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Spectra Data Reduction Techniques

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					          Spectra: Data Reduction Techniques
2 Wavelength Calibration and Coordinate Transformations
Science spectra should always be acquired in conjunction with a pair of arc-lamp calibration spectra.
These arc spectra are needed to establish the dispersion relation (the mapping between wavelength
and pixel) for the science spectrum. To use these spectra to find the dispersion solution and then
apply that solution to the science spectra, proceed as follows.

    • For each science spectrum, identify which arc spectra are associated with it. Create a ‘master
      arc spectrum’ for each science spectrum by combining any associated arc spectra into a single
      spectrum (using imarith or imcombine), or by copying the single associated spectrum if
      there is only one (using imcopy). Note that a single arc spectrum may provide calibration
      for more than one science spectrum (e.g., if you alternated taking science and arc spectra,
      then each science spectrum would be associated with the two flanking arc spectra, and each
      arc would be associated with two flanking science spectra). It is useful to name the master
      arc spectrum for each science spectrum by a readily recognized name (say, the name of the
      science spectrum with a ‘c’ appended) 1 . Having produced a master arc spectrum for each
      science spectrum, select one of the master arc spectra to begin the wavelength calibration.2

    • Load the noao.twodspec.longslit package, and run the identify task on the selected master
      arc spectrum (hereafter referred to as the ‘reference arc spectrum’). First, use epar to set
      some parameters. The SECTION should be set to “[*,10]” (i.e., the first useful line of the
      image), and the COORDLIST should be a feature list file for the type of source you’re using
      (e.g., neon, argon). Choose the fitting function and a default fit order to start with. Avoid
      spline fits since they can easily fit incorrect features; try using “legendre” or “chebyshev”. A
      good default fit order is probably 4; if you find later that a higher order would be better, then
      you can change it while running the task.
      The objective for this task is to identify the emission features in the spectrum with wavelengths
      listed in the the coordinate list. This is done by first establishing a rough calibration using
      a few known and readily recognized features. The identify task will bring up an interactive
      graphic tool, showing the spectrum for the first section of your image3 . Mark a few known
      features using the ‘m’ key, entering the expected wavelength (to within an ˚ or so) at the
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   1
     E.g., if you have a science spectrum of the object 3C273 in the file oct1203.fits it is useful to name the master arc
spectrum oct1203c.fits. It isn’t so useful to name it 3C273c.fits, particularly if you have more than one observation
of 3C273!
   2
     If your master arc spectrum has a lot of continuum contribution in addition to the emission features, you may
want to remove the continuum component by fitting a 2D surface to the image using a task such as imsurfit in the
images.imfit package. Just make sure that the order of the fit is low enough that you are not removing any of the
desired emission features.
   3
     A few hints on using graphic tools in IRAF:
   – pressing ‘?’ at any time will call a help file which explains the various keystroke options.
   – You can zoom in to a region of a plot by typing ‘w’, then using ‘e’ and ‘e’ to define the corners of the region.
     Zoom out to full by typing ‘w’, then ‘a’.



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      prompt. If a matching wavelength is found in the featurelist, it will be reported on the next
      line. It is useful to be somewhat imprecise when entering the wavelength, as the change
      between what you enter and is then reported makes it obvious that a match has been found.
      Repeat this procedure for a few features.
      In some cases, such as when working with a grating/spectrograph/wavelength-region you have
      never used before, you often do not know ANY feature wavelengths. There are several ways to
      get around this problem. One is to go to one of the science spectra and attempt to establish
      a low-order dispersion solution by hand by using recognizable sky features. The other is to
      use some form of feature atlas, in which someone else has gone to the effort of identifying the
      features. The best atlas to use is one from the same telescope/spectrograph as your data,
      as the detailed response of each system is somewhat different; of course, such an atlas is
      not always available. The Kitt Peak Observatory (the primary American national facility in
      the continental U.S.A.) maintains an online interactive atlas which may also be useful. See
      http://www.noao.edu/kpno/specatlas.

• Once you have identified a few features, enter the fitting portion of the identify task using
  the ‘f’ key. This activates a standard IRAF fitting package, where the inputs are the pixel
  centroids and wavelengths of the features you have identified. The most instructive plots to
  look at are the non-linear component of the fit and the residual (get these using the ‘l’ and
  ’j’ keys respectively). You can change the order of the fit on the fly in this task; for instance
  if you want to change to a third order fit simply type “:order 3”. Features which lie off the
  mean relation can be deleted using the ‘d’ key, and the relation can be re-fit using the ‘f’ key.
      When you are satisfied with the initial fit, return to feature identification mode using the ‘q’
      key. Then simply press the ‘l’ key, and identify will try to pick out and match all peaks in
      the spectrum. Having done this, return to the fitting routine, and produce a final fit to all
      the points, deleting outliers as appropriate. It is often useful to go back and forth between
      the feature identification and fitting several times, to ensure that you converge on the correct
      wavelength solution4 . Note that you should also delete features which are very weak, or too
      crowded by other features; in either case it may not be possible for the identify task to
      calculate an accurate centre for the feature, and your wavelength solution can be less accurate
      as a result.

• When you are satisfied with the dispersion solution for that line of the image, move on to
  the next line by typing ‘k’ (in feature identification mode; this won’t work in fitting mode).
  Note that you will probably not be moved to the next line — e.g., you may move from line 10
  to line 20 rather than to line 11. This depends on the value of NSUM, the parameter which
  controls how many lines are averaged in each fit. It is useful to use NSUM> 1, so that any
  hot pixels etc. are averaged over, and to increase the feature strength in an image with poor
4
    A few hints for the feature identification mode of identify:
– ‘.’ selects the nearest marked feature (whose wavelength etc. will then be printed at the bottom of the plot).
  With ‘+’ and ‘-’ you can select the next feature to the right or left. Use ‘z’ to zoom in on a selected feature,
  and ‘p’ to pan back out again.
– You can use ‘s’ to shift the feature to a new location, which is especially useful when propagating your solution
  from one line to the next — if a feature has moved slightly, you can shift the mark accordingly.



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  S/N. And there’s no need to fit a new solution to every feature since the dispersion relation
  is unlikely to change that fast.

• When you have found the dispersion solution for all lines in the image quit the identify task,
  making sure to save the output in the database.

• The next step in establishing the dispersion solution is to propagate the initial solution on
  this arc spectrum to all the master arc spectra. This is done using the reidentify task. For
  this task, SECTION should be set to that used in the identify task, and NEWAPS should be
  set to “yes”. All other parameters are self-explanatory or can be left unchanged.

• With a mapping between x, y and x′ , λ now established at a large number of x, y pairs on
  each master arc spectrum, the next step is to produce a polynomial representation of this
  mapping. This is done using the fitcoordinates task. The first few times you use this task
  on a particular dataset, it is best to do so interactively, so as to establish the appropriate
  orders to use for the fit. Try to find the lowest order fit (there are several types to choose
  from) which leaves only random residuals. Having found this, run the task on all the master
  arc spectra non-interactively.

• Finally, use the transform task to apply the fitted polynomial to the associated science
  spectrum. You should now have a set of 2D wavelength-calibrated, distortion-corrected science
  spectra.




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