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Data reduction

Data reduction includes three steps: intensity calibration, pixels-to-coordinates conversion, spectra and photometric data extraction.

Intensity calibration

The FBS plates do not have photometric calibration, then a characteristic curve for each plate cannot be built up. Therefore, the original transparency values, that is the Data Numbers (DN) resulting from the scanning, were converted to relative intensity by utilizing the formula (De Vaucouleurs 1968): I=(V-B)/(T-B), where I is the (linear) intensity, V, B and T are the transparency values obtained for the unexposed plate corner, for the black corner and for a given pixel respectively. In the immediate future an absolute calibration will be developed by using the energy distribution of known stars in the plates.

Pixels-to-coordinates conversion

The software for the astrometric solution was written by H.J.Hagen by adapting the dedicated software for the Hamburg Quasar Survey (Hagen et al, 1995). The Second Guide Star Catalogue (GSC-2) was used as reference positional input. Starting from the plate center and the brightest stars in the field, an iterative procedure converges to the astrometric solution typically in 1-2 minutes. Up to 800 stars of progressively decreasing brightness were used in each field and up to 7 approximations have been carried out to achieve the best solution.

The plate scale is 1.54 arcsec/pixel. The best accuracy achieved corresponds to a root mean square (rms) of 0.87 arcsec; anyhow the typical accuracy, corresponding to a rms of 1 arcsec or 0.6 pix, is sufficient for a confident object identification (a spectrum is typically 5 pix wide). The total time needed for the astrometric solution of each plate was 5 minutes; the procedure was applied for all 1874 DFBS plates.

Spectra and photometric data extraction


A dedicated software named bSpec was created in order to provide automatic extraction and classification of the spectral data in a DFBS image. This software was developed by the MIGG s.r.l. team in the context of a collaborative project with the "La Sapienza" University group; it was coded under Linux using the Borland Kylix compiler.

The extraction of the individual spectra from the two dimensional images requires the definition of the star position and of the spectral contours. To do this, a catalogue driven procedure downloading a list of objects with B < 17 from the USNO-A2 catalogue was utilized. Starting from the catalogue coordinates, each spectrum was recentered by optimizing the combination of two parameters: peak position and baricenter. Through the distribution of the whole set of objects, a mean spectrum direction angle was computed for each image and adopted as the spectrum direction for all the spectra of the plate. To avoid noisy objects limits in brightness and ellipticity where imposed.

Finally, all spectra of the objects selected from the catalogue were automatically extracted by performing a correction for the adjacent sky. This correction was determined as the lowest value between the mode of an area of 50 x 50 pixels centered on each spectrum and the average value deduced from two strips (3 pixels in width) running parallel to the spectrum at a distance of 10 pixels. The abscissa scale was defined by setting pixel 20 at the 'red head' of each spectrum, where the sensitivity of the plates sharply drops to zero. A disadvantage of this approach is that we can lose a number of variable or moving objects present in the plate but below the adopted threshold magnitude in the catalogue. A second procedure based on the software SExtractor (Bertin \& Arnouts 1996) has been tested for the extraction of the spectra. The obtained results indicate this method as good for finding all objects, but reveal some non negligible disadvantage: indeed, defects and artifacts are taken as objects and faint objects are missed. Therefore, at moment, it can be used for relatively low-density fields and bright objects; in the future, it could be applied producing a modified database from the present one.

To obtain a wavelength calibration, the red cutoff of the FBS spectra, defined as the point where the intensity is half of the peak value, is rather sharp and can be used as a reference point, for the wavelength calibration, even if it is mildly sensitive to the brightness and spectral type (color) of the object. To perform the wavelength calibration, some well-exposed spectra of planetary nebulae, white dwarfs, subdwarfs, cataclysmic variables, and QSOs were used. The pixel-to-lambda conversion formula is:


where lambda is in nanometers, k is the running pixel, irb is the position of the red cutoff.
Due to the fact that the dispersion is strongly non-linear, the obtained wavelength calibration scale is approximate: it is about 22 A/pix at the blue edge and 60 A/pix at the red edge, with a mean dispersion of 32.7 A/pix. At H-gamma, it is about 28.5 A/pixel.


Photometric information from the DFBS spectra can be obtained by separately integrating the spectra blueward (typically ranging between the pixels 55 and 90 in the spectrum abscissa scale) and redward (pixels 20 - 40) of the green sensitivity gap typical of IIF plates, thereby deriving an instrumental `blue" and `red" magnitude. These spectral regions are very similar to the POSS O (4050\AA) and E (6450\AA) emulsions sensitivity ranges and therefore can be reliably related to the B and R magnitudes given by the USNO-A2 catalogue. A polynomial fit of these magnitudes against their USNO-A2 magnitudes provided a calibration curve which was then used to compute the DFBS magnitude of all the objects in the plate.