3. Data reduction
We first averaged the bias and flat field frames separately for each night. As we could not detect any significant change in the mean bias level we computed the median of the bias frames of the four nights and found that the bias level showed a gradient across the image, increasing from the lower left corner to the upper right corner by about 1%. We fitted the bias with a linear approximation along both axes and used this fit as a bias for the further reduction. As no overscan was recorded we could not adjust the bias level. Bias frames taken during the night, however, revealed no significant change in the mean bias level. The mean dark current determined from long dark frames showed no structure and turned out to be negligible (33 e-/hr/pixel).
We determined the spectral energy distribution of the flat field lamp by averaging the mean flat fields of each night along the spatial axis. These one-dimensional "flat field spectra" were then heavily smoothed and used afterwards to normalize the dome flats along the dispersion axis. The normalized flat fields of the first three nights were combined. For the fourth night we used only the flat field obtained during that night as we detected a slight variation in the fringe patterns of the flat fields from the first three nights compared to that of the fourth (below 5%).
For the wavelength calibration we fitted 3rd-order polynomials to the dispersion relations of the HeAr spectra which resulted in mean residuals of 0.1 Å. We rebinned the frames two-dimensionally to constant wavelength steps. Before the sky fit the frames were smoothed along the spatial axis to erase cosmic ray hits in the background. To determine the sky background we had to find regions without any stellar spectra, which were sometimes not close to the place of the object's spectrum. Nevertheless the flat field correction and wavelength calibration turned out to be good enough that a linear fit to the spatial distribution of the sky light allowed the sky background at the object's position to be reproduced with sufficient accuracy. This means in our case that after the fitted sky background was subtracted from the unsmoothed frame we do not see any absorption lines caused by the predominantly red stars of the clusters. The sky-subtracted spectra were extracted using Horne's (1986) algorithm as implemented in MIDAS (Munich Image Data Analysis System).
Finally the spectra were corrected for atmospheric extinction using the extinction coefficients for La Silla (Tüg 1977) as implemented in MIDAS. The data for the flux standard stars were taken from Hamuy et al. (1992) and the response curves were fitted by splines. The flux-calibration is helpful for the later normalization of the spectra as it takes out all large-scale sensitivity variations of the instrumental setup. Absolute photometric accuracy is not an issue here.
© European Southern Observatory (ESO) 2000
Online publication: July 27, 2000