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AGA0414 Espectroscopia II
• Grating (Rede de difração) • Filtros (blocking order filters)
• Dichroics (espectrógrafos duplos ou múltiplos)
• Dispersão linear do espectro
• Disenho básico de espectrógrafos
• Wavelength calibration lamps
• Grisms
Prof. Jorge Meléndez
1
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Interferência de ondas de luz
2 © Physics for Scientists and Engineers
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Interferência de ondas de luz
3 © Physics for Scientists and Engineers
Interferência construtiva
Interferência construtiva Interferência
destrutiva
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Dispersion by a diffraction grating (rede de difração)
4
Type -------- Capacity --- Track pitch how many per mm (1 mm = 103 mm)?
CD -------------- 0.7 Gb --- 1.6 μm 103um/1,6um = 625 lines/mm DVD ------------ 4.7 GB --- 0.74 μm 103um/0,74um = 1351 lines/mm Blu-ray Disc --- 25 GB ---- 0.32 μm 103um/0,74um = 3125 lines/mm
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Rede de difração
5
Luz branca Foto microscópica de parte de uma rede de difração de 1180 linhas/mm © Gray, Stellar Photospheres, 3rd ed., Fig. 3.2 (p. 55)
+ -
s
s: distância entre os sulcos
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Interferência construtiva em redes de reflexão
6
Ao sairem da rede, o caminho óptico dos raios X e Y diferem por Dt = AB – CD = s sin a - s sin r Dt = s sin a + s sin q
s sin a + s sin q = ml
a
s q
a r
r = 360 - q
a
a
r
r
AB = s sin a CD = s sin r
X Y
Interferência constructiva quando Dt = m l , m = 0, ±1, ±2, …
Equação da rede :
© To Measure the Sky
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7
s sin a + s sin q = ml
order m = 0, ±1, ±2, …
Equação da rede :
Interferência construtiva em redes de transmissão
© To Measure the Sky
A light bulb of a flashlight seen through a transmission grating, showing three diffracted orders. The order m = 0 corresponds to a direct transmission of light through the grating. In the first positive order (m = +1), colors with increasing wavelengths (from blue to red) are diffracted at increasing angles.
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Angular dispersion of a grating
8
s(sin a + sin q) = ml
sin q = ml/s - sin a
Differentiating the grating equation :
- cos q changes only slowly with l, então a dispersão angular da rede é aproximadamente constante com o comprimento de onda
- Dispersão pode ser aumentada usando ordens maiores
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Poder Resolvente de uma rede de difração (o poder resolvente do espectrógrafo sempre é menor)
9
N: numero de linhas (iluminadas) da rede
m: ordem
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Poder Resolvente de uma rede de difração (o poder resolvente do espectrógrafo sempre é menor)
10
R: poder resolvente N: numero de linhas (iluminadas) da rede
m: ordem
Exemplo: rede 600 linhas/mm e largura de 100mm. N = 600*100 = 60000
Para ordem m=1, R(máximo) = 60 000
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Superposição angular de ordens da rede
11 © To Measure the Sky
sin q = ml/s - sin a
q
l1 = 2l2 = 3l3 = ... = mlm
lm = l1 /m
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Free spectral range
12
l1 = 2l2 = 3l3 = ... = mlm
Por exemplo, teriamos o mesmo ângulo q para
l1 = 8000 Å l2 = 4000 Å l3 = 2666 Å
… lm = l1 /m
lm+1 = l1 /(m+1) Rede de difração
order 0
(m+1) lm+1 = m lm
sin q = ml/s - sin a
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Exemplo
• Para o comprimento de onda 480nm em segunda ordem, qual o comprimento de onda de superposição da terceira ordem?
• Método 1:
• l2 = 480nm
• l3 = l2+1 = 480nm * 2/(2+1) = 320nm
• Método 2:
• l2 = 480nm. Como l2 = l1 /2, então l1 =960nm
• l3 = l1 /3 = 320nm
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Cobertura “pratica” de uma ordem
14
l1 = 2l2 = 3l3 = ... = mlm Se queremos observar
máximo em l = lmax, qual o l da seguinte ordem
que afetara meus dados ?
Rede de difração
order 0
Por exemplo, para lmax = 9000 Å na 1a ordem teremos contaminação para l = 4500 Å da 2a ordem. Introduzindo um filtro
para bloquear l < 4500 Å, podemos observar em 4500-9000 Å.
sin q = ml/s - sin a
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Filtros • Espectrógrafos que usam prismas não
precisam de filtros
• Espectrógrafos que usam redes de difração podem precisar filtros para bloqueiar a luz de outras ordens
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Order blocking filters
16 Exemplos do 1.5-m R-C Spectrograph: http://www.ctio.noao.edu/spectrographs/60spec/filters.html
100 Tr
ansm
issã
o (
%)
Comprimento de onda (A)
4000
Bloqueia Transmite
6000 8000 10000
3000 5000 7000 9000
80
60
40
20 Transmite
Bloqueia
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Order blocking filters
17 http://www.as.utexas.edu/mcdonald/facilities/2.7m/lcs.html
99%
90%
50%
10%
1%
Tran
smis
são
Comprimento de onda (nm) 200 300 400 500 600 700 800 900 1000 1100
0,1%
Bloqueia Transmite
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Exemplo: Filtros para espectrógrafo Cassegrain do OPD
(corte no azul)
18
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Red blocking filters
19
Bloqueia Transmite
http://www.noao.edu/kpno/manuals/l2mspect/
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Exemplo: Filtros para espectrógrafo Cassegrain do OPD (corte no vermelho)
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Free spectral range (DlFSR)
21
A faixa espectral livre (free spectral range : FSR)
é a cobertura em l não bloqueiada pelo filtro
Rede de difração
order 0
Lambda mínimo:
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Faixa espectral livre (DlFSR)
22
Rede de difração
order 0
Exemplo: para lmax = 900nm na 1a ordem teremos DlFSR = 450nm. Isto é, podemos observar de 450 - 900 nm (será necessário bloqueiar l < 450nm)
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Faixa espectral livre (DlFSR)
23
Rede de difração
order 0
Exemplo: para lmax = 900nm na 2a ordem teremos DlFSR = 300nm. Isto é, podemos observar de 600 - 900 nm (será necessário bloqueiar l < 600nm)
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Blazed gratings (redes com blazing)
24 © Kitchin
Uma desvantagem da rede de difração é que a luz e perdida na ordem 0 e em outras ordens.
Nas redes com blazing a face de cada risca tem um dado ângulo que concentra a maior parte da luz em uma dada ordem
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25
Blazed gratings Melhor “tilt” para ter toda a luz em uma ordem:
© To Measure the Sky
No livro “To Measure the Sky” é a, mas está errado
= ml/s
sin e cos b - sin b cos e + sin e cos b + sin b cos e = ml/s
2 sin e cos b = ml/s
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26
Blazed gratings Melhor “tilt” para ter toda a luz em uma ordem:
© To Measure the Sky
2 sin e cos b = ml/s
l = 2s sin e cos b / m
lb : comprimento de onda do blazing
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Exemplo
27
Diffraction
Gratings available for LCS
grating number
lines/mm blaze (Å)
effective blaze (Å)
dispersion l/ one-pixel Dl
(TI1 CCD)
40 300 4200 3900 550
41 300 7500 6000 550
42 300 10000 9200 550
43 600 4000 3700 1100
44 600 7500 6900 1100
45 600 10000 9200 1100
46 1200 4000 3700 2200
47 1200 6000 5500 2200
48 1200 7500 6900 2200
Gratings are blazed for use in first order.
http://www.as.utexas.edu/mcdonald/facilities/2.7m/lcs.html
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Exemplo: redes do Cassegrain/OPD
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Cobertura útil devido à eficiência do blazing
A eficiência máxima é para lb, com a eficiência decrescendo a 50% para aproximadamente:
• linferior= 2/3 lb
• lsuperior= 3/2 lb
Exemplo, lb = 6000 Å, entao podemos cobrir com eficiência > 50% (da eficiencia máxima): 4000 – 9000 Å.
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Important points 1. Due to blazing, the grating is optimized for a particular
region of the spectrum (although you can observe different regions using different gratings).
2. Devido à superposição de diferentes ordens a cobertura espectral é limitada ao free spectral range (DlFSR).
3. Diversos elementos (e.g. CCD) podem ser otimizados para uma determinada região espectral
É complicado cobrir todo o espectro “visível” (300-1000nm) com apenas um espectrógrafo
30
“Double spectrograph”
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Espectrógrafo doble (2 braços)
31
Double spectrograph para o telescópio Palomar (5m). O lado VERMELHO cobre 550-1000 nm O lado AZUL é otimizado para 300-550 nm
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Dichroics : dividem a luz para os braços do espectrógrafo multiplo
espelhos refletem um intervalo espectral e transmitem em outro
32
Exemplo : Palomar Double Spectrograph
3000 4000 5000 6000 7000 8000 9000 10000
Wavelength (A)
Tran
smit
tan
ce (
%)
100
80
60
40
20
0
Reflete Transmite
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Gratings for the Palomar double spectrograph
1st Order Useful Range (Å) Red Camera Blue Camera
lines/mm Blaze (Å) (to blaze 1/2-
intensity) Dispersion
(Å/mm) Dispersion
(Å/mm)
158 [a] 7560 5000-11300 201 1st [c] 135 2nd [d]
300 [b] 3990 2700-6000 - 140 1st
316 [a] 7150 4800-10700 102 1st -
600 [b] 3780 2500-5700 - 71 1st
600 [a] 9500 6300-14300 54 1st -
1200 [b] 4700 3100-7100 - 36 1st
1200 7100 4700-10700 27 1st 36 1st
1200 9400 6300-14100 26 1st 35 1st
33
(F) GRATING SPECS (lines/mm, blaze, dispersion)
NOTE: "Useful Range" gives the wavelength limits at which diffracted intensity drops to 1/2 of its peak value (2/3 and 3/2 of the blaze wavelength, by a common rule of thumb). [a] silver coating...can be used only longward of 3500 Å. [b] can be used only in blue spectrograph. [c] first order. [d] second order.
R ~ 1,000 to 10,000
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X-shooter no VLT/ESO 3 braços: 300 – 2500nm oferecido desde 2009
34
UVB, covering 300-559.5 nm VIS, covering 559.5-1024 nm NIR, covering 1024-2480 nm
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Dispersão linear do espectro (válido para prismas e redes de
drifração)
35
Dispersão angular do prisma Dispersão angular da rede
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Dispersão linear dx/dl
36
CCD
Linear dispersion
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Example for a = 60O
37
Valor típico para dq/dl = 1,39 x 107 °m-1
Qual o dq para dl = 1 Å ?
dq = 1,39 x 107 x 1 x 10-10 °
dq = 1,39 x 10-3 O
dq = 5 arcsec Linear dispersion no CCD ?
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Linear dispersion dx/dl
38
Valor típico para dq/dl = 1,39 x 107 Om-1
dq/ dl = 1,39 x 107 Om-1
CCD Linear dispersion:
1 degree = 0,0174 radians dq/ dl = 2,426 x 105 radians m-1
Example for f2 = 50 cm Estimate dx in dλ=2Å.
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Linear dispersion dx/dl
39
CCD Linear dispersion:
dx/dl = f2 dq/ dl = 0,5m x 2,426 x 10 5 radians m-1
= 1,21 x 105
dx = dl x 1,21 x 105 = 2Å x 1,21 x 105 = 2,42 x 105 x 10-4mm dx = 24 mm. Se o pixel for de 12 mm, cabem 2 pixels
Example for f2 = 50 cm Estimate dx in dλ=2Å
dq/ dl = 2,426 x 105 radians m-1
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Disenho básico de espectrógrafos
40
Razão focal do colimador e do telescópio devem ser similares:
~
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Properties of the basic spectrograph
41
© To Measure the Sky
Dco
l Largura da fenda (slit): ws
Dtel, ftel: abertura e distância focal efetiva do telescopio
Dtel
ftel
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Qual a distância angular da fenda no céu ?
42
© To Measure the Sky
Dco
l
The angular size of the slit on the sky is :
Dtel
ftel
Largura da fenda (slit): ws
ws pode ser tb o diâmetro da fibra
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Resolução dl0 do espectrógrafo
43
© To Measure the Sky
Dco
l
Dtel
ftel
Rede de difração:
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Poder resolvente R (= l/dl0) do espectrógrafo
44
© To Measure the Sky
Dco
l
Dtel
ftel
Para fontes pontuais (p.ex. estrelas) o ângulo da fenda no céu
Se o seeing (FWHM) for menor que usar para o R
Na verdade podem existir vários tamanhos de fendas
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Poder resolvente do espectrógrafo em função de m, s, fcol , ws
45 m: ordem, s: distância entre riscas da rede fcol : distância focal do colimador, ws: largura da fenda
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Poder resolvente do espectrógrafo
46
Dco
l
m: ordem, s: distância entre riscas da rede fcol : distância focal do colimador, ws: largura da fenda
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Resolution vs. slit width ws
• EXAMPLE with PHOENIX spectrograph, slits available: 2 pixel (54 mm), 3 pixel (81 mm), and 4 pixel (107 mm)
• ws = 4 pixels on detector R = 50 000
• ws = 2 pixels on detector
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Phoenix spectrograph at Kitt Peak (2m & 4m)
• ws = 3 pixels on detector
devia ser R = 100 000
devia ser R = 75 000
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Resolution vs. slit width ws
48
Deckname Length (") Width (") Resolution (calculated)
Resolution (measured*)
Resolution (measured+)
B1 3.5 0.574 72,000 67,000 66,400
B2 7.0 0.574 72,000 67,000 66,400
B3 14.0 0.574 72,000 67,000 66,400
B4 28.0 0.574 72,000 67,000 66,400
B5 3.5 0.861 48,000 49,000 50,000
C1 7.0 0.861 48,000 49,000 50,000
C2 14.0 0.861 48,000 49,000 50,000
C3 28.0 0.861 48,000 49,000 50,000
C4 3.5 1.148 36,000 37,000 37,500
C5 7.0 1.148 36,000 37,000 37,500
D1 14.0 1.148 36,000 37,000 37,500
D2 28.0 1.148 36,000 37,000 37,500
D3 7.0 1.722 24,000 24,000 24,700
D4 14.0 1.722 24,000 24,000 24,700
D5 0.119 0.179 pinhole
E1 1.0 0.400 103,000 84,000 86,600
E2 3.0 0.400 103,000 84,000 86,600
E3 5.0 0.400 103,000 84,000 86,600
E4 7.0 0.400 103,000 84,000 86,600
E5 1.0 0.800 51,000 52,000 52,000
* Using UV cross-disperser. Average of 5 Th/Ar lines near 4100 A. + Using Red cross-disperser. Average of 4 Th/Ar lines near 5240 A.
HIRES spectrograph on 10m Keck telescope
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Res
olu
tio
n v
s. s
lit w
idth
49
UVES spectrograph on 8m VLT telescope
http://www.eso.org/sci/facilities/paranal/instruments/uves/doc/
UVES red arm
UVES blue arm
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Resolution vs. slit width ws - Coudé OPD
50
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Calibration lamps (a.k.a. arcs) (para calibrar o comprimento de onda)
51 http://mthamilton.ucolick.org/techdocs/instruments/nickel_spect/arcSpectra/
Pixel number
l =
58
52
,49
Å
l =
72
45
,17
Å
l =
84
95
,36
Å
NEON arc (observed with a 600 lines/mm grism)
0 200 400 800 1000 1200
Flu
x
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SOAR Goodman
HgAr
52
l =
36
50
,14
6 Å
l =
86
67
,94
4 Å
l =
69
65
,43
1 Å
l =
54
60
,73
5 Å
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HgAr arc 600 l/mm
Goodman /SOAR
53
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He-Ar, espectrógrafo Cassegrain do OPD
54
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55
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56
He-Ar do OPD (3000-6300A)
© Prof. Marcos Diaz, 1996
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Além de prisms e gratings, o dipersor também pode ser um grism
57
Prism
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Grism = Grating + Prism
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Para uma faixa de comprimento de onda, o desvio do feixe de luz to prisma é contrarestado pelo desvio da rede, portanto o feixe segue reto
O instrumento pode servir para imageamento apenas retirando o grisma do caminho otico.
Grismas
CCD
Camera lens
Colimador
http://mthamilton.ucolick.org/techdocs/instruments/nickel_spect/hw_overview/