The spectro2d pipeline works in two stages. First, it reduces the data from each chip from each fifteen-minute exposure separately, and then it combines the results from each exposure.
After bias subtraction, each raw image is divided by a uniformly illuminated flat to take out pixel-to-pixel variations. The flat-field spectra (i.e., the flat-field observed through the fibers) are then traced on the CCD: for each fiber, the flat-field image centroid in column position is fit by a polynomial in row number. The flat-field spectra are optimally extracted, assuming a Gaussian profile for each one, simultaneously fitting a low-order polynomial to scattered light. These fits will also be used for the first-order object extraction of the science and arc frames, allowing for small offsets. The arc lamp spectra are extracted as well and centroids of the lines are measured, to which we fit a fifth-order Legendre polynomial.
The flat-field spectra are then wavelength-calibrated, normalized, and combined to form a ``superflat'' for each spectrograph camera, by stacking the 320 normalized flat-field spectra and performing an iterative least-squares bspline fit with outlier rejection on this oversampled dataset to obtain an effectively continuous function. For each fiber, the superflat is resampled at every pixel and divided into the extracted flat-field spectrum to form the ``fiber flat.'' In this way, flat-field variations between fibers are removed, as are small-scale features in the wavelength dependence of the system response.
For the science exposures, the object and sky fibers are spatially traced, with tweaking from the flat-field trace, and optimally extracted. In the extraction, the Gaussian fiber profile fitting can also be tweaked from the fiber-flat image. Scattered light is removed by a fourth order Chebyshev polynomial fit. Outlying pixels are rejected and masked. The extracted spectra are then flat-fielded by dividing by the fiber flats, and the wavelength solution is applied, using a vacuum wavelength scale, adjusting slightly to match the known positions of certain sky lines, and correcting to the heliocentric frame. The wavelength calibration is accurate to of order 10 km s or better.
As with the flats, an oversampled ``supersky'' is constructed from the 32 sky fibers per plate. For each fiber, the supersky is resampled at every pixel in the object spectrum and subtracted.
Telluric absorption in four wavelength regions in the red spectra is removed using spectrophotometric and reddening standard stars: these are used to construct four ``superTelluric'' spectra using the bspline fitting procedure.
Next, spectro2d performs a spectrophotometric flux calibration of the individual exposures: the counts in each exposure are placed on the same scale, and the wavelength scale is rebinned to a simple polynomial in log .
If a smear exposure exists, the counts in each exposure are corrected to match a low-order fit to the smear counts; this corrects for light which falls outside the 3'' fiber aperture because of seeing, guiding errors, and atmospheric refraction. However, since the smear exposure procedure was implemented part way through commissioning, many of the plates included in the EDR do not have smear exposures (see Table 4).
Next, the spectra are flux-calibrated by matching the counts in the mean of the high S/N spectra of the spectrophotometric and reddening standards on the plate, and equating this to the synthetic composite F8 subdwarf spectrum from Pickles (1998). This is placed on an absolute scale by matching the synthesized fiber magnitudes of these stars to the SDSS photometry. This procedure removes the instrument response as a function of wavelength in each spectrograph camera. The absolute accuracy of the spectrophotometry is not well-measured at this point, but can probably be trusted to 20% for point sources when smear exposures are available. Note that for extended sources (galaxies), the smear technique effectively corrects the spectrophotometry to a aperture; in the presence of spectral gradients (e.g., nuclear emission lines), the results may be difficult to interpret.
Finally, for each object, the individual science frames, both red and blue halves, are stacked and fit with the iterative bspline, with inverse variance weighting. In the process, outliers due to cosmic rays are rejected and masked, and errors in the fluxes estimated. The combined, merged spectra are resampled in constant velocity pixels (), with a pixel scale of 69 km sec. If possible, exposures on multiple nights are combined. If a plate is re-plugged, however, only the exposures with a given plugging are combined.
Mask bits are set for each pixel of the reduced spectra, as described in Table 13. Two masks are given for the final combined spectra, the bits in the OR mask set if the relevant flag was set in any of the individual exposures entering the combination, while the AND mask indicates that the flag was set in all of the exposures for that pixel. For most purposes, one should examine the OR mask to be safe. Pixels flagged FULLREJECT, NOSKY, NODATA, or BRIGHTSKY, or those with error set to identically zero are likely to be corrupted. Many of these are due to bad columns on the CCD's, or cross-talk from very bright objects in neighboring fibers (see the flag NEARWHOPPER).
On occasion, the spectra exhibit unphysical wiggles due to problems in the spectrophotometry, especially in the region of the dichroic split (Å); this will be improved in future releases.