In this section, the pre-processing steps needed to convert raw data frames to 2D spectra suitable for analysis by ELFIT2D are described. The first steps were the overscan and bias corrections. Each CCD pixel value starts from a different initial value. These pixel-to-pixel zero-point differences seen in zero second exposures called bias frames are usually described by the sum of a mean zero-point level and a bias structure. The bias structure has zero mean as it gives only the fluctuations about the mean zero-point level. The bias structure usually does not change from frame to frame, but temperature variations in the CCD electronics environment introduce changes in the mean zero-point level. These changes are removed by subtracting the overscan value row by row from each frame including bias frames. Each frame has a section which is continuously clocked during an exposure. The overscan value of a given row is the mean value of the same row in the overscan region. The overscan-subtracted bias frames give the bias structure. Eleven bias frames were taken every night and were ``average combined'' after overscan subtraction using the IRAF task IMCOMBINE. The highest and lowest pixel were rejected at each pixel location before the average was computed. The resulting bias structure frame was subtracted from all overscan-subtracted data frames taken on the same night.
In addition to pixel-to-pixel zero-point variations, CCD detectors have pixel-to-pixel variations in sensitivity which introduce an extra variance in the noise proportional to the flux received during the exposure. There may also be large scale sensitivity variations across the CCD chip. These sensitivity variations are removed by dividing data frames by uniformly illuminated images (dome lights or twilight sky) called flat fields. Flat field images were taken on nights when direct images were taken. The flat field images for each night were scaled by their mode and average combined with a 3-
clipping to remove bad pixel values. Data frames were then divided by the combined flat image to produce flat fielded images. This flat fielding successfully removed ``rings'' on the direct images caused by dust particles on the CCD dewar window. Spectroscopic data were not flat-fielded for the following reasons: (1) Every time a correction is applied to a data frame, there is degradation of the original signal-to-noise ratio. Since flat field noise is proportional to flux and flux levels were very low, flat field noise was not significant. (2) spatially-resolved emission lines are very small in extent compared to the total area of the detector. Large scale variations in sensitivity do not affect velocity and size measurements, but they do preclude direct comparisons of the measured emission-line fluxes.
Since the spectroscopic data frames were read-out noise limited, it was important to limit the number of exposures on a given object. In many cases, only 2 long exposures were taken. The passage of cosmic ray secondaries or radioactive decay products through CCD detectors can produced hundreds of spikes of charge on the images. Each spike is usually confined to a few pixels. The cosmic ray rates at a high altitude site such as Mauna Kea is much larger than at sea level. Having a small number of exposures complicates cosmic ray removal. Hubble Space Telescope images are particularly affected by cosmic rays, and the number of exposures is also typically small. Cosmic ray removal on HST data is performed by comparing the difference in pixel values in consecutive images taken at the same telescope position to the background noise of the images. Pixels with values differing by more than 10, say, have probably been hit by a cosmic ray [\protect\astronciteWindhorst et al.1994]. The same approach was adopted for the present data. Series of consecutive data frames were summed together using an IRAF/SPP task called REMCOS. Pixels with consecutive values differing by more than 10 were flagged by a large negative value (
9999.99). The spatially-resolved emission-line analysis program ELFIT2D recognizes this large negative value as a cosmic ray pixel and does not include these pixels in its synthetic rotation curve fits (see chapter 
). Such a high rejection threshold should not bias pixel values in the final summed frames. Indeed, image statistics and pixel value histograms of the final frames were the same as those of the individual images before summation.
In order to isolate the emission line flux, it was necessary to perform two background subtractions: sky (rows) and continuum (columns). Sky subtraction was performed on the 2D spectra using the IRAF/LONGSLIT task BACKGROUND. BACKGROUND was used to fit the 2D spectra row-by-row with a second order Legendre function with one 2.5 rejection iteration. The continuum was removed by fitting the 2D spectra column-by-column in two continuum windows, one on each side of the emission line. The result of these background subtractions was a 2D image of the emission line flux. For each galaxy, it was important to find the center of the [OII] emission. In most galaxies, the continuum was used to define the x-coordinate (i.e. the position along the slit) of the center, and the y-coordinate of the center was taken to be the point where the [OII] emission crossed the continuum. In the absence of a continuum, an [OII] intensity-weighted centroid was used to define the [OII] center. Finally, a small image section was extracted with IRAF/IMCOPY around each spatially-resolved line for synthetic rotation curve analysis (see chapter ). The final sample was made up of 22 spatially-resolved [OII] spectra.