Astronomische Waarneemtechnieken (Astronomical Observing Techniques) 10 th Lecture: 24 November 2010 Based on “Observational Astrophysics” (Springer) by P. Lena, Wikipedia, ESO, and “astronomical spectroscopy” by Massey & Hanson Content: 1. Formation of Spectral Lines 2. General Principle of a Spectrometer 3. Dispersers: Gratings and Filters 4. Advanced Spectrometer Concepts 5. Spectral Line Analysis
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Astronom
ische Waarneem
technieken(Astronom
ical Observing T
echniques)
10thLecture: 2
4 Novem
ber 2
010
Based
on “Observational A
strophysics” (S
pringer) by P. Lena,
Wikiped
ia, ESO, and
“astronomical spectroscopy” b
y Massey &
Hanson
Conte
nt:
1.Form
ation of Spectral Lines
2.General Principle of a S
pectrometer
3.Dispersers: G
ratings and Filters
4.Advanced
Spectrom
eter Concepts
5.Spectral Line A
nalysis
Form
ation of S
pectra
l Line
s
Macroscopically, th
e received rad
iation can be ch
aracterized by th
e specific intensity I(v,θ
) at frequencyνand
direction
θand
polarization.
Microscopically, th
e transition betw
een two energetic states E
1 , E2
requires the em
ission or absorption of a ph
oton of frequency:
Energy levels could
be due to splitting at several fund
amental levels:
h
EE
12
0
−=
ν
()
()
I
JJ
JE
2
12
+=h
Excita
tion Processe
s•Electronic transitions d
ue to the ch
ange of the principal quantum
num
bers of th
e electronic states (visible).
•Electronic fine structure transitions d
ue to the coupling of electron
spin and nuclear spin.
•Electronic h
yperfine structure transitions due to th
e interaction of the nuclear m
agnetic moment w
ith the m
agnetic field of th
e electron.
•Molecular transitions such
as rotational (change in angular m
omentum
) •Molecular transitions such
as rotational (change in angular m
omentum
) and
vibrational (ch
ange in vibrational energy) transitions*, requiring
dipole m
oment and
moment of inertia I (
near-far-IR
).
•Nuclear lines d
ue to nuclear excititations or electron-positron
annihilation (
MeV range)
•Transitions in solid
s (ices) due to vib
rations phonons (
near-far-
IR).
* rotational transitions are generally weaker and
often coupled to vib
rationaltransitions
vibrational
transitions split further: com
plex structure of vib
rational-rotationaltransitions.
Excita
tion Processe
s –Energy
Range
s
Three General T
ypes of S
pectra
Continuous spectrum
Emission line spectrum
Absorption line spectrum
Physica
l Processe
s causing a
Line
-Shift
•Doppler effect: th
e emitter is in m
otion relative to the ob
server with
a relative line-of-sight velocity com
ponent v|| . T
he resulting frequency
shift is:
Doppler im
agingc v
c v
c v
||
0
||
2/1
2 2||
0
1
1
1ν
νν
≈
−
−
−=
∆
•(norm
al) Zeem
an effect: magnetic field
splits line in three
components (th
e linearly polarized πcom
ponent at ν0and
the tw
o elliptically polarized
σcom
ponents at ±Δνwith :
•Einstein effect: a strong gravitational field
s causes a redshift of th
e ligh
t:
Bm
eB
e
10
10
4.1
4⋅
==
∆π
ν
2
2/1
21
21
Rc
GM
Rc
GM
≈−
−=
∆ν ν
The Basic Priciple
Main ingred
ients of a spectrometer:
1.A slit
(ontwhich the ligh
t of the telescope is focused
)
2.A collim
ator(diverging
parallel/collimated
light)
3.A disperser
(to spectrally disperse th
e light)
4.A cam
era (to focus the spectrum
onto the detector)
Characte
ristics of a Spectrom
eter
•the spectral resolution or spectral resolving pow
eris:
Δλis called
a spectral resolution element.
•the instrum
ental profile P(v) broad
ens a theoretically infinitely
narrow line to th
e observed
line width:
()
()0
0ν
νδ
ν−
=I
()
()
()ν
νν
0I
PI
∗=
λ λ∆=
R
Usually the instrum
ental profile determines the spectral resolution
element, w
hich is typically Nyquist-sam
pled.
•the beam
étenduedeterm
ines the ligh
t gathering pow
er of the
instrument. Larger étend
ues require larger dispersive elem
ents (A)
or highly inclined
beam
s (Ω).
•the transm
issiondeterm
ines the th
roughput
()
()
()ν ν
νη
in
ou
t
I I=
For unresolved
lines, both the S/N and
the line/continuum
increases with increasing resolution:
Spectra
l Resolution a
nd S/N
Mo
de
l sp
ectra
of C
2 H2
at 9
00
K a
nd
HC
N a
t 60
0K
(assu
me
d D
op
ple
r bro
ad
en
ing ~
4 k
m/s
) at
diffe
ren
t sp
ectro
gra
ph
reso
lutio
ns (fig
ure
pro
vid
ed b
y F
. La
hu
is).
R=
20
00
R=
50
00
0
General Principle
of a Grating
Use a d
evice that introd
uces an optical path
difference = fangle to th
e surface
The cond
ition for constructive interference is given b
y the grating equation:
()β
αλ
sinsin
±⋅
=a
m
m= ord
er of diffraction
λ= wavelength
a = distance b
etween equally spaced
grooves
a
Gratings are usually operated
in a collimated
beam
at the pupil.
The m
aximum resolution is given b
ywhere N
is the num
ber of
(illuminated
) periods (grooves), and
the angular d
ispersion is.
mN
R=
a = distance b
etween equally spaced
grooves
α= angle of incom
ing beam
β= angle of reflected
beam
a md
d~
/λ
θ
Blaze Angle
Generally, th
e energy of the beam
diffracted
by a period
ic structure is uniform
ly distrib
uted over th
e different ord
ers m.
If we ob
serve only one arbitrary ord
er this is very inefficient.
For b
lazed gratings th
e directions of constructive interference and specular reflection coincide :
()
2
2
αβ
θθ
αβ
α−
=⇒
+=
+B
B
Advantage:
•High efficiency
Disadvantage:
•Blaze angle θ
B(and
hence b
laze wavelength
λB ) are fix
ed by construction.
Free Spectra
l Range
…
A light bulb seen through a transm
issivegrating, show
ing three diffracted orders. m = 0
corresponds to direct transmission;
colors with increasing w
avelengths (from
blue to red) are diffracted at increasing angles. S
ource: Wikipedia
Different d
iffraction orders overlap w
ith each
other:
The free spectral range is th
e largest wavelength
range for a given order th
at does not overlap th
e same range in an ad
jacent order.
()
()λ
βα
λ′
+=
+=
1sin
sinm
am
mfree
λλ
λλ
′= ′
−=
∆
…and Cross-
Dispe
rsionTo spatially separate th
e orders and
avoid overlap, an ad
ditional
optical element w
ill be need
ed:
A low
-dispersion prism
/grating with a d
ispersion direction
perpendicular to th
at of the high-dispersion grating
hig
h d
ispersio
n
cross
dispersion
hig
h d
ispersio
n
Echelle Gratings
α=
β=
θ
a md
d~
/λ
θTo get h
igh dispersion
one could either
increase the
groove density, or
use large groove periods (a >> λ) and
a large angle of incid
ence, and operate at a very h
igh ord
er of diffraction (m
>~50).
If α= β
=θLittrow
configuration
α=
β=
θ
Θ=
sin2
am
Bλ
In Littrowconfiguration th
e grating equation becom
es:
Grism
s
Grism
= transmission G
Rating + prIS
M
For a given w
avelength and
diffraction ord
er the refraction of grating
and prism
may com
pensate each oth
er and the optical ax
is remains
(almost) unch
anged.
Advantages:
•ideal to b
ring in and out of a collim
ated
beam
(“filter wheel”)
beam
(“filter wheel”)
•red
uces coma (if in non-collim
ated beam
)
Disadvantage:
•difficult to m
anufacture (either b
y replication and
gluing or by direct ruling.
•can b
e quite “bulky” (
filter w
heel)
Inte
rference
(Transm
ission) Filte
rs
Principle: interference layers deposited
on a substrate.
The transm
ission is maximal w
here
ππ
λk
dn
22
21
=+
•spectral resolution typically R
~ few
-1000
•need
s often multiple interference layers
•filters are often tilted
with respect to th
e optical axis to
avoid reflections
shift of λ
0
•wavelength
s farther from
λ0(for w
hich the ab
ove equation is also satisfied
) need a b
locking or absorb
ing filter.
Fabry-Perot E
talon
The transm
ission is:
and has transm
ission peaks where
()
()
1
2
2
2
0co
s2
sin1
41
1
−
−+
−=
id
kr r
r
rI
Iπ
d mk
2=
Two parallel plates (F
abry-Perot etalon) of h
igh
reflectivity rand
transmission t = 1-r.
Here, m
is the ord
er of the interferom
eter, dis th
e separationof th
e plates, and
Δk= 1/2
dthe free spectral range.
d2
The perform
ance of a Fabry-Perot is ch
aracterized by:
1.The finesse
,
2.The resolution
, and
3.The m
aximum through
put (S = illum
inated area of th
e etalon).
r rF
−=
1 π
mF
k kR
=∆
=
R SU
π2=
OH Suppre
ssion Spectrogra
phs
OHS filter out th
e wavelength
s of atmosph
eric OH lines, w
hich
contribute th
e major part of th
e near-IR background
.
http://sub
arutelescope.org/Introduction/instrum
ent/img/O
HS_concept.gif
Multi-
Object S
pectrogra
phs
Use num
erous “slits” in the focal plane
simultaneously
multiple source pick-ups
using fibers
or mirrors.
Need
s different slit m
asks for d
ifferent fields.
Hectospe
c (SAO) w
ith rob
otic fiber positioning
Align all spectra on th
e same
detector:
Inte
gral F
ield Spectrogra
phs
Cut an area on th
e sky in several adjacent slices or sub
-portions, realign them optically into one long slice and