Section 4: Spectroscopic Measurements Flashcards
what are the quantities we obtain from a spectrum
-precise wavelength determination of features ie lines and edges
-spectral energy density of the continuum
-spectral line shape (intensity, width(
quantities obtained from a spectrum are interpreted using
physical models for the production of radiation
or laboratory or other standard measurements to derive parameters like density, temperature, velocity etc
most spectrometers in use are based on
diffraction gratings or interference filters
(fourier transform spectrometers based on michelson are also used for high spectral-resolution work, especially in the infrared)
Modern spectrometers often imaging spectrometers, called Integral Field Units, giving spectrum for
multiple x.y positions in image
grating spectrometer results
spectral resolving power
angular dispersion
grating response width
spectral resolving power
Rg = Ξ»/delta Ξ» = Ngm
angular dispersion
d theta /dΞ» = m/acos theta
grating response width
Wg=Ξ»/Nga
lower limit to the angular width of lines produced by spectrometer
problems with raw spectra
usual CCD problems (cosmic ray hits, flatfieldβ¦)
spectral lines tilted on detector
no wavelength identification
For ground-based instruments, wavelength calibration for gratings or prisms is sometimes done using
absorption lines from the Earthβs atmosphere (telluric lines)
alternative method for ground-based instruments, wavelength calibration is done using
reference spectral emission lamp
(the spectrum from the source and from the calibration lamps is imaged onto the same CCD)
standard reference lamps include
Thorium/Argon and He/Ne/Ar
x is the position on the CCD, expressed in
βpixel numberβ
the dispersed reference spectrum or the reference telluric lines provide calibration as follows
- strong lines/patterns of lines from reference spectrum identified using spectral atlas
- fit spectral profile (eg gaussian) on CCD to find x position of central Ξ» of ref lines
- a curve is fitted to these identifications, giving Ξ»(x)
CCD-based spectroscopes provide a
2D image of the spectrum
the dispersed emission line spectrum consists of
multiple images of the spectroscope slit, spread in colour/position along the CCD
ideally, slit images should be as
narrow as possible and aligned with CCD columns
to get a spatially integrated spectrum, sum
down columns to produce spectrum
In practice, there might be slight mis-alignments of the optics, which
will result
in tilted slit images
in a ground-based instrument, tilted slit images could, in principle, be corrected by
rotating the detector
in a space-based instrument, tilted slit images need to be correct in the
data analysis phase
ie rotation of the spectral lines so they are aligned with the y-axis
however this remapping can cause other issues
what if the remapped pixel values are not integers, how to we assign the counts to actual pixel positions
this is done by interpolating the data to the integer pixel positions
(consider the 1D problem and assume that the data follows a piecewise linear cure)
interpolation - the gradient between i1β and i2β is
m=N(i2β)-N(i1β) / i2β-i1β
(denominator is approx 1)
interpolation - the value of N(iβ) at pixel iβ is
starting point:
N(iβ)=N(i1β) +m(1- deltaiβ)