AGA5802 Spectroscopy III

• Gratings

• Filtros (blocking order filters)

• Dichroics (espectrógrafos duplos)

• Linear dispersion of the spectrum

• Basic design of spectrographs

• Wavelength calibration lamps

• Grisms

Bibliography: To Measure the Sky, Kitchin, Lena and others

Prof. Jorge Meléndez

1

Dispersion by a diffraction grating (rede de difração)

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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

Rede de difração

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While light

Microscopic picture of part of a difraction gratting of 1180 lines/mm © Gray, Stellar Photospheres, 3rd ed., Fig. 3.2 (p. 55)

+ -

s

Constructive interference in reflection gratings

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When exiting the grating, the optical path of rays X & Y differ by 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

Constructive interference when Dt = m l , m = 0, ±1, ±2, …

Grating equation:

© To Measure the Sky

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s sin a + s sin q = ml

order m = 0, ±1, ±2, …

Grating equation :

© 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.

Constructive interference in transmission gratings

Angular dispersion of a grating

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s(sin a + sin q) = ml

sin q = ml/s - sin a

Differentiating the grating equation :

- cos q changes only slowly with l dispersion of the grating does not change much with wavelength

- Dispersion can be increased at higher orders

Resolution R of the grating

R = N m

N: number of lines across the grating

m: order

Example: grating 500 lines mm-1 in a 10mm grating at second order: R = 500 x 10 x 2 = 104

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Angular overlap of grating orders

8 © To Measure the Sky

sin q = ml/s - sin a

q

l1 = 2l2 = 3l3 = ... = mlm

lm = l1 /m

Free spectral range

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l1 = 2l2 = 3l3 = ... = mlm

For ex., we would have the same angle q for:

l1 = 8000 Å l2 = 4000 Å l3 = 2666 Å

… lm = l1 /m

lm+1 = l1 /(m+1)

order 0

(m+1) lm+1 = m lm

sin q = ml/s - sin a

Diffraction grating

Practical coverage of an order

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l1 = 2l2 = 3l3 = ... = mlm In order to observe up to l = lmax, the l of the next

order that would affect the results is:

Diffraction grating

order 0

For example, for lmax = 9000 Å at 1st order, we will have contamination for l = 4500 Å of the 2nd order. Introducing a

filter to block l < 4500 Å we can observe in 4500-9000 Å.

sin q = ml/s - sin a

Order blocking filters

11 Examples from 1.5-m R-C Spectrograph: http://www.ctio.noao.edu/spectrographs/60spec/filters.html

100 Tr

ansm

issi

on

(%

)

Wavelength (A)

4000

Blocks Transmits

6000 8000 10000

3000 5000 7000 9000

80

60

40

20 Transmits

Blocks

Order blocking filters

12 http://www.as.utexas.edu/mcdonald/facilities/2.7m/lcs.html

99%

90%

50%

10%

1%

Tran

smis

são

Wavelength (nm) 200 300 400 500 600 700 800 900 1000 1100

0,1%

Blocks Transmits

Red blocking filters

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Blocks Transmits

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

Free spectral range (DlFSR)

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The free spectral range (FSR) is the coverage in

l that is not blocked

order 0

For example, for lmax = 900nm at 1st order we would have DlFSR = 450nm we can observe in the range 450 - 900 nm

Lambda minimum:

Diffraction grating

Blazed gratings (redes com blazing)

15 © Kitchin

Disadvantage: much light is lost at order 0 and in other orders. In gratings with blazing the facet of each ruling has an angle, concentrating most of the light in a given order

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Blazed gratings Best tilt to concentrate all light in an order:

© To Measure the Sky

In the book “To Measure the Sky” is a, but is wrong

Blazing’s efficiency

The efficiency is maximum at lb, with the efficiency decreasing to 50% at:

•lmin= 2/3 lb

•lmax= 3/2 lb

Example, lb = 6000 Å we can cover with efficiency > 50% (max efficiency): 4000 – 9000 Å.

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Example

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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

Important points 1. Due to blazing, the grating is optimized for a particular

region of the spectrum (although you can use several gratings, of course).

2. Due to order overlapping, the spectral coverage is limited

3. Different elements (e.g. CCD) could be optimized for a given spectral region

Is complicated to cover all the optical spectrum (300-1000nm) with only 1 spectrograph

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“Double spectrograph”

Double spectrograph (2 arms)

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Double spectrograph for the Palomar telescope (5 meters). RED side covers 550-1000 nm BLUE side is optimized for 300-550 nm

Dichroic: dichroic reflecting coating on one surface

& antireflection coating on the opposing surface

21 https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=3313

Substrate: UV fused silica

ThorLabs: Longpass Dichroic Mirrors/Beamsplitters: 650 nm Cutoff Wavelength

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

Dichroic: light into different l double spectrograph

refletem em um intervalo espectral e transmitem em outro

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Example : Palomar Double Spectrograph

3000 4000 5000 6000 7000 8000 9000 10000

Wavelength (A)

Tran

smit

tan

ce (

%)

100

80

60

40

20

0

Reflects Transmits

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

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(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

Linear dispersion of the spectrum (valid for both prisms & gratings)

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Angular dispersion of prism Angular dispersion of grating

Linear dispersion dx/dl

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CCD

Linear dispersion

Example for prism (a = 60O)

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Typical value for dq/dl = 1,39 x 107 Om-1

Compute dq for dl = 1 Å

dq = 1,39 x 107 O m-1 x 10-10 m

dq = 1,39 x 10-3 O = 5 arcsec

Linear dispersion on CCD ?

Linear dispersion dx/dl

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dq/ dl = 1,39 x 107 Om-1

CCD Linear dispersion:

1 degree = 0,0174 radians dq/ dl = 2,426 x 10 5 radians m-1

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 = 1,21 x 105 x 2Å = 2,42 x 105 x 10-4mm dx = 24 mm. If pixel is 12 mm 2 pixels

Example for f2 = 50 cm Estimate dx in dλ=2Å. How many 12-mm pixels ?

Typical value for dq/dl = 1,39 x 107 Om-1

Reciprocal linear dispersion p (plate factor)

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CCD

Linear dispersion:

p = dl/dx = 2 Å / 24 x 10-3mm p = 83 Å / mm

In last example dλ=2Å dx = 24 mm = 24 x 10-6m = 24 x 10-3mm

Reciprocal linear dispersion:

f2

High dispersion (high resolution) and low dispersion (low resolution) spectroscopy

high dispersion (spectroscopy) means:

Large linear dispersion

or small plate factor for ex.: p ~ 5Å/mm

low dispersion (spectroscopy) means:

Low linear dispersion, i.e. large plate factor, por ex.: p ~ 100 Å/mm

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Basic design of spectrographs

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Properties of the basic spectrograph

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© To Measure the Sky

Dco

l Slit Width: ws

Dtel, ftel: aperture & effective focal distance of the telescope

Dtel

ftel

Angular size of the slit on the sky

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© To Measure the Sky

Dco

l

The angular size of the slit on the sky is :

Dtel

ftel

Slit Width: ws

ws could also be the diameter of the fiber

How to define the collimator’s focal ratio f/#?

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© To Measure the Sky

Dco

l

Dtel

ftel

Slit width (or diameter of the fiber): ws

The optimal design must satisfy :

For fibers :

The fiber may degrade the focal distance of the transmitted bean, therefore the relation includes a factor gf , which could be < 1, depending on the extension & quality of the fiber

What is the size of the slit (or fiber) on the detector ? • Without the disperser:

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For example: If ws = 0,04 mm, fcam = 10 cm, fcol = 40 cm

w0 = ¼ ws = 0,01 mm

However, the disperser introduces a magnification factor (anamorphic magnification) ran

What is the size of the slit or fiber on the detector (w0)?

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© To Measure the Sky

Dco

l

Dtel

ftel

ran = cos a/ cos q = DCOL / DCAM

What is the size of the slit or fiber on the detector (w0) using the angle subtended by the slit on the sky?

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© To Measure the Sky

Dco

l

Dtel

ftel

Angle of the slit on the sky:

We know

ran = DCOL / DCAM

Resolution dl0 of the spectrograph

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© To Measure the Sky

Dco

l

Dtel

ftel

Using:

dl0 = w0 p

ran = DCOL / DCAM

Other forms :

Resolving power R (= l/dl0) of the spectrograph

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© To Measure the Sky

Dco

l

Dtel

ftel

Ideally the angle of the slit on the sky should be < seeing:

However, if seeing is lower than use for R

Actually, we can have different slit sizes

Can we use a spectrograph designed for a different telescope?

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PHOENIX INFRARED HIGH-RESOLUTION SPECTROGRAPH At the 2.1 m the 4 pixel slit is 1.4 arcsec wide. At the 4 m it is 0.7 arcsec wide

http://www.noao.edu/kpno/phoenix/

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 should be R = 100 000, but due to problems in the optics it is actually R = 75 000

• ws = 3 pixels on detector should be R = 75 000, but it is actually R = 63 000

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Phoenix spectrograph at Kitt Peak (2m & 4m)

Resolution vs. slit width ws

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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

Res

olu

tio

n v

s. s

lit w

idth

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UVES spectrograph on 8m VLT telescope

http://www.eso.org/sci/facilities/paranal/instruments/uves/doc/

UVES red arm

UVES blue arm

Resolution vs. slit width ws - Coudé OPD

44

Calibration lamps (a.k.a. arcs) (to calibrate wavelength)

45 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

SOAR Goodman

HgAr

46

l =

36

50

,14

6 Å

l =

86

67

,94

4 Å

l =

69

65

,43

1 Å

l =

54

60

,73

5 Å

HgAr arc 600 l/mm

Goodman /SOAR

47

Grism = Grating + Prism

48

The deviation of the light beam by the prism is compensated by the deviation due to the grating light passes straight through

The instrument could serve as an imager, removing the grism from the optical path

Grisms

CCD

Camera lens

Collimator

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

49 EFOSC2 @ESO NTT

50

.@ISaviane

51

Punching EFOSC2 MOS Plates

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X-Shooter @ESO VLT

53

54

55

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Functional diagram of X-shooter. The light path runs from the top to the bottom of the figure. Each element is described in Sect. 2.

57

58

Fig. 4. The combined efficiency of the two dichroic beam splitters. In blue: reflection on the first dichroic; in orange: transmission through the first dichroic and reflection on the second dichroic; in red: transmission through both dichroics.

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However, as Gemini staff, we have no vested interest in building an instrument, so our chief purpose is to encourage further debate and out-of-the-box thinking.

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