Astronomical Spectroscopy Notes from Richard Gray, Appalachian State, and D. J. Schroeder 1974 in

1
Astronomical SpectroscopyNotes from Richard
Gray, Appalachian State, andD. 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

• ElementsResolutionGrating EquationDesigns

2
Schematic Spectrograph
Camera
Collimator
Detector (CCD)
Slit
Converging light from telescope
Disperser (prism or grating)
3
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.

4
Why use a slit?

• A slit fixes the resolution, so that it does
• not depend on the seeing.
• 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.
5
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.
6
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
Optimally, p should have a width equal to two
pixels on the detector.Resolution element ??
wavelength span associated with p.
7
Design Considerations Spectral Resolution vs.
Spectral Range
8
Dispersers
Prisms disperse light into a spectrum because
the index of refraction is a function of the
wavelength. Usually n(blue) gt 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.
9
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.
10
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 sina and b d sinß. Thus, the two reflected
rays will interfere constructively if
d
11
Meaning Let m 1. If a ray of light of
wavelength ? strikes a grating of groove spacing
d at an angle a with the grating Normal, it will
be diffracted at an angle ß from the grating. If
m, d and a are kept constant, ? is clearly a
function of ß. Thus, we have dispersion.
12
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.
13
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.
Massey Hanson 2011arXiv 1010.5270v2.pdf
Overlap equation
Meaning that a wavelength of ?m in the mth order
overlaps with a wavelength of ?m1 in the m1th
order.
14
(No Transcript)
15
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 (dß/d?) is given by
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 spectrog
raphs coudé (long f3) and echelle (high m).
16
Grating Spectrographs

• Reciprocal dispersion P(d cosß)/(mf3) (often
  quoted in units of Å/mm)
• Free spectral range m(???)(m1)? ? ???/m?
  difference between two orders at same ß
• Blaze angle with max. intensity whereangle of
  incidence angle of reflection

17
Blaze wavelength

• ß ?B ?B a
• ?B (aß)/2d/2 (ß-a)/2
• Insert in grating eq.?B2d sin?B cos(d/2)
• Blaze ? in other orders?m ?B /m
• Manufacturers give?B for aß (Littrow)

18
Blaze function FWHM?/m
19
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.
20
High-resolution spectrographs Echelle
Echelle grating coarse grating (big d) used at
high orders (m 100 tan ?B 2).
Kitt Peak 4-m Echelle
Orders are separated by cross dispersion using a
second disperser to disperse ? in a direction
perpendicular to the echelle dispersion.
21
Hamilton echelle spectrum formatVogt 1987,
PASP, 99, 1214
m
?