Download Lecture Notes on Practical Spectroscopy

(Very) Basic Spectroscopy
Spectroscopy vs. Imaging I
Imaging yields
data products
like this…
1
While spectroscopy yields data products like this…
and this…
2
Of course, imaging is in some ways just “Low-Resolution”
Spectroscopy…
…but that’s oversimplifying
the real physical differences in the process.
The Real Story
Imaging – flux in each pixel is a function of the position angle
and luminosity of objects at that pixel’s position in the
detector plane (filters add some simple wavelength
dependence).
Spectroscopy – flux in each pixel is a function of wavelength
and the luminosity at that wavelength of the object
illuminating the dispersion element (and position angle
too, for spatially resolved spectroscopy!)
Note: We’ll focus on spectroscopy in the visual range for
now, and discuss other wavelength regimes later.
3
Basic Spectral Features
Continuous Spectra/Continuum Flux
Absorption Lines
Emission Lines
4
What can spectroscopic data tell me?
Radial velocity – Doppler shift of spectral lines
• global, internal kinematics
• distance proxy
Spectral Line profiles
• chemical abundances
• density
• temperature
5
6
7
8
9
10
11
Basic Spectrograph Design
Focal Plane
collimator
camera
detector
Dispersing element
Slit
Telescope
Spectrograph
12
13
Dispersion by a Prism
θ
L
α
d
C1

3
d
L sin 
Note the very strong,
negative dependence
on wavelength.
14
Dispersion by a Grating
Dispersion produced by diffraction gratings differs from
that of prisms in three major ways:
1. Red light is dispersed more than blue light.
2. The dispersion is uniform over meaningful ranges of
wavelength space.
3. Several spectra are formed on either side of a central
image.
For these last two reasons in particular – not to mention basic
engineering concerns – diffraction gratings are by far the most
common form of dispersive element in modern spectrographs.
15
I1
I2
D1
α
D2
β
Reflected light
(zero order
diffraction).
σ
θ
The physical reason this works is the difference in the path length
between rays I1 and I2. If this difference is equal to an integral
number of wavelengths, then we have constructive interference.
This condition is summarized in the “grating equation”:
m   (sin   sin  )
where m is the order number of the diffraction pattern. The
angular location of maximum constructive interference in
each order for any wavelength is then given by:
d
m
sin   sin 


d  cos 
 cos 
Note that this dispersion is proportional to the diffraction order
m and inversely proportional to the groove spacing σ.
16
Now you might have noticed there is a serious issue with this
diffraction + interference game – anywhere m1λ1 = m2λ2 , we’ve
got an ugly degeneracy. For example, if λ1 = 6000Å, then the first
order maximum (m=1) emerges at the same angle as the second
order maximum (m=2) for λ2 = 3000Å – and (m,λ) = (3, 2000), (4,
1500), (5, 1200), etc. – with increasing overlap at higher order!
17
One solution to this problem is achieved through adjusting the
blaze angle (θ) of the grating. Proper blazing can cause as much
as 70% of the light to be focused into one order (this is also how
we get around the fact that, without blazing, most of the light
would fall into the zero order!). Filters can then also be used to
remove any unwanted light from other orders.
Another solution involves
passing the overlapping
orders through a second
dispersing mechanism
that separates the light
orthogonally to the first
axis of dispersion. Such
echelle spectrographs can
collect photons across
many overlapping orders,
often of surveying the
entire optical wavelength
regime in one image.
18
The Value of Dispersion
Now that we have our light dispersed as an angular function
of wavelength, proper placement of a detector into the focal
plane of the instrument produces a linear dispersion, with
each set of pixels measuring flux at a different wavelength.
This linear dispersion is often referred to in a shorthand way
as the resolving power (or resolution) of the spectrograph:
R = λ / Δλ
, where Δλ is the smallest resolvable element in wavelength
space – generally the difference in wavelength between sets
of adjacent pixels. Low resolution spectrographs have R <
10,000, while some spectrographs have resolutions as high
as R > 200,000!
19
The Value of Dispersion
Some examples relating the linear dispersion of a
spectrograph to the Doppler shift of a light source might make
some of this more clear:
R = λ / Δλ ~ c / v
What resolution would you need in order to view the
recession of a distant galaxy? Proper motions of nearby
stars? The reflex motion induced by extrasolar planets?
These physical questions are often the deciding factors in
determining which spectrograph you want to use!
Finally, Some Practical Spectroscopy Issues –
Good News, Bad News
Some pluses –
– Bad seeing? No problem! Poor focus? No problem! As
long as you can clearly get your object on the slit, it
doesn’t matter much (unless you’re doing spatiallyresolved spectra – more on that later).
– No sky flats! (Lamp flats instead – muy muy facíl!)
Some minuses –
– Most (but not all!) spectrograph designs can only observe
one object at a time (more about this next time!).
– Limited per-pixel bandwidth means fewer photons! This
worsens for higher resolution.
20
New Reduction Steps I
Wavelength-to-Pixel Mapping: Calibration lamps
• optics map flux to pixels as a function of wavelength.
• observe emission lamps with precisely measured rest
wavelengths for a large number of lines encompassing the
entire observed range.
• examples: Thorium-Argon, Helium-Neon
Example: Th-Ar Lamp
21
In Practice…
At least one set of calibration lamp images should be taken
every evening. Depending on the wavelength/velocity
resolution needed, you may need to take additional lamp
images throughout the night (all the way up to taking a
calibration image simultaneously with every science image:
finding extrasolar planets!).
New Reduction Steps II
Telluric (Earth-based) lines: “Hot stars” images
• absorption/emission lines are present in the Earth’s
atmosphere.
• observe “featureless” stellar spectra from fast-rotating,
early-type stars – almost all spectral features are telluric.
• strength of lines is a function of airmass.
22
Near IR Spectra
from a G-type
dwarf before
(top) and after
(bottom)
dividing out the
spectra from a
B2-type star
In Practice…
At least one “hot star” image should be taken every evening.
Since the strength of the telluric features scale with how
much air you’re looking through, you should observe your
“hot star” at a similar airmass to your science targets. If your
targets span a large range in airmass ( ~ 1), consider taking
multiple “hot star” images over a similar range.
23
Spectroscopic Resources
Calibration Lamps
http://www.noao.edu/kpno/specatlas/index.html – NOAO
http://hebe.as.utexas.edu/2dcoude/thar/ – UTexas
Solar Spectra
http://bass2000.obspm.fr/solar_spect.php – BASS2000
24