Data reduction for CCD spectroscopy

This section discusses the basics of astronomical CCD spectroscopic data reduction. We start with Figure 6.6, which presents a raw, unprocessed 2-D CCD spectroscopic image of a point source. This figure illustrates a number of the observational and reduction items we discuss below. The initial reduction steps for CCD spectroscopy are exactly the same as previously discussed for imaging applications. Bias (or dark) frames and flat field calibration images are needed and used in the same way. After performing these basic reduction procedures for the CCD images, there are additional steps one must take that are specifically related to spectroscopy. These extra steps involve the use of spectra of spectrophotometric flux standards and wavelength calibration (arc) lamps. We will not discuss some minor, yet important, processing steps such as cosmic ray removal, bad pixel replacement, and night sky emission line

Fig. 6.6. Raw CCD image of a spectrum of a point source. The entire rectangular image is the size of the windowed CCD (100 pixels tall by 3092 pixels long) while the smaller illuminated rectangle is the part of the CCD illuminated by light passing through the slit. The spectrum of the star of interest is the narrow streak running horizontally across the image (the dispersion direction) and it covers ~3200 A (left) to ~7000 A (right). Note that the night sky emission lines cut entirely across the star spectrum, as the sky illuminates the entire slit. The point source, on the other hand, is only as wide as its "seeing" size. The sky lines in this 900 second exposure consist of bright emission lines, such as He 5015 A (just right of center), from the Earth's upper atmosphere, as well as solar absorption lines (e.g., Ca II H&K are easily seen left of center) as the observation was obtained near full moon. Other items of note are the fully bright region at the left end of the spectrum caused by a LED (a bad pixel working in reverse) on the CCD and the nonuniform background illumination pattern across the image caused by a combination of the grating response, the CCD QE, and nonuniform sky illumination of the slit. Both of these issues are dealt with in the reduction process.

complexities. Detailed instructions for CCD spectroscopic data reduction can be found in Massey, Valdes, & Barnes (1992) and Pogge (1992). The article by Wagner (1992) is particularly useful, being the best review of the subject to date.

Figure 6.7 illustrates the five types of CCD spectral image needed for complete reduction and calibration of spectroscopic observations. The images shown in Figure 6.7 were all obtained with the same CCD, spectrograph grating, and telescope on two nights in June 2004. The spectral dispersion is 1 A per pixel in the blue (1st order) and 2 A per pixel in the red (2nd order) and the dispersion runs from red to blue (left to right).1 Some items of note are 1) the bias level underlying the FeAr arc exposure, 2) the width of the flat field exposures compared with the point source stars (note spectrum d has been rescaled here to show the fringing in the red (left) part of the spectrum and thus looks thinner (see Appendix C)), 3) the absorption and emission lines in the spectra, and 4) cosmic rays in image g. These images do not show the full range of wavelength coverage shown in Figure 6.6 as they were expanded for clarity.

1 Raw spectra are often displayed at the telescope in the manner they are read out from the CCD. While we all might like spectra displayed as blue to red or increasing wavelength from left to right, at times, raw spectra are displayed opposite to that as shown here. One quickly develops a mental flip ability while observing or learns the needed plot command to display the spectrum "correctly."

Ccd Spectrum Image

Fig. 6.7. The five necessary types of CCD image needed for spectral reduction. Image a is a bias frame, b is an FeAr calibration lamp (arc) exposure, c is a quartz lamp projector flat field in the blue spectral region, d is the same in the red region, e is a blue observation of the spectrophotometric flux standard star BD +26 2606, f is the same in the red region, and g and h are the stars of interest, SX Her and Z UMa respectively. See Figure 6.8.

Fig. 6.7. The five necessary types of CCD image needed for spectral reduction. Image a is a bias frame, b is an FeAr calibration lamp (arc) exposure, c is a quartz lamp projector flat field in the blue spectral region, d is the same in the red region, e is a blue observation of the spectrophotometric flux standard star BD +26 2606, f is the same in the red region, and g and h are the stars of interest, SX Her and Z UMa respectively. See Figure 6.8.

Figure 6.8 shows line plots of each of the images in Figure 6.7. The bias frame shows that this CCD has an increase in noise by 10-15 ADU at the very end (left) of the readout near the output amplifier. This is fairly typical and of no concern as it covers only a few columns and is accounted for in the reduction process. The FeAr arc lamp shows nothing but emission lines whose known wavelengths are used to determine the CCD pixel number to reduced wavelength solution. We see that the blue quartz flat field, c, rises to the red (as quartz lamps are red, peaking redward of your eye's sensitivity) while the red flat field shows the characteristic fringing caused by the long wavelength red photons passing through the CCD, reflecting back, and interfering with themselves. This horrid looking fringe pattern is also accounted for and removed during reduction. The high count rate flat fields also show the typical spike at the ends of the readout (due to amplifier turn on/off) and the small overscan region (little flat portion at the bottom right of the plots) of the CCD. We also show the same standard star (BD +26 2606)

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Fig. 6.8. Plots of the raw spectra shown in Figure 6.7. These plots show the full spectral range of the instrument (3096 pixels =~1200A in the blue range and ~2400A in the red range - see Figure 6.9) and are plots of a single CCD row taken through the middle of the spectra in Figure 6.7. These raw data are plotted as pixel number (x-axis) vs. ADU (y-axis) as is typical, with red being to the left. Note the spectral shapes, which are dominated here by the source convolved with the grating response and the CCD QE. The conversions from pixel number and ADU to wavelength and flux (as well as a proper spectral shape) are done in the reduction process.

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in the red and blue regions to illustrate its differences. The blue region (e) shows the Balmer absorption series in this sdF star and a cosmic ray (narrow emission spike near Hj8) while the red region shows the fairly large atmospheric absorption bands due to molecular oxygen (the A and B bands) and fringing. The two objects of interest are SX Her, a long period variable star with emission lines due to a recent shell ejection, and Z UMa, a cool supergiant with strong TiO absorption bands.

For a point source, the final product desired is a 1-D spectrum consisting of wavelength versus relative or absolute flux. It is assumed that you have in hand CCD spectra of your object(s) of interest, at least one observation of a flux standard, wavelength calibration spectra of arc lamps, and bias and flat frames (see Figure 6.7). The first step with the reduced two-dimensional CCD image, after the standard processing with bias and flats is performed, is to extract the spectrum itself and collapse it into a 1-D image of pixel number versus ADU/pixel. In the simplest (and unrealistic) case, the imaged spectrum lies exactly along one row (or column) of the CCD and one can extract it simply by extracting the single row from the final image. Generally, the imaged spectrum covers two or three or more rows (or columns) and the extraction process involves some manner of summing a few adjacent rows perpendicular to the dispersion (an "after-the-fact" pixel binning) at each point along the dispersion. Furthermore, in practice it is often found that CCD spectra are not precisely aligned with the CCD pixels and are curved on the detector as the result of the camera optics, instrumental distortions, or CCD flatness issues. Fainter sources present additional complexities, as centroiding the spectrum (by, for example, using cuts across the dispersion direction) in order to extract it is often difficult or impossible. A typical example might be a spectral observation of a faint continuum source that contains bright emission lines. Details of the spectral extraction process, sky subtraction, and optimal extraction techniques are discussed in Schectman & Hiltner (1976), Horne (1986), Robinson (1988b), Robinson (1988c), Pogge (1992), and Wagner (1992).

At this point, your extracted spectrum will have an x axis that is in pixels and we wish to convert this to wavelength. The procedure to perform such a task involves observations of calibration arc spectra obtained often during your observing run. The idea is to match the x-axis pixel scale of the calibration arc lamps with their known wavelengths and then apply this scaling procedure to your object data. Calibration arc spectra of sources such as hollow cathode Fe lamps or He-Ne-Ar lamps contain numerous narrow emission lines of known wavelength. Use of these emission lines during the reduction procedures allows a conversion from a pixel scale to a (possibly rebinned linear) wavelength scale. Correction for atmospheric extinction (Hendon & Kaitchuck, 1982), similar in manner to photometric corrections already discussed but generally a bit more complex due to the larger wavelength coverage, can now be applied to all obtained spectra. Since you are relying in this step on the hope that the arc emission lines fall onto specific CCD pixels and define a wavelength scale that is identical to that of your object, you want to obtain arc data in as similar a manner as possible to that used to gather your object spectra. Instrument flexure caused by telescope motion throughout the night or movement of the CCD within the dewar are two of many possible effects that will invalidate the wavelength to pixel scaling procedure.

We now have to deal with our collected spectra of flux standards. These stars are observed solely for the purpose of converting the collected pixel count values into absolute or relative flux values. Application of all of the above steps to your spectra of spectrophotometric flux standards will produce 1-D data with a wavelength scale (x axis) versus counts on the y axis. We now wish to have the y axis of ADUs or counts converted into flux units such as ergs s-1cm-2A-1. Most observatories and data reduction packages (such as IRAF and MIDAS) contain lists of spectrophotometric flux standards appropriate to observe and use for fluxing of your spectroscopic data. Within the reduction software, tables of wavelength versus flux are kept for a large number of spectrophotometric flux standards. To understand and appreciate the details involved in setting up even a single spectrophotometric standard star, see Tug, White, & Lockwood (1977), Jacoby, Hunter, & Christian (1984), and Massey et al. (1988). In a similar manner to the method by which we took the known arc wavelengths and converted their pixel scale into a wavelength scale, we can now take the known fluxes of the standard stars and convert pixel counts into relative or absolute fluxes. The difference between relative and absolute is essentially the difference between a narrow or large slit width as mentioned above. The conversion of counts to flux is performed under the assumption that slit losses, color terms, transparency, and seeing were similar between the standard star observations and the object(s) of interest.

One can never have too many calibration data and must always trade off time spent collecting CCD frames of standard stars and arcs with collection of data for the objects of interest. Instrument flexure, nonphotometric conditions, color terms, and accurate wavelength calibration are crucial to the production of accurate final spectroscopic results such as that shown in Figure 6.9.

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Fig. 6.9. Final reduced CCD spectra of the two stars of interest as shown in Figure 6.8. We see that the y-axis values of counts in ADU have been transformed into flux in units of ergs s-1 cm-2A-1, using the standard star observations. The x-axis units are now wavelength in A increasing to the right. Narrow emission lines of the Balmer series as well as Ca II H&K absorption are seen in SX Her and Z UMa's spectrum is dominated by TiO absorption bands.

Fig. 6.9. Final reduced CCD spectra of the two stars of interest as shown in Figure 6.8. We see that the y-axis values of counts in ADU have been transformed into flux in units of ergs s-1 cm-2A-1, using the standard star observations. The x-axis units are now wavelength in A increasing to the right. Narrow emission lines of the Balmer series as well as Ca II H&K absorption are seen in SX Her and Z UMa's spectrum is dominated by TiO absorption bands.

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