VI. Basic Reductions for Spectroscopic Data

NOTE: for a much more complete and detailed picture of spectral reductions, see the tutorial: A User's Guide to Reducing Slit Spectra with IRAF, by Phil Massey, Frank Valdes, and Jeannette Barnes at NOAO.

VI. A) Spectral Reduction Overview

The first steps in reducing spectra are identical to reducing images: perform dark and flat field correction as described in section V. A. - F. We then need to combine our spectra, however we cannot use the same alignment procedure as with images in section V. G.

NOTE: When flat fielding, if the spectral flat is not high signal to noise, then don't use it. Often the small systematics in CCDs are not worth adding extra noise from the flat field.

After generating a final combined spectrum, we will then generate a wavelength solution, which means that we will determine the mapping between pixel number along the spectrum and wavelength.

B) Define the Dispersion Axis

It may be necessary to define the dispersion axis. This is controlled by the DISPAXIS keyword in the header. Check the header by using the imhead task with the long keyword set:

Look for the DISPAXIS keyword in the output. Additionally one could also use the UNIX grep command to pick out the DISPAXIS keyword:

grep is case sensitive so be sure to capitalize accordingly (or use the -i option with grep).

For a spectra with the dispersion axis horizontal, DISPAXIS should be 1, for vertical spectra, DISPAXIS should be 2.

If the DISPAXIS header keyword needs to be altered or added, use the hedit task:

If your spectra is vertical, use 2 as the value for DISPAXIS in hedit.

Note: I've put the add keyword in explicitly, it is only necessary if the DISPAXIS header keyword doesn't exist in the image.

C) Preparing APALL

NOTE: The apall procedure for extracting the trace of the spectrum is primarily designed for continuum spectroscopy. It may be possible to use it with nebular spectroscopy, but I won't go into that here. In this tutorial, it is assumed that we are working with a continuum spectrum. If you are working with a nebular spectrum, then parts C-G should be replaced by another method (e.g. see the IRAF tutorial linked at the top of this page). One simple method is described here.

apall is a multi-step task which defines and extracts the data from your 2D CCD image. To access apall, load the noao, onedspec, twodspec, and apextract packages:

Now we must edit the apall parameters:

change find to no, recenter to no, and resize to no (as I have them above).

NOTE: apall has many parameters, I've only shown the first page of them here.

Also we need to edit the apextract parameters:

change dispaxis to 1 (along lines).

D) Running APALL: Defining the Aperture

To run apall and extract a spectrum:

this will bring up an interactive window where one can define the various apertures:

Fig. 1

this is a plot of pixel values as a function of y, a stellar spectrum is represented by the peak (in this case around line 250 or so). We want to set an aperture which gathers all of the light in that peak. First we need to zoom in on that spectrum. To do this we use the w and e commands. Type w to zoom, then use e to define the lower left and the upper right of the region we want to zoom in on. For example, if I typed w then e at the location of the cursor showing in Fig. 1, and then typed e again after pointing to the upper right of the peak, I would get what is shown in Fig. 2. You can use the key combination w a to reset the zoom to default.

Fig. 2

now we can see in more detail. The region outlined by the bar with the numeral 1 above it is a automatically defined aperture which has been selected by IRAF. In this case it looks reasonable, but let's go though the exercise of redefining it. We can define the center of the aperture either using the cursor (point to the center and type n) or by using the cursor as a starting point and having IRAF centroid the profile (point near the center and type m). You can use the d key to delete previously defined apertures (each aperture will be numbered 1, 2, 3, etc.). The width of the aperture can be defined using the y key, which sets the width to whatever the width is at the y position that the cursor is pointed at (experiment with this to get a feeling for how it works). Conversely you can set the upper and lower boundaries to the width of the aperture using the u and l keys (for upper and lower boundaries respectively).

E) Running APALL: Fitting the Background

Once you have set the aperture, hit b to move on to setting the background apertures. Again there will be a preselected fit by IRAF there for you as in Fig. 3.

Fig. 3

I would recommend setting a wider view which emphasizes the background using the w e e and w a commands as shown in Fig. 4.

Fig. 4

Now we can see the background. Those four horizonatal lines at the bottom define the region where the background is being sampled. The horizontal dashed line is the fit which is obviously incorrect, so we'll need to redefine the background sections. We can use the s key to set new regions to be used in the background fit. press the s key at either end of the region you want to use for the background fit then hit the f key to perform the fit and the dashed line should move (you can delete previously defined fitting regions with the z key). I would recommend using a large swath of background on either side of the aperture as seen in Fig. 5.

Fig. 5

Now you can see that the background fit (dashed line) accurately represents the background. Once you are satisfied with the background fit, type q to return to the aperture edit mode.

VI. F) Running APALL: Defining the Trace

The trace is what determines the shape of the aperture as you move along the dispersion axis. For example if your stellar spectrum is not horizontal or if it is curved, IRAF needs to determine its shape to accurately extract the spectrum.

Hitting q in the aperture edit mode will take you to the trace fit as seen in Fig. 6:

Fig. 6

Here the data points (plus signs) represent the trace of the spectrum and the dashed line indicates the fit. The difference looks dramatic until you realize that the y-axis of this plot is just 3 pixels high, so the deviation from the straight line fit is just a few pixels. To increase the order of the fitted polynomial, use the :or command (don't forget the colon). After typing :or enter the order of the polynomial you want to fit. In this case I'll use 4th order and then hit f to perform the fit, and you can see that the fit tightens up nicely (Fig. 7). The fit still isn't prefect, but we are within about 0.1 pixels everywhere along the trace.

Fig. 7

All of the apertures we've just defined are stored in a file called database/apscience_exposure_filename in the current directory. This way you can come back to this image later and still retain the aperture definitions. To work on another exposure but using the same apertures you can use apall as

VI. G) Running APALL: Extracting the Spectrum

To extract spectra from your data, hit q to quit the trace fitting routine and answer the questions asked by apall.

There are two options for extracting the spectrum. First, one can simply add up all of the counts in the aperture and subtract off the background. This however, has a couple of potential problems. One is that small numbers of photons in the wings increase the noise. Another is that cosmic ray hits can throw off the sum. The second option is a variance weighting in which the sum is weighted by the signal to noise in that pixel. This method is more resistant to a few noisy pixels and does a pretty good job rejecting cosmic rays. The disadvantage is that the method assumes only read noise (no dark current noise) and you have to explicitly enter the gain and read noise in epar apall.

Your extracted spectrum will be written as a one dimensional spectrum in the file science_exposure_filename.ms.fits.

VI. H) Generate a Wavelength Calibration Solution

IRAF has a routine for generating a wavelength calibration solution using a list of line wavelengths in your calibration lamp exposure. I have taken the SBO calibration lamps and generated this list (sbo_HeAr.dat). Use the identify task to associate these lines with features in your calibration lamp exposure.

The l1 and l2 parameters are the lines which will be averaged to generate the spectrum (since this is a wavelength calibration we will not worry about extracting a detailed aperture and just use the lines).

It has come to my attention that the section='line l1 l2' may not work properly. If it appears that the lines are not being averaged properly, you can use the method for adding lines described in the alternative to apall page to average the lines in the calibration exposure.

Use the calibration lamp plots from the SBO manual to identify two or three lines, point the cursor at the centers of these lines and hit m (for mark) and enter the wavelengths as requested. Hit f to fit a rough wavelength solution. Hit q to return to the display of the spectrum. Now that IRAF has a rough idea of what the solution is, it can look at the line list and identify additional lines in your spectrum and determine their wavelengths from the sbo_HeAr.dat database. This will give several more point in the fit to the function relating wavelength to pixel number. To have IRAF automatically identify additional lines, hit l.

Now we have to check whether IRAF's automatic identification worked properly. Use the z,d,+,p keys to eliminate any false markings (see the identify help page for more info). Hit f again to fit the wavelength solution with the new markings. Use d to delete any outlier points in the fit. When you are satisfied with the fit, hit f, and then quit the IDENTIFY program (hit q twice). You have now generated a wavelength solution which is probably stored in a subdirectory called database.

VI. I) Associate the Wavelength Solution with the Image

Now we need to associate that wavelength solution with the science exposures to which it applies. To do this we add a keyword to the science exposure header. To modify a header use the hedit task (be sure to apply it to the file that was output from apall):

If the header field REFSPEC1 already exists in the header, use add-

VI. J) Apply the Wavelength Solution

Now to apply the wavelength solution to the image using the dispcor task:

Now you can use splot to inspect and analyze your data with a dispersion axis in units of angstroms rather than pixels.

VI. K) Use SPLOT to View the Calibrated Spectrum

We will use splot to view the calibrated spectrum. If you have properly used identify and dispcor then the horizontal axis of the splot window should be in wavelength units (angstroms). If you move the curson over a point on the spectrum and hits space, then splot will print out the coordinates of the cursor at the bottom of the screen

The splot task has a number of interactive tools for analyzing your spectrum. As with most interactive IRAF tasks hitting the ? key brings up a short help page on the interactive commands. We'll go through a few of the most useful commands one at a time.

Display Commands: Zooming In and Out

You can rescale the axis and "zoom in" on a particular section of spectrum by using the a key to deliniate the corners of a box you would like to zoom in to. Point the cursor at the part of the spectrum that you would like to be in the lower left corner of the new view and hit a. Then point at the upper right corner and hit a. The view will zoom to a box defined by the points you specified.

To redraw the screen and zoom out to the full view, simply press c.

One other command which can be useful is the :hist command. This simply toggles between two different line types for the plot. Turning it on goes to a historgram style line plot, otherwise each point in the spectrm is simply connected by a straight line in the plot. Test out both to see which you prefer (Fig. 11 below is in the default style, not histogram style).

Determining Line Centers and Fluxes: The Deblending Command

In many cases you will want to determine the exact wavelength of line center and the integrated flux in a line. To do this we must fit a line profile to the data, sometimes several line profiles. The deblend command in splot is a quick and easy way to do this. Deblending is a multi-step process, so we'll go through it one step at a time.

First, use the a key to zoom in on the line(s) you wish to study.

Second, point the curson at a point in the continuum well to the left of the lines and hit d, then point at a point in the continuum well to the right and hit d again. This defines the continuum level. Choosing how far away from the lines to select can be tricky. You want to grab a large enough segment of continuum, so that its level can be fit accurately, however the fit is simply a lines with some slope, so if your continuum is non-linear, you'll need to select a smaller segment which is approximately linear. At the end of the fitting process we'll see a graphical representation of the background fit, so you can check that the fit is reasonable then.

Third, now we need to select which features in the spectrum to fit. You'll notice that at the bottom of the splot window, you get a menu saying something like:

What you need to do is point the cursor at a line (you only need to line up horizontally with the line, where you point vertically does not matter) and hit a key indicating which type of line fit you'd like to do. Let's do the simple example of fitting a gaussian, so we'll point at a line at hit g. Do this for all lines in the deblending segment that you defined with the d key even if you are not interested in the properties of those lines. If you do not fit a line, then those values will be assumed to be part of the background and may throw off the background fit. Each time you indicate a line to fit with, for example, the g key, it will be marked with a short vertical line. Once you have marked all the lines you want to fit, hit q to quit and move on to the next deblending step. Once you do that, you will see a question at the bottom of the splot screen:

IRAF is asking whether you want the centers (positions) of the lines to be a variable in the fit. Unless you have some reason not to do this, hit a, to indicate that you want all of the line positions to be variables in the fit.

Now you will be confronted with a new question:

Now it is asking whether the widths of the lines should be a variable in the fit. Note, this question may vary depending on which type of profile you used to mark the lines. For most purposed, hitting a to indicate that all lines should have their widths fit is a good choice.

Again you will be confronted with a new question:

IRAF is asking whether it should fir the background (or continuum) flux. In most cases, you want to hit y for yes, fit the background.

Now IRAF will dislay the results of the fit as shown in Fig. 11. First check to see that the fit is reasonable. The green dashed line shows the fit of the background level. You want this to be a good measurement of the average, in Fig. 11 this looks reasonable since the green line goes through the noise at a reasonable level. The red dashed lines show the line profiles that have been fitted. Do they roughly match the lines in the spectrum?

Fig. 11

The line of text at the bottom of the splot window gives you information about the fitted lines numbered 1 though n from left to right. In Fig. 11 we see that the low, noisy, broad line on the left is centered at 6551.11 angstroms, has a flux of 637.4 (this is a measurement of the area under the line, so the units are counts*angstroms), the equivalent width is undefined (INDEF) because this is an emission line, not an absorption line, and the Gaussian FWHM is 8.55 angstroms. To see the same information about the other two lines you can use the + and - keys to cycle through lines 1, 2, and 3. Pressing the r key prints out the RMS noise of the background for comparison to the flux in the lines.

Pressing q will quit these results. You may be asked several of the previous questions again to see if you want to try the fit with different parameters. To exit deblending, hit q for each of these questions. When you have exited deblending you will see a Deblending done message at the bottom of the screen and you are back in regular splot, hitting q again will exist splot completely.