JGR 19 Apr 2001 1 Basics of Spectroscopy Gordon Robertson (University of Sydney)
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Transcript of JGR 19 Apr 2001 1 Basics of Spectroscopy Gordon Robertson (University of Sydney)
JGR 19 Apr 2001 1
Basics of Spectroscopy
Gordon Robertson
(University of Sydney)
JGR 19 Apr 2001 2
Outline
• Aims of spectroscopy– Variety of instrumentation - formatting to a 2D detector
• Diffraction gratings– Optical setups, Grating equation, Spectral resolution
• Prisms• Volume Phase Holographic gratings • The A product• Conclusion
JGR 19 Apr 2001 3
Science goals of spectroscopy
1. Elemental composition and abundances
2. Kinematics
3. Redshifts / cosmology
i.e. what is it, where is it, what are its internal motions….
For stars, star clusters, nebulae, galaxies, AGN, intervening clouds etc...
JGR 19 Apr 2001 4
Aims of spectroscopic observations
Ideally….
A data cube, covering a wide range in each of ,,
With good ….spatial resolution , , wavelength resolution ,and efficiency
BUT detectors are 2-dimensional, so the data must be formatted to fit them.
Many interesting new ways of dealing with this.
JGR 19 Apr 2001 5
Spectral formats
Long-slit spectroscopy
Narrow band imaging
Echelle
Multi-slit
Focal-plane mask
Multi-fibre
Focal-plane fibre feed
Integral field
Focal-plane IFU
spat
ial
cross-disp.
JGR 19 Apr 2001 6
Types of spectroscopic observations
JGR 19 Apr 2001 7
Dispersive elements
A grating, prism or grism…..
Sends light of different wavelengths in different directions…
hence (via the camera) to different positions on the detector.
So incident light must be collimated
JGR 19 Apr 2001 8
Reflection grating geometry
Path difference = a (sin + sin )( is negative in this case)
a
a sin
a sin ||
JGR 19 Apr 2001 9
The grating equation
m = a(sin + sin )
a
m = order of diffraction, most often 1
JGR 19 Apr 2001 10
Telescope - slit - collimator
fTel fColl
slit (width s in m)
DTelescopeobjective
Collimator
b (beam diam)
Reduction scale factor = b/D = fColl/fTel
JGR 19 Apr 2001 11
Reflection grating optics (schematic)
grating
camerad
collimator
idetector
cc
slit
b
JGR 19 Apr 2001 12
Spectral resolution of a grating
Idealised image of slit at neighbouring wavelengths:
Intensity
Position on detector
+
The observed spectrum is convolved (smoothed) by the line spread function (in practice more Gaussian than rectangular)
Wavelength equivalent of slit width
JGR 19 Apr 2001 13
Spectral resolution formula
αcos
βsintan
θs
D
bR Where s is the slit angle on the
sky (radians).
sθ
αtan 2
D
bR In Littrow configuration ( = ):
Implications:
• Larger telescopes (D) need larger spectrographs (b) for same R
• If slit width (s) can be reduced, spectrograph size can be contained
• The geometric factor is maximised at large deviation angles (fine rulings, high order)
JGR 19 Apr 2001 14
Resolution and grating ‘depth’
Grating depth = b tan
In Littrow configuration ( = ):sθ
αtan 2
D
bR
,b
becomessθ
(depth) 2
DR
JGR 19 Apr 2001 15
RGO Spectrograph Resolution vs Wavelength; 25 cm camera; 1.5 arcsec slit
100
1000
10000
100000
3000 5000 7000 9000 11000 Wavelength /A
Res
olu
tio
n
1200/1, bl coll
250/1, bl coll
1200/2, bl cam
1200/1, bl cam
Resolutionin km/s
10
100
1000
JGR 19 Apr 2001 16
Spectral resolution from general texts
mNR
λ
λ
But physics and optics texts give the resolution of a grating as:
Where N is the total number of (illuminated) rulings
E.g. for the RGO spectrograph, 1200 l/mm gratings in 1st order, this gives R > ~ 180,000 (i.e. ~ 0.03Å)!
This assumes perfectly collimated input, i.e. diffraction-limited slit.
Astronomers use wider slits, because of atmospheric seeing
JGR 19 Apr 2001 17
Grating blaze
0 +1
+2-1
0
+1
-1
JGR 19 Apr 2001 18
Prisms as dispersive elements (1)
Advantages:•Can have high efficiency (no multiple orders)•More than one octave wavelength range possible
Disadvantages:•Low spectral resolution•Non-uniform dispersion (higher in blue, less in red)•Size, mass•Requirements for homogeneity, exotic materials, expense
JGR 19 Apr 2001 19
Prisms as dispersive elements (2)
Derivative of refractive index - LF5 glass
1
10
100
3000 4000 5000 6000 7000 8000 9000 10000
Wavelength /A
dn
/d(l
am
bd
a (
A))
*10
^6
LF 5 Refractive Index
1.56
1.57
1.58
1.59
1.6
1.61
1.62
1.63
1.64
1.65
3000 4000 5000 6000 7000 8000 9000 10000
Wavelength /A
Re
fra
ctiv
e I
nd
ex
1%
JGR 19 Apr 2001 20
Prisms as dispersive elements (3)
t
b
bD
ddn
bt
R
s
resolution Spectral
E.g. D = 3.89 m (AAT); (b = 150 mm); t = 130 mm; s 1.5; = 5500 Å;
LF5 glass gives R = 250 ( = 22 Å)
JGR 19 Apr 2001 21
• Peak efficiency up to ~90%• Line densities from ~100 to (6000) l/mm - 1st order• Wavelength of peak efficiency can be tuned• Transmission gratings - Littrow config. or close to it• DCG layer (hologram) is protected on both sides• Each grating is an original, made to order• Large sizes possible
Introduction to Volume Phase Holographic (VPH) gratings
JGR 19 Apr 2001 22
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
400 500 600 700 800 900 1000
Wavelength (nm)
Eff
icie
nc
y
f/2.2
f/1.7
Ralcon 1516 l/mm grating - June 2000
Note: no antireflection coatings
Test of a prototype VPH grating
JGR 19 Apr 2001 23
Now we know how to disperse the light - using interference/diffraction or variation of n() in glass.
What other fundamental constraints apply to spectrographs?
JGR 19 Apr 2001 24
The A product
A1
A3
3
1
E.g. f/8 beam half-angle = 3.6°,
and 1´´ seeing in AAT Focal spot diam = 0.15 mm
A11 = 0.72 mm2 deg2
E.g. f/2.5 camera half-angle = 11.3°,
and 1´´ seeing Focal spot diam = 0.047 mm
A33 = 0.72 mm2 deg2
A2
2
E.g. 150mm collimated beamAngular spread = 1´´ D/b = 26´´
A22 = 0.72 mm2 deg2
On primary, angular spread = 1´´
and diameter b = 3.89 m
A = 0.72 mm2 deg2
A is equivalent to entropy of the beam. It cannot be decreased by simple optics. It is also known as etendue
JGR 19 Apr 2001 25
A can be degraded...
Like entropy, A can be increased (degraded):
E.g. focal ratio degradation (FRD) in an optical fibre increases while leaving A unchanged.
As a result, spectrograph loses some light, or has to be larger and more expensive, or loses resolution.
Seeing has degraded A before we get the light.
So .. Best if A of the beam is as small as possible,But best if an instrument accepts the largest possible A
JGR 19 Apr 2001 26
A can be reformatted….
An integral field unit (or other image slicer) can decrease the spread on the ‘wavelength’ axis at the expense of increasing it in the spatial direction.
A is conserved, but we end up with better wavelength resolution
A can be decreased in an adaptive optics (AO) system, by using information about the instantaneous wavefront.
For large telescopes, AO allows good resolution at managable cost
JGR 19 Apr 2001 27
Optical design for ATLAS spectrograph
(D. Jones, P. Gillingham)
focal plane
collimator
VPH grating
camera
CCD detector
JGR 19 Apr 2001 28
A few practical details
In practical spectrograph designs, we have to take account of:
• Field size at the focal plane– collimator needs to be larger than ‘b’
• Optical systems must deliver good image quality– aberration broadening < ~1 pixel (eg 10m rms radius)
• Adequate sampling at the detector– at least 2 pixels/FWHM, preferably ~3
JGR 19 Apr 2001 29
Putting it all together….
• The incoming ,, data have to be formatted to 2D detector– resulting in a wide variety of instruments, with different emphases
• Principal dispersive elements are gratings– normally in a collimator - grating - camera - detector system– large systems are required, especially with large telescopes– spectral resolution
• depends on beam size • is generally much lower than the diffraction-limited maximum
• The size and cost of instruments depends on the A that they have to accept
• Challenge for the future: feasible systems for 30 - 50 m telescopes