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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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
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.
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.
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 Δλ = wavelength span associated with p.
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
A combination of the two is called a
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
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
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.
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.
illustrated is a
These orders will overlap, which produces problems for grating
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
Meaning that a wavelength of λm in the mth order overlaps with a
wavelength of λm+1 in the m+1th order.
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:
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).
Littrow (not commonly used in
Ebert: used in astronomy, but
p = s. Note camera = collimator.
Czerny-Turner: most versatile
design. Most commonly used
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