
WhilelightMicroscopicpictureofpartofadifracKongraMngof1180lines/mm©Gray,StellarPhotospheres,3rded.,Fig.3.2(p.55)
+ -
α
d
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SpectrumformedbydiffracKongraKng
4hTps://opentextbc.ca/physicstestbook2/chapter/mulKple-slit-diffracKon/
graK
ng
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5
GraKngequaKon
dsinθ=mλ
Light
Linesareformed(construcKveinterference):
m=0,±1,±2,…
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6
αθ
d
dsinθ
θ
dsinα
α
θαα
d
GraKngequaKon:dsinθ+dsinα =mλm=0,±1,±2,…
GraKng
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AngulardispersionofagraKng
7
d(sinα+ sinθ)=mλsinθ = mλ/d � sinα
DifferenKaKngthegraKngequaKon:
- cosθchangesonlyslowlywithλàdispersionofthegraKngdoesnotchangemuchwithwavelength
- Dispersioncanbeincreasedathigherorders
d
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ResoluKonRofthegraKngR=Nm
N:numberoflinesacrossthegraKngm:order
Example:graKng500linesmm-1inagraKngoflength=10mm,atsecondorder:R=500x10x2=104
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Thishighresolvingpowerisactuallylimitedbytheslitwidthofthespectrograph,thereforeitisrarelyachievedinpracKce.
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AngularoverlapofgraKngorders
9©ToMeasuretheSky
sinθ = mλ/d � sinα
θ
λ1 = 2λ2 = 3λ3 = ... = mλm λm = λ1 /m
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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
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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
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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
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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
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Redblockingfilters
14
BlocksTransmits
hTp://www.noao.edu/kpno/manuals/l2mspect/
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Freespectralrange(ΔλFSR)
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Thefreespectralrange(FSR)isthecoverageinλthatisnotblocked
order0
Forexample,forλmax=900nmat1storderwewouldhaveΔλFSR = 450nmàwecanobserveintherange450-900nm
Lambdaminimum:
DiffracKongraKng
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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:
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Blazing’sefficiency
Theefficiencyismaximumatblazewavelengthλb,withtheefficiencydecreasingto50%at:• λmin=2/3λb• λmax=3/2λbExample,λb=6000Åàwecancoverwithefficiency>50%(maxefficiency):4000–9000Å.
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Example
19
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
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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
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Doublespectrograph(2arms)
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DoublespectrographforthePalomartelescope(5meters).REDsidecovers550-1000nmBLUEsideisop4mizedfor300-550nm
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Dichroic:dichroicreflecKngcoaKngononesurface&anKreflecKoncoaKngontheopposingsurface
22hTps://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3313
Substrate:UVfusedsilica
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ThorLabs:LongpassDichroicMirrors/BeamspliTers:650nmCutoffWavelength
23hTps://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3313
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Dichroic:lightintodifferentλàdoublespectrograph
reflect&transmitlight
24
Example:PalomarDoubleSpectrograph
300040005000600070008000900010000Wavelength(A)
Tran
smifan
ce(%
)
100
80
60
40
20
0
Reflects Transmits
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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
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Lineardispersionofthespectrum(validforbothprisms&graKngs)
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Angulardispersionofprism AngulardispersionofgraKng
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Lineardispersiondx/dλ
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CCD
Lineardispersion
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Exampleforprism(α=60O)
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Typicalvaluefordθ/dλ=1,39x107Om-1
Computedθfordλ=1Å
dθ=1,39x107Om-1x10-10mdθ=1,39x10-3O=5arcsec
LineardispersiononCCD?
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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
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Reciprocallineardispersionp(platefactor)
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CCDLineardispersion:
p=dλ/dx= 2Å/24x10-3mmp=83Å/mm
Inlastexampledλ=2Ådx=24µm=24x10-6m=24x10-3mm
Reciprocallineardispersion:
f2
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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.
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Basicdesignofspectrographs
32
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ProperKesofthebasicspectrograph
33©ToMeasuretheSky
Dcol
SlitWidth:wsDtel,ftel:aperture&effecKvefocaldistanceofthetelescope
Dtelftel
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Angularsizeoftheslitonthesky
34©ToMeasuretheSky
Dcol
Theangularsizeoftheslitontheskyis:
Dtelftel
SlitWidth:ws
wscouldalsobethediameterofthefiber
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Howtodefinethecollimator’sfocalraKof/#?
35©ToMeasuretheSky
Dcol
Dtelftel
Slitwidth(ordiameterofthefiber):ws
TheopKmaldesignmustsaKsfy:
Forfibers:
ThefibermaydegradethefocaldistanceofthetransmiTedbean,thereforetherelaKonincludesafactorgf,whichcouldbe<1,dependingontheextension&qualityofthefiber
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Whatisthesizeoftheslit(orfiber)onthedetector?• Withoutthedisperser:
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Forexample:Ifws=0,04mm,fcam=10cm,fcol=40cm
àw0=¼ws=0,01mm
However,thedisperserintroducesa(anamorphic)magnificaKonfactorran
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Whatisthesizeoftheslitorfiberonthedetector(w0)?
37©ToMeasuretheSky
Dcol
Dtelftel
ran=cosα/cosθ=DCOL/DCAM
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Whatisthesizeoftheslitorfiberonthedetector(w0)usingtheanglesubtendedbytheslitonthesky?
38©ToMeasuretheSky
Dcol
Dtelftel
Angleoftheslitonthesky:
Weknow
ran=DCOL/DCAM
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ResoluKonδλ0ofthespectrograph
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©ToMeasuretheSky
Dcol
Dtelftel
Using:
δλ0=w0p
ran=DCOL/DCAM
Otherforms:
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ResolvingpowerR(=λ/δλ0)ofthespectrograph
40©ToMeasuretheSky
Dcol
Dtelftel
Ideallytheangleoftheslitontheskyshouldbe<seeing:However,ifseeingislowerthanàuseforR
Actually,wecanhavedifferentslitsizes
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TheresoluKondoesnotchangeifweusethespectrographatothertelescope,becauseitdepends
onlyonproperKesofthespectrograph
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Resolvingpowerdependsonthefocaldistanceofthespectrograph’scollimatorfCOL,theslitwidthws,anddispersionofthegraKngdθ/dλ
R = λdλ
=λ fCOLranws
dθdλ
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Canweuseaspectrographdesignedforadifferenttelescope?
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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:
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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)
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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
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ResoluKo
nvs.slitwidth
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UVESspectrographon8mVLTtelescope
hTp://www.eso.org/sci/faciliKes/paranal/instruments/uves/doc/
UVESredarm
UVESbluearm
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ResoluKonvs.slitwidthws-CoudéOPD
46
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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
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SOARGoodmanHgAr
48
λ=3650,146Å
λ=8667,944Å
λ=6965,431Å
λ=5460,735Å
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HgArarc600l/mm
Goodman/SOAR
49
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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/
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PunchingEFOSC2MOSPlates
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X-Shooter@ESOVLT
55
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FuncKonaldiagramofX-shooter.ThelightpathrunsfromthetoptotheboTomofthefigure.EachelementisdescribedinSect.2.
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Fig.4.ThecombinedefficiencyofthetwodichroicbeamspliTers.Inblue:reflecKononthefirstdichroic;inorange:transmissionthroughthefirstdichroicandreflecKonontheseconddichroic;inred:transmissionthroughbothdichroics.
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However,asGeministaff,wehavenovestedinterestinbuildinganinstrument,soourchiefpurposeistoencouragefurtherdebateandout-of-the-boxthinking.
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Slidesfrom2017
• GraKngequaKonfollowingthebook“ToMeasuretheSky”
66
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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
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σ sinα+σ sinθ=mλ
orderm=0,±1,±2,…
Gra4ngequa4on:
©ToMeasuretheSky
AlightbulbofaflashlightseenthroughatransmissiongraKng,showingthreediffractedorders.Theorderm=0correspondstoadirecttransmissionoflightthroughthegraKng.InthefirstposiKveorder(m=+1),colorswithincreasingwavelengths(frombluetored)arediffractedatincreasingangles.
Construc4veinterferenceintransmissiongra4ngs