Astronomical Spectroscopy
Notes from Richard Gray, Appalachian State, and
D. J. Schroeder 1974 in “Methods of Experimental
Physics, Vol. 12-Part A Optical and Infrared”, p.463.
See also Chapter 3 in “Stellar Photospheres” textbook
Elements
Resolution
Grating Equation
Designs
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Schematic Spectrograph
Collimator
Camera
Detector (CCD)
Slit
Converging light
from telescope
Disperser
(prism or
grating)
2
Slit Spectrographs
• Entrance Aperture: A slit,
usually smaller than that
of the seeing disk
• Collimator: converts a
diverging beam to a
parallel beam
• Dispersing Element:
sends light of different
colors into different
directions
• Camera: converts a
parallel beam into a
converging beam
• Detector: CCD, IR array,
photographic plate, etc.
3
Why use a slit?
1) A slit fixes the resolution, so that it does
not depend on the seeing.
2) A slit helps to exclude other objects in
the field of view
A spectrograph should be
designed so that the slit
width is approximately
the same as the average
seeing. Otherwise you
will lose a lot of light.
4
Design Considerations: Resolution vs Throughput
Without the disperser, the spectrograph optics
would simply reimage the slit on the detector.
With the disperser, monochromatic light passing
through the spectrograph would result in a single
slit image on the detector; its position on the detector
is determined by the wavelength of the light.
This implies a spectrum is made up of overlapping
images of the slit. A wide slit lets in a lot of light,
but results in poor resolution. A narrow slit lets in
limited light, but results in better resolution.
5
Design Considerations: Projected slit width
f2
f3
Collimator focal length
Camera focal length
Let s = slit width, p = projected slit width (width of slit on detector).
Then, to first order:
 f3 
p  s
 f2 
Optimally, p should have a width equal to two pixels on the detector.
Resolution element Δλ = wavelength span associated with p.
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Design Considerations: Spectral Resolution vs. Spectral Range

R

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Dispersers
Prisms: disperse light into a spectrum
because the index of refraction is a
function of the wavelength. Usually:
n(blue) > n(red).
Diffraction gratings: work through
the interference of light. Most modern
spectrographs use diffraction gratings.
Most astronomical spectrographs use
reflection gratings instead of transmission
gratings.
A combination of the two is called a
Grism.
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Diffraction Gratings
Diffraction gratings are made up of very narrow grooves which
have widths comparable to a wavelength of light. For instance,
a 1200g/mm grating has spacings in which the groove width is
about 833nm. The wavelength of red light is about 650nm.
Light reflecting off these grooves will interfere. This leads
to dispersion.
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The Grating Equation
Light reflecting from grooves A and
B will interfere constructively if the
difference in path length is an
integer number of wavelengths.
The path length difference will
be a + b, where a = d sinα and
b = d sinβ. Thus, the two
reflected rays will interfere
constructively if:
d
m  d (sin   sin  )
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m  d (sin   sin  )
Meaning: Let m = 1. If a ray of light of wavelength λ strikes
a grating of groove spacing d at an angle α with the grating
Normal, it will be diffracted at an angle β from the grating.
If m, d and α are kept constant, λ is clearly a function of β.
Thus, we have dispersion.
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m  d (sin   sin  )
m is called the order of the spectrum. Thus, diffraction gratings
produce multiple spectra. If m = 0, we have the zeroth order,
undispersed image of the slit. If m = 1, we have two first order
spectra on either side of the m = 0 image, etc.
Diffraction grating
illustrated is a
transmission grating.
These orders will overlap, which produces problems for grating
spectrographs.
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Overlapping of Orders
If, for instance, you want to
observe at 8000Å in 1st order,
you will have to deal with the
4000Å light in the 2nd order.
This is done either with blocking
filters or with cross dispersion.
Overlap equation:
m1
m
 m
m1
Massey & Hanson 2011
arXiv 1010.5270v2.pdf
Meaning that a wavelength of λm in the mth order overlaps with a
wavelength of λm+1 in the m+1th order.
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14
Dispersion & Resolution
Dispersion is the degree to which the spectrum is spread out.
To get high resolution, it is really necessary to use a diffraction
grating that has high dispersion. Dispersion (dβ/dλ) is given by:
d
m

d d cos 
f 3 d
R

p d
Thus, to get high resolution, three strategies are possible:
long camera focal length (f3), high order (m), or small
grating spacing (d). The last has some limitations. The
first two lead to the two basic designs for high-resolution
spectrographs: coudé (long f3) and echelle (high m).
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Grating Spectrographs
• Reciprocal dispersion P=(d cosβ)/(mf3)
(often quoted in units of Å/mm)
• Free spectral range
m(λ+Δλ)=(m+1)λ  Δλ=λ/m
λ difference between two orders at same β
• Blaze angle with max. intensity where
angle of incidence = angle of reflection
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Blaze wavelength
• β – θB = θB – α
• θB = (α+β)/2
δ/2 = (β-α)/2
• Insert in grating eq.
λB=2d sinθB cos(δ/2)
• Blaze λ in other orders
λm = λB /m
• Manufacturers give
θB for α=β (Littrow)
17
Blaze function FWHM≈λ/m
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Three basic optical designs for spectrographs
Littrow (not commonly used in
astronomy).
Ebert: used in astronomy, but
p = s. Note camera = collimator.
Czerny-Turner: most versatile
design. Most commonly used
in astronomy.
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High-resolution spectrographs: Echelle
Echelle grating: coarse grating (big d) used
at high orders (m ~ 100; tan θB = 2).
Kitt Peak 4-m Echelle
Orders are separated by cross
dispersion: using a second
disperser to disperse λ in a
direction perpendicular to the
echelle dispersion.
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Hamilton echelle spectrum format:
Vogt 1987, PASP, 99, 1214
m
λ
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