Download Spectroscopy

Spectroscopy & Spectrographs
Roy van Boekel & Kees Dullemond
Overview
• Spectrum, spectral resolution
• Dispersion (prism, grating)
• Spectrographs
– longslit
– echelle
– fourier transform
• Multiple Object Spectroscopy
Spectroscopy: what do we measure?
• Spectrum = the intensity (or flux) of radiation as a function of
wavelength
• “Continuous” sampling in wavelength (as opposed to
imaging, where we integrate over some finite wavelength
range)
– Note: In practice, when using CCDs for spectroscopy, one also
integrates over finite wavelength ranges – they are just very narrow
compared to the wavelength itself: Pixel width Δν << ν
• Sampling is continuous but the spectral resolution is limited
by the design of the spectrograph
• Spectrum in classical sense holds no direct spatial
information. Many spectrographs allow retrieving spatial info
in 1 dimension, some even in 2 (“integral field units”)
Spectral resolution
• Smallest separation in wavelength that can still be distinguished
by instrument, usually given as fraction of  and denoted by R:
R


or alternatively
R


useful, though somewhat arbitrary working definition
Basic spectrograph layout
• a means to isolate light from the source in the focal plane,
usually a slit
• “collimator” to make parallel beams on the dispersive element
• dispersive element, e.g. a prism or grating. Reflection gratings
much more frequently used than transmission gratings
• “Camera”: imaging lens to focus beams in the (detector) focal
plane + detector to record the signal
Dispersion
Splitting up light in its spectral components achieved by one of
two ways:
• differential refraction
– prism
• interference
– reflection/transmission grating
– fourier transform
– (Farby-Perot)
6
Prism
• Refractive index n of material depends on wavelength
• Several approximate formulae exist to describe n().
“Sellmeier” equation is accurate over a large wavelength
range and used by manufacturers of optical glasses:
B12
B2 2
B3 2
n ( )  1 2
 2
 2
  C1   C2   C3
2
• Bi and Ci are empirically determined coefficients. With 3
terms the Sellmeier approximation is accurate to 1 part in

~510-6 in the whole optical and near-infrared range
Prism
• general light path through prism:
one can show that:
• dispersion is maximum for a symmetrical light path
• dispersion is maximum for grazing incidence. Corresponding top angle 
depends on refractive index of material. E.g. ~74° for heavy flint glass
• However: most light is reflected instead of refracted for grazing incidence.
In practice, smaller  are used (60° and 30° are common choices)
Prism dispersion curve
strongly non-linear,
dispersion in blue
much stronger than
in red part of spectrum
9
Prism spectrograph layout
10
Credit: C.R. Kitchin “Astrophysical techniques”
CRC Press, ISBN 13: 978-1-4200-8243-2
Young’s double slit experiment
double slit
lens
incident
wave
θ
d
θ
screen
Young’s double slit experiment
double slit
Optical path difference:
P  dsin 
Phase difference:
  2
P
lens
incident
wave
d

Add the two waves:
ΔP
θ
E(t)  E1e i t  ei( t  )  E1ei t 1 ei 
Intensity is amplitude-squared:
I  E 12 1 ei 1 ei  E12 2  2cos
 4E 12 cos2 ( /2)  4E 12 cos2  d sin  / 
screen
Young’s double slit experiment
N=2
Now a triple slit experiment...
triple slit
Optical path difference:
P  dsin 
Phase difference:
  2
P

lens
incident
wave
d
ΔP
θ
Add the three waves, and take the norm:
I  E 12 1 ei  e2i 1 ei  e2i 
screen
Now a triple slit experiment...
N=3
Adding more slits...
N=4
Adding more slits...
N=5
Adding more slits...
N=6
Adding more slits...
0th order
N=16
1st order
2nd order
General formula of pattern
N=4
 2Nd sin  
sin 


I(0)
 


I( )  2
N  2d sin   
sin 


   


Exercise: Show that
the 1/N2 normalization
is correct.
Width of the peaks
N=4
 2Nd sin  
sin 


I(0)
 


I( )  2
N  2d sin   
sin 


   


For
d sin 

1

one has I( )  0
N
Width of the peaks
N=4
 2Nd sin  
sin 


I(0)
 


I( )  2
N  2d sin   
sin 


   


For
d sin 

n

N
one has I( )  0
with 1  n  N
Width of the peaks
N=4
For
d sin 

n

with 1  n  N
N
one has I( )  0
Peak width is therefore:
 sin  

Nd
(Later: Relevance for spectral resolution)
Now do 3 different wavelengths
0th order
1st order
2nd order
N=4
Green is here the reference wavelength λ.
Blue/red is chosen such that its 1st order peak lies in green’s first
null on the left/right of the 1st order.
 1 
blue  green 1 
 N 
red
 1 
 green 1 
 N 
Now do 3 different wavelengths
0th order
1st order
N=8
Keeping 3 wavelengths fixed, but increasing N
2nd order
Now do 3 different wavelengths
0th order
1st order
N=16
Keeping 3 wavelengths fixed, but increasing N
2nd order
Now do 3 different wavelengths
0th order
1st order
2nd order
N=4
Green is here the reference wavelength λ.
Blue/red is chosen such that its 1st order peak lies in green’s first
null on the left/right of the 1st order.
 1 
blue  green 1 
 N 
red
 1 
 green 1 
 N 
Now do 3 different wavelengths
0th order
1st order
2nd order
N=8
Green is here the reference wavelength λ.
Blue/red is chosen such that its 1st order peak lies in green’s first
null on the left/right of the 1st order.
Spectral resolution:
 1 
 1 
 1
blue  green 1 
red  green 1 

 N 
 N 
 N
Let’s look at the 2nd order
0th order
1st order
2nd order
N=8
Green is here the reference wavelength λ.
Blue/red is chosen such that its 1st order peak lies in green’s first
null on the left/right of the 1st order.
Spectral resolution:
 1 
 1 
 1
blue  green 1 
red  green 1 

 N 
 N 
 N
Let’s look at the 2nd order
m=0 m=1 m=2 m=3 m=4
N=8
Green is here the reference wavelength λ.
Blue/red is chosen such that its 1st order peak lies in green’s first
null on the left/right of the 1st order.
 1 
blue  green 1 
 N 
red
 1 
 green 1 
 N 
Let’s look at the 2nd order
m=2
N=8
Zoom-in around
2nd order
Green is here the reference wavelength λ.
Blue/red is chosen such that its 1st order peak lies in green’s first
null on the left/right of the 1st order.
 1 
blue  green 1 
 N 
red
 1 
 green 1 
 N 
Let’s look at the 2nd order
m=0 m=1 m=2 m=3 m=4
N=8
Green is here the reference wavelength λ.
Blue/red is chosen such that its 1st order peak lies in green’s first
null on the left/right of the 1st order.
 1 
blue  green 1 
 N 
red
 1 
 green 1 
 N 
Let’s look at the 2nd order
m=0 m=1 m=2 m=3 m=4
N=8
Green is here the reference wavelength λ.
Blue/red is chosen such that its 2nd order peak lies in green’s first
null on the left/right of the 2nd order.
Spectral resolution:
 1 
 1 

1
blue  green 1 
red  green 1


 2N 
 2N 
 2N
Let’s look at the 3rd order
m=0 m=1 m=2 m=3 m=4
N=8
Green is here the reference wavelength λ.
Blue/red is chosen such that its 3rd order peak lies in green’s first
null on the left/right of the 3rd order.
Spectral resolution:
 1 
 1 

1
blue  green 1 
red  green 1


 3N 
 3N 
 3N
General formula
m=0 m=1 m=2 m=3 m=4
N=8
Green is here the reference wavelength λ.
Blue/red is chosen such that its mth order peak lies in green’s first
null on the left/right of the mth order.
Spectral resolution:


1 
1 

1
blue  green 1
red  green 1



 mN 
 mN 
 mN
Building a spectrograph from this
Place a CCD chip here
Make sure to have small enough pixel size to resolve the
individual peaks.
Overlapping orders
m=0 m=1 m=2 m=3 m=4
N=8
Going to higher orders means higher spectral resolution.
But it also means: a smaller spectral range, because the
“red” wavelengths of order m start overlapping with the
“blue” wavelengths of order m+1
Effect of slit width
triple slit
incident
wave
d
w
lens
screen
Effect of slit width
single slit
incident
wave
As we know from the
chapter on diffraction:
This gives the sinc
function squared:
w
 w sin  
sin 2 

w sin  
  
I( )  I(0)sinc 
 I(0) 
  
 w sin  2 
 
 

  

lens
screen
Effect of slit width
triple slit
At slit-plane:
Convolution of N-slit
and finite slit width.
incident
wave
d
At image plane:
Fourier transform of
convolution =
multiplication
w
 w sin   Nd sin  
2
sin 2 
sin 

    

I( )  I(0) 
 w sin  2  2 d sin   
 sin 
 
 
        
lens
screen
Effect of slit width
N=16
d/w=8
Effect of slit width
N=16
d/w=8
Grating
• many parallel “slits” called “grooves”
• Transmission gratings and reflection
gratings
• width of principal maximum
(distance between peak and first
zeros on either side):
 


Ndcos
Credit: C.R. Kitchin “Astrophysical techniques”
CRC Press, ISBN 13: 978-1-4200-8243-2

• “Blazing”: tilt groove surfaces to
concentrate light towards certain
direction  controls in which order
m light of given  gets concentrated
blazed reflection grating
Grating, spectral resolution
• resolution in wavelength:
d
  
d
d
  cos 
m



Nm

R
 Nm

blazed transmission grating
Reflection grating with groove width w
and groove spacing d
w
-i

d
Basic grating spectrograph layout
46
Credit: C.R. Kitchin “Astrophysical techniques”
CRC Press, ISBN 13: 978-1-4200-8243-2
Basic grating spectrograph layout
Note: The word “slit” is
here meant with a different
meaning: Not a dispersive
element, but a method to isolate a
source on the image plane for
spectroscopy. From here onward,
“slit” will have this meaning.
Dispersive slit = groove on a grating.
47
Credit: C.R. Kitchin “Astrophysical techniques”
CRC Press, ISBN 13: 978-1-4200-8243-2
• Very basic setup: entrance slit in focal plane, with dispersive element
oriented parallel to slit (e.g. grooves of grating aligned with slit)
• 1 spatial dimension (along slit) and 1 spectral dimension
(perpendicular to slit) on the detector
• Spectral resolution set by dispersive element, e.g. Nm for grating.
• Spectrum can be regarded as infinite number of monochromatic
images of entrance slit
• projected width of entrance slit on detector must be smaller than
projected size of resolution element on detector, e.g. for grating:
s
f1
Ndcos
where s is the physical slit width and 1 is the collimator focal length
• slit width often expressed in arcseconds:
206265 f1
where F is the effective focal length of
sarcsec 
the telescope beam entering the slit
F Nd cos
spatial direction 

Longslit spectrum

spatial direction 
Example longslit spectrum
wavelength 
• high spectral resolution longslit spectrum of galaxy
• Continuum emission from stars, several emission lines
from star forming regions in galaxy
Gratings: characteristics
• Light dispersed. If d ~ w most light goes into 1 or 2 orders at given .
Light of (sufficiently) different  gets mostly sent to different orders
• Light from different orders may overlap (bad, need to deal with that!)
• Spectral resolution scales with fringe order m and is nearly constant
within a fringe order  ~linear dispersion (in contrast to prism!)
• Gratings are often tilted with respect to beam. Slightly different
expression for positions of interference maxima:
m

  asin  sin i
 d

or equivalently
sin   sin i 
m
d
i is the angle between the grating and the incoming beam. This
expression is called the “grating equation”


The “blaze function” describes the transmittance of light transmitted
or reflected into each order. It is the “envelope” of the interference pattern
(i.e. diffraction due to finite width of single groove, D)
long  go into low m,
short  go into high m
I
m
m
m
 + i [deg]
Blaze function vs. wavelength
I
m
m
m
Free spectral range
• “White” light coming in with
wavelength between 1 and 2
• light of wavelength  in first order
(m1) is diffracted in same direction
as light of /2 in m2, /3 in m3, etc.
• Free spectral range: largest 
interval in a given order that doesn’t
overlap the same  interval in an
adjacent order.
b   a 
a  1
b
a
a
m
Credit: www.shimadzu.com
shaded area: free spectral
range of order 2 light
practical example:
• We want to measure a spectrum starting from  = 400 nm in first order.
What spectral range can we cover?
Free spectral range is 400 nm in this case  400-800 nm
b   a
• We must insert a filter that blocks light of  < 400 nm and
 > 800 nm to get a “clean” spectrum
• The optimum blazing angle  is such that the direction in which light of
~600 nm (~middle of  range) corresponds to the angle of geometrical
reflection (with  and i defined
m
in same direction w.r.t. normal):
sin   sin i 
  2  i
d
m
 i
1
  asin   sin i
 d
 2
2

a
m
practical example (cont’d):
• If we wish higher spectral resolution, we may use a higher order.
Smaller free spectral range, e.g. 400-600 for m = 2, 400-533 nm for m =
3, etc. Use appropriate filters to block light outside these  ranges
• We can of course choose a different starting wavelength, e.g. 600-800
nm in order 3.
• Each combination of central wavelength order has its own optimum
blazing angle . But for a given grating,  is fixed. Tilting the grating
(i.e. change i) allows to control to which order light of given  is sent.
Order overlap in grating
•
•
Each order gives its own spectrum. These can overlap in
the focal plane: at a given pixel on the detector we can
get light from several orders (with different )
We must reject light from the unwanted orders. Solution:
1)
2)
For low orders m (low spectral resolution, large free spectral
range) one can use a filter that blocks light from the other orders
For high orders m (the free spectral range is very small), use
“cross disperser”: a second dispersive element (usually a prism),
mounted with the dispersion direction perpendicular to that of the
grating. Causes different orders to be spatially offset on the chip.
Advantage: multiple orders can be measured simultaneously.
High spectral resolution and large  coverage can be obtained
simultaneously. “Echelle spectrograph”
Echelle grating
• R  m. For high spectral resolution, use high order.
• Relatively large groove spacing (few grooves/mm) but very high
blazing angle. Concentrate light in high orders.
• Strong order overlap (solution: “cross-dispersion”, more later ...)
Echelle grating
Credit: C.R. Kitchin “Astrophysical techniques”
CRC Press, ISBN 13: 978-1-4200-8243-2
Echelle grating: cross dispersion
CCD
m=103
m=102
m=101
m=100
m=99
m=98
m=97
m=96
Without cross dispersion: different wavelength ranges overlap.
With cross dispersion: You get multiple short spectra.
Note of caution: Above cartoon is not exact: colors should be sorted vertically; but it shows the principle of separating orders.
Echelle grating: cross dispersion
CCD
m=103
m=102
m=101
m=100
m=99
m=98
m=97
m=96
Strong blazing angle means that you focus the light on the part
of the focal plane where the CCD is. Avoids waste of light.
optical layout
Echelle spectrograph
spectrum on detector
order m 
• Cross dispersion with prism placed
before grating
• high blaze angle, grating used in
very high orders (up to m~200)
• coarse groove spacing (~20 to
~100 mm-1) at optical wavelengths
 w > few  most light
concentrated in 1 direction  at
given  most light in 1 order
• Each order covers small  range,
but many orders can be recorded
simultaneously
60
Blaze function
order=
spectrum on detector
order m 
• Blazing angle defines in
which order light of given
 (mostly) ends up
• If sum of angles of
“incoming” and “exiting”
rays equals m/d (d is
groove spacing), all light
goes into order m
(assuming “perfect”,
lossless grating)
• For slightly smaller ,
part of the light goes into
order m+1
optical layout
Blaze function: “efficiency” of (an order of a) grating as a function of 
prism dispersion
Format of crossdispersed
Echelle spetrogr.
(Lick Observatory)
echelle
dispersion
Stellar spectrum
Spectroscopy & Spectrographs II
Roy van Boekel & Kees Dullemond
Some applications of spectroscopy
• Stellar spectroscopy: temperature, composition, surface gravity,
rotation, micro-turbulence
• Temperatures of interstellar medium, intergalactic medium
• radial velocities, mass and internal structure of stars,
exoplanets
• Dynamics & masses of milky way and other galaxies (dark
matter)
• Cosmology / redshifts
• spectro-astrometry (direct spatial information on scales << /D,
relative between continuum emission and spectral lines)
• composition of dust around young & evolved stars, ISM
Different Resolution for Different
Scientific Applications
•
•
•
•
Active galaxies, quasars, high-redshift objects: R ≈ 500 - 1,000
Nearby galaxies (velocities 30…300 km/s): R ≈ 3,000 - 10,000
Supernovae (expansion velocity ≈ 3,000 km/s): R > 100
Stellar abundances:
Hot stars: R ≈ 30,000
Cool stars: R ≈ 60,000 - 100,000
• Exoplanet radial velocity measurements. E.g. R ≈ 115,000
(HARPS). Best accuracy currently reached ~1 m/s, “effective” R
≈ 300,000,000. How: centroid of a single line measured to
much higher precision than spectral resolution + use many
lines, precision scales like 1/sqrt(Nlines)
Exoplanet detection by
radial velocity measurement
Planet is very difficult to
observe directly.
But planet and star rotate around
common center-of-mass
Star wobbles: Measure radial velocity of star (doppler).
Small effect: Need Δv=1 m/s effective spectral resolution
This means: Reff=c/Δv=3x108 !
Exoplanet detection by
radial velocity measurement
Beat the spectral resolution limit!
Flux
λ
Shifts of line centroid can be measured even if they are much
smaller than the line width.
Need: High signal-to-noise ratio and/or many lines.

Fourier transform spectrometer
• Incoming light is split 50:50
into two beams, then
reflected. Both beams are
combined, then focused onto
detector
• one mirror is moveable,
introduces path difference P
• for monochromatic source the
intensity on the detector is:
P
2


2P 
I(P)  Imax 1 cos

  

• interference pattern,
modulation with optical path
difference (OPD)
by wavenumber
I(k)
by OPD position
I(P)
k
P
Fourier transform spectrometer
• for a given position P the
intensity modulation due to
light interfering from all
wavelengths is:
Typical FTS interferogram
2P 
I(P)   Icos
d
  
 0

or, equivalently:
 P 
I(P)   I cos2
 d

c 
0

I(P)
Take I(-ν)=I(ν) so that we get:
 P 
I(P)   I  cos2
 d

c 


1
2
P (mm)
Fourier transform spectrometer
• Thus, the output signal is the Fourier
transform of the spectrum I()
•
Note: Fourier Transform of a symmetric function is
real-valued, so the output signal is the complete
Fourier transform (no imaginary part exists).
• Inverse Fourier transform of the
interferogram I(P) yields source
spectrum I()
• Spectral resolution scales directly
with total length of OPD scan (say, x):
 2x
R

 

• x can be up to ~2m  R can be
several million in the optical
example spectrum taken with an FTS
Multiple object spectroscopy
• Often you want spectra of many objects in the same region on
the sky
• Doing them one by one with a longslit is very time consuming
• When putting a slit on a source in the focal plane, the photons
from all other sources are blocked and thus “wasted”
• Wish to take spectra of many sources simultaneously!
• Solution: “multiple object spectrograph”. Constructed to guide
the light of >>1 objects through the dispersive optics and onto
the detector(s), using:
– a small slit over each source (“slitlets”)
– a glass fiber positioned on each source
– “integral field unit”
Multiple slit(lets) approach
• A slitlet is a longslit, but of much shorter length than most “single”
longslits
• Normally done using focal plane “masks”: metal plates in which
slitlets are cut, nowadays mostly done automatically by cutting
devices using high-power lasers
• Advantages:
– (can do many objects simultaneously)
– small longslits: sample object and sky background in each slitlet  good
sky correction in each spectrum
– slits can be cut in almost any shape (useful for extended sources)
• Disadvantages:
– a new mask must be made for each field, often more than 1 mask/field
– not complete freedom where to put slits (spectra should not overlap on
detector)
Multi-object spectroscopy with slitlets
CCD
slit
CCD
Wasted CCD real estate
Wasted CCD real estate
Multi-object spectroscopy with slitlets
CCD
CCD
• First do pre-imaging to find the stars/objects of interest + reference object
• Create mask using computer program (mask is then cut in metal plate with laser)
• Go back to telescope, do acquisition to center slits on objects
• Do spectroscopic integration
Multi-object spectroscopy with slitlets
CCD
CCD
• But: Some slit combinations are forbidden: They would result in overlapping
spectra
Credit: unknown
near infrared multipleobject spectroscopy
with SUBARU/MOIRCS
Slitlets approach, “peculiarities”
• Optical layout essentially the same as with normal (single)
longslit, but instead of single slit ~centered in focal plane,
multiple slits distributed over focal plane. Consequences:
– all slitlets have same dispersion direction  all slitlets must have
similar orientation ~perpendicular to dispersion direction (simple
straight slits exactly perpendicular to dispersion direction in most
cases)
– wavelength scale is different for each slitlet, depending on its
position
– if chip size limits spectral range (end - start) that fits on detector,
then start and end depend on position of object (slit) on sky
– if two slits are close together in spatial direction but far apart in
dispersion direction, spectra can overlap due to optical distortions
Slit width issues
• Spectral resolution is limited by R of the spectrograph...
• ...but also by the slit width.
• Conversely: Slit width ~ brightness of the spectrum on the CCD
Lower R
Brighter on CCD,
but also more
background noise
Higher R
Weaker signal,
but less background
noise
• Optimum slit width is balance between low slit losses (wide slit)
versus low background and high spec. res. (narrow slit)
• In general: Higher R requires longer exposure for same
Signal-to-Noise ratio
MMT / Hectochelle
MOS with fibers
• instead of putting a slitlet on each
source in the focal plane, position
the head of a glass fiber on each
source (movable)
• fibers pass light of each object into
the instrument
• put the other end of all fibers in a
row and feed light into spectrograph
• result: one spectrum for each
source, all spectra “nicely” aligned:
wavelength scale the same for all
spectra, and spectra regularly
spaced in spatial direction
• Disadvantage: no spatial info,
background subtraction using “sky”
fibers.
fiber head close-up
Integral Field Units
•
•
•
A multiple object spectrograph is good at getting spectra
of many sources in the same field
Sometimes we would like to take a spectrum at every
position of a spatially extended object (e.g. a galaxy).
This can be done with an Integral field unit (IFU)
We need to “catch” the light at each position, guide it
through dispersive optics and project the spectrum of
each position onto (a different part of) the detector. This
can be done in two basic ways:
1)
2)
•
Using an “image slicer”
Using “lenslets” and fibers
NOTE: It will have low spatial resolution, because 2D
space + 1D λ have to fit on a 2D CCD...
JWST / MIRI
Image Slicer
• Many narrow (~spatial
resolution element)
long slits, each with
slightly different tilt
• effectively, do a large
number of longslits
simultaneously, send
each slit into a different
direction
• slits imaged next to
each other on detector
Credit: unknown
Gemini / CIRPASS
“Lenslets” &
Fibers
• Focal plane filled with
“lenslets”. Each lenslet
injects (nearly) all light
falling onto it into a
fiber
• Fibers are fed into a
spectrograph, in the
same way as with the
fiber Multiple Object
Spectrograph
85
Spectroscopy: procedure
• Recording the data
– science observation
– calibration observations: flatfield, “arcs” ( calibration), spectrophotometric standard stars
• Data analysis/calibration
– going from raw data to a calibrated spectrum in e.g. [erg/s/cm2/Hz]
• Interpretation of spectra, i.e. what do we learn about the
object?
– Use laws from your physics textbook or more elaborate numerical
models of your science target to derive:
•
•
•
•
Chemical composition of sources
Thermal structure of objects
Velocity structure of objects
...
Spectroscopic flat field
(Dome flat or twillight flat)

slit “imperfections”
spatial direction 



87
dispersion direction

Wavelength calibration
• We measure intensity I as a function of pixel
position on a CCD
Part of the CCD
spectrum of target
...but the CCD does
not “see color”
Wavelength calibration
• We measure intensity I as a function of pixel
position on a CCD
• How do we know which pixel corresponds to
which wavelength?
Part of the CCD
spectrum of target
Part of the CCD
spectrum of lamp with known lines
“arc”
...the CCD sees this
Illuminate spectrograph
with a lamp with known
lines before or after your
observation.
spatial direction 
Wavelength calibration: “arc”
90
dispersion direction

Telluric + flux calibration
•
Find nearby spectro-photometric standard star, which
has known flux-calibrated spectrum
Extract the spectrum of the standard star(s). If the
standard was taken immediately before and/or after the
science exposure you can get a science spectrum that
is corrected for telluric absorption and is flux calibrated
as follows:
•
Fraw, science
Fcalibrated, science  Fstandard
Fraw, standard
where Fstandard is the (known)
spectrum of the standard star

Telluric + flux calibration
More general approach if science target and standard star were
not taken at (nearly) the same airmass:
Possibility 1: observe standards at various airmasses and fit the instrument
response R and the atmospheric extinction coefficient A (i.e. the same
procedure as for photometry, but now at each wavelength instead of
integrating over a filter). Calculate the calibrated science spectrum F
from the raw science spectrum S observed at airmass am using
F = S exp(A am) / R
Possibility 2: Use a theoretical model for the Earth atmosphere and fit this to
the calibrator observation and then extrapolate to the airmass of the
science observation, or fit it to the science observation directly. Divide by
synthetic spectrum to correct for Atmosphere. Use the standard star
observation(s) for flux calibration.
Choosing standard stars
A “good” standard star has the following properties:
•
•
•
•
it is comparatively bright (so we don’t need much time for calibration)
its intrinsic spectrum is known perfectly
it has as little spectral structure as possible, i.e. a “smooth” spectrum
it is close to your science target on the sky
The “best choice” depends on the application and 
regime:
• Hot stars (spectral type B, the hotter the better) are much used because:
– they have relatively little spectral structure: H lines, weak lines of He and ionized
metals, weak Balmer discontinuity
• If we study H lines in science target, calibrator should have no H lines
– G stars have relatively weak, narrow H lines (but many other lines, careful!)
• For mid-IR applications, we need mid-IR bright calibrators
– often limited to K and M type giant stars, + nearest hot stars
A note on telluric calibration
Optical regime:
• in most of the optical regime (~350 to ~1000 nm) the Earth atmosphere has
no “structure” in its absorption spectrum, i.e. no atomic/molecular
absorption lines. In the “red” part there are some lines (mainly O2 and
H2O). There is, of course, scattering off molecules and aerosols causing
substantial but smooth extinction.
• For work requiring no absolute calibration, e.g. measuring equivalent
widths of lines in astronomical sources, no telluric calibration is required
Infrared regime:
• Strong spectral structure in the atmospheric absorption spectrum (and in its
emission spectrum!)
• Very careful telluric calibration needed, even if no absolute flux calibration
is required.
Very high R work: peculiarities
• For accurate  calibration, need to take Earth motion into account
(orbital motion up to 30 km/s corresponding to R = 104, daily rotation
up to 460 m/s corresponding to R = 6.5105)
• In the infrared, at high resolution the atmospheric opacity breaks up
into very many narrow absorption lines. A specific spectral line you
wish to measure may coincide with a telluric line and not be
measurable at some instant, but due to the Earth’s orbital motion it
may have red- or blue shifted out of the telluric absorption line later in
the year. “Best time of year” depends on position of source w.r.t.
ecliptic and the source radial velocity
• When  calibration must be extremely good (e.g. for Exoplanet radial
velocity measurements) we cannot use separate  calibration frames,
calibration must be done simultaneously with science observation.
Use gas absorption cell or telluric lines
Quantifying “line strength”
The term “line strength” is not uniquely defined.
Various ways of quantifying it exist:
1) Peak intensity
– Problem with low spectral resolution, because each
“pixel” is an integral over the pixel width:
Flux
λ
Quantifying “line strength”
The term “line strength” is not uniquely defined.
Various ways of quantifying it exist:
1) Peak intensity
– Problem with low spectral resolution, because each
“pixel” is an integral over the pixel width:
Flux
Peak strength is
underestimated
λ
Quantifying “line strength”
The term “line strength” is not uniquely defined.
Various ways of quantifying it exist:
2) Frequency-integrated flux in the line
Advantage: Can also be measured with low-resolution
spectrographs (if no continuum is present)
Flux
λ
Quantifying “line strength”
The term “line strength” is not uniquely defined.
Various ways of quantifying it exist:
3) Equivalent width
Only when a continuum is present
Flux
continuum
absorption
line
λ
Quantifying “line strength”
The term “line strength” is not uniquely defined.
Various ways of quantifying it exist:
3) Equivalent width
Only when a continuum is present
EW
Flux
continuum
absorption
line
λ
Spectro-astrometry
Beat the spatial resolution limit!
Flux
x [“]
• At each velocity channel the emission might
be slightly shifted in space.
• Plot spatial shift as a function of velocity
Spectro-astrometry
Offset [AU at 160 pc]
Beat the spatial resolution limit!
SR 21
0.006”
0.003”
0.000”
-0.003”
-0.006”
From: Pontoppidan et al. 2008
Diffraction limited resolution of VLT at 4.7 μm is 1.22λ/D=0.15”
Spectro-astrometry
Beat the spatial resolution limit!
1000x
higher
resolution
than this
radio
image!
Brown et al. 2009
P Cygni line profiles: Stellar winds
wind
star
Flux
blue
Star emits emission line.
Wind is cooler at large radii.
So the wind makes absorption line.
But blue-shifted!
red
v [km/s]
P Cygni line profiles: Stellar winds
λ [Å]
Gemini Observatory/AURA, Travis Rector
Aspin et al. 2009
• McNeal’s nebula is a reflection of
light from a just-born star.
• This reflection appears only nowand-then: when the star has a
“hickup” (outburst).
• The P Cyg Hα profile shows: mass
is ejected during this outburst!
Example of low-R
Infrared spectroscopy
-
-
Origin of dust species in disk around
young stars, solar system comets, and
building blocks of planets
Young star undergoes accretion
outburst
Amorphous dust turns into crystals
Credit: Spitzer Science Center
Abraham et al. 2009