Relatively bright spectra in the prism data are automatically detected and their coordinates are input to a triangle matching program (Valdes et al. 1995) to determine the linear coordinate transformation to the direct catalog. The spectrum position in the dispersion direction is defined by the point of half maximum brightness at the red end sensitivity cutoff. Although this definition will depend on spectral type (by pixels), we use it to establish the mean offset and not to set the zero point on an individual basis.
The relatively bright spectra are automatically detected by convolving the image with a matched filter (a 2-D template of the red end cutoff), and then searching for vertical strings of relative maxima that monotonically increase in brightness. Strings of some minimum length (e.g., ten pixels, possibly diagonally connected) reliably locate the distinctive red end cutoff and hence the entire spectrum (which is pixels long). Object detection algorithms used in photometry (i.e., connecting pixels above a brightness threshold) are less useful due to the extreme overlap problem and the segmentation of an object into multiple detections depending on the spectral energy distribution.
The software applies the coordinate transformation to the direct catalog, predicting the spectrum locations to within (except near photographic plate edges in the DSS data). This accuracy is required to reliably extract faint spectra and set the wavelength zero point to within %. The accuracy of the transformation is monitored throughout the drift scan by using the brightest spectra per image frame as ``guide stars'' (least squares fits to the position residuals refine the transformation). The extraction of 1-D spectra is currently done using a box of width and uniform weighting.
nincr = c[e] - c[b-1] mean = (w[e] - w[b-1]) / nincr q25 = ibsearch(c[b-1] + nincr / 4) q50 = ibsearch(c[b-1] + nincr / 2) mode = 3 * q50 - 2 * mean sig = 1.482 * (q50 - q25)
where ibsearch indicates a binary search of the cumulative histogram with an interpolated output index. Convergence (when the mode changes by less than some threshold) occurs rapidly by using q25 and q50 to form a robust approximation of the histogram . This method is times faster than techniques that require fully sorting the data. First masking out the pixels within the spectrum extraction boxes did not improve the background estimation.
The software builds a contamination map using the positions and magnitudes of objects in the input sky catalog, and empirical 2-D template spectra produced from bright, uncrowded spectra. Currently a single, representative late type spectrum is used although an improvement would be to create templates as a function of color. The template spectra are added into the map with an intensity scaling of 10(m/(-2.5)). For each spectrum extracted from the data, the ratio of the contamination map to the 2-D template for that spectrum gives the (multiplicative) contamination correction at each pixel.
This method is fast, easy to implement, and handles arbitrarily complicated overlaps of many objects without excessive approximation. In addition, the overlap calculation can be done independently of the spectrum extraction pipeline. Thus, the overlap calculation does not need to be repeated for each drift scan to be coadded, and the calculation can be improved at any time without repeating the spectrum extraction. Because the input sky catalog contains ID numbers for all objects to be extracted, it is straightforward to match each spectrum to its contamination array (and coadd spectra from different CCDs and nights).
With the broad bandpass of the spectra, spectral classification and quasar selection can be improved by using the continuum information in addition to spectral features. A reasonable approach is to find the smallest RMS deviation between each spectrum and a series of template spectra (or similar technique based on cross-correlation). However, two significantly different spectra can have the same RMS deviation from a given template (e.g., one spectrum has an emission feature while the other has a slightly different continuum slope). In other words, the best matching template is selected using a distance criterion, independent of direction, in flux-wavelength space.
Figure 1 shows an alternative using Principal Component Analysis (PCA) to provide a fast, automated measure of the deviation of a given spectrum from the common energy distributions. This allows the selection of quasars (and other unusual objects) to fainter magnitudes than line-only searches without making assumptions about the variance of quasar spectra. In practice, the representative set of common spectra is defined from the data itself (by clustering analysis on a sample of relatively bright, unblended spectra).
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