5 Data reduction

A program has been developed as a part of the CDS software which allows both raw data corrections and intensity calibration. Various corrections and checks have been applied to the spectra in order to calibrate them. The checks included dead time corrections and short term gain depression. Corrections for flat field and long term gain depression were not included since they are not yet available. It is known, however, that these corrections are very small.

The telescope effective area, as calculated from the pre-flight calibration (Bromage et al. 1996), has been used to convert the count rates to phot cm^-2 s^-1 arcsec^-2. This is shown in Table 5. These values are the mean sensitivities over the wavelength range of each of the four detectors. Bromage et al. (1996) report that there was no evidence of wavelength-dependence for the sensitivity of each detector.

After applying the various correction factors, spatially averaged spectra were formed, in order to increase the signal to noise ratio. Monochromatic images of the rastered areas on the Sun were obtained by summing up the pixel intensities of the brightest lines. These were examined for inhomogeneity in the emitting regions, before spatially averaging the spectra. This is necessary because, as noted by Landi & Landini (1997), the L-functions will cross each other only if the emitting plasma is homogeneous. In case there are inhomogeneities it is possible that some departures of the L-functions from the expected behaviour may occur due to lines emitted in different solar conditions, making it more difficult to determine possible intensity calibration problems.

The emission appeared fairly uniform over the QS region, and there was no evidence of significant inhomogeneities, while the AR images showed large variations in the intensity in the hottest lines, revealing a very complex morphology, the structure varying with temperature. A map of the intensity ratio of two Fe XIII strongly density-sensitive lines 202.0 Å/203.8 Å indicated considerable variations in electron density. As a result, only the area with ratio values between 1.2 and 1.4 was used to form an average AR spectrum. This selected region broadly covered the hottest part of the total emitting area, and had an electron density $\simeq 10^{9.4}$ cm^-3.

  

Figure 2: Effects of different smoothing procedures applied to a portion of the GIS 1 active region spectrum. a) Original spectrum; b) Box-smoothed spectrum; c) Fourier-filtered spectrum; d) Gaussian-convolved spectrum

5.1 Fixed patterning and line profiles

The fixed patterning effects are shown in Fig. 2. In this figure a portion of GIS 1 fixed-patterned spectrum is shown (Fig. 2a), together with the same spectral region smoothed with three different smoothing methods (Figs. 2b, c and d). It is possible to see in Fig. 2a that strong line profiles are heavily changed, making it very difficult to fit line profiles and calculate their intensity. The smoothed spectra reveal the presence of weaker lines that in the raw spectrum were not easily distinguishable from the background and so were difficult to fit. It is therefore necessary to apply some kind of correction in order to restore the original line profiles without altering the total intensity of the lines. This is particularly important in the case of unresolved blended lines. It is impossible to rebuild the original pixel intensities from the observed spectrum, but because the spectral lines seen on the detectors are many pixels wide, it is possible to use a simple smoothing technique, which does not change total count-rates.

Four different methods were compared: boxcar filtering with 3 pixel width; convolution with a Gaussian function with a 2 pixel-wide $\sigma$; Fourier filtering; 4-pixel Hanning smoothing. Checks were made to verify that these methods preserve the total number of counts.

The widths of the boxcar and Hanning smoothing and the $\sigma$ of the Gaussian smoothing were chosen as optimum compromise between a reasonable cleaning of the spectrum and the smallest broadening of the line profiles.

Figure 2 displays the comparison between the original GIS 1 spectrum and the results of smoothing between 169 Å and 176 Å. The shape of the spectrum is much improved by all three smoothing procedures.

Boxcar and Hanning smoothing give nearly identical results; they are not able to remove completely the effects of fixed patterning (Fig. 2b), though these are greatly reduced. Resulting spectral lines show double peaked line profiles, more evident for most of the GIS 1 lines and less pronounced in the lines observed in the other detectors.

Fourier filtering (Fig. 2c) produces nearly Gaussian line profiles and a very clean spectrum, but alters the background, making it very difficult to identify and fit weak lines.

The Gaussian convolution is able to clean line profiles (Fig. 2d), and the resulting lines are very close to Gaussians, with flat background.

In most cases it seems that only heavy smoothing is able to provide Gaussian profiles, at the price of significant loss of spectral resolution. Moreover boxcar and Hanning smoothing are able to produce Gaussian line profiles only if the adopted width is larger than 10 pixels. This width is large compared to the width of the fixed patterning spikes, suggesting that the observed double peaked line profile should not be ascribed to fixed patterning effects only but to the instrumental response. The origin of this double peaked line profile is probably an optical effect, from a small mis-alignment of the telescope, scan mirror, grating, and detectors.

Since it is important to understand the impact of the smoothing procedures on the final line intensities, the line profile fitting CFIT package (Haugan 1997), part of the CDS software, has been used on each of these four spectra in order to calculate line intensities, position, width and the value of the background. A large number of lines from the four detectors has been used for this comparison.

The agreement between the results obtained from the smoothed spectra is always better than 10%. Only a few very weak lines show greater differences between the Fourier filtered spectrum and the others due to the strong background alteration of the former. Moreover there is good agreement between the results obtained from fitting smoothed spectra and those summing counts over the width of the line. The difference in intensity was found to be less than 5% in most cases. The intensities obtained by fitting the raw data may be up to 20% less than from simply summing the counts in the line, because the fit often follows dips due to fixed patternng within the true profile of the line. Fitting the data smoothed by any of these four methods (or summing counts) therefore gives a consistently better result.

No significant change is found in line positions, while Gaussian smoothing increases the line widths, thus reducing the GIS spectral resolution.

In the present work 3-point boxcar smoothing has been adopted since it represents the best compromise between adequate smoothing and minimum distortion of the true line shape.

Even with the more strongly double-peaked lines, Gaussian fitting after boxcar smoothing yielded intensities within 5% of those obtained from summing counts.

  

Figure 3: Probable ghosting regions for the GIS 1 wavelength range. Similar examples are available in the CDS software for the other detectors. The main frame displays the observed (smoothed) spectrum; the top two panels display the blue-shifted and red-shifted spectrum. The bottom panel marks with a black line the regions where ghosts from the blue- and red-shifted spectra are likely to affect the observed spectrum

5.2 Ghosts

Figures 3 and 4 show the red- and blue-shifted spectrum for the GIS 1 detector together with the regions which are likely to be unaffected by the ghosting problem (dashed line in the bottom panel). The regions more likely are indicated by a bold line. It is currently not easy to calculate precisely the positions where ghosts occur, and the boundaries of the regions shown in Figs. 3 and 4 are currently uncertain.

Understanding where the ghosts of each line fall is important, since the shifted counts reduce its apparent intensity and often fall close to other spectral lines, enhancing their intensity. An example of this is reported in Fig. 4, where the 173-182.5 Å spectrum is displayed. It is possible to see that the three relatively weak spectral features observed in the red-shifted spectrum are ghosts of the Fe X 174.5 Å, Fe X 177.2 Å and Fe XI 180.4 Å; in the blue-shifted spectrum the ghosting affects three other lines: Fe XII 192.4 Å, Fe XII 195.1 Å and the Fe XIII 197.4 Å. Only when a ghost appears in a region of the spectrum free of lines, is it possible to correct the ghosting line from which it came, while it is usually very difficult to distinguish between the ghost and any real lines with which it is blended.

One more complication is that ghosted lines are often themselves the source of ghosts, causing considerable problems in the analysis of the spectra. For example the Fe XII 192.4 Å line is probably ghosting the Fe X 174.5 Å, increasing the confusion in this spectral range.

Two methods are proposed to help in locating the ghosts more precisely. Once several non-ghosted and isolated lines have been identified with confidence, it is possible to use the diagnostic technique to identify a ghost. The ghost will enhance the intensity of the ghosted line, resulting in an L-function which is higher than expected. The contribution due to the ghost can then be found and traced back to its source line, and both the ghosting and ghosted lines can then be corrected. Progressing in this way, the spectrum may be reconstructed. However, the main limitation of this method is that the effect of ghosts can be confused with those of atomic physics and intensity calibration uncertainties, both of which cause the L-function values to be higher than expected. For this reason great caution is required in such a study. The other method is to try to relate each unidentified line position to the most probable ghosting line that could have produced it, with the assumption that the unidentified line is a ghost. If this assumption is correct it is possible to measure directly the shift between the ghost and its parent line; using several unidentified lines the ghosting line-ghost position relation could be determined. Using this empirical relationship it is possible to trace back the ghosts blending some identified line. Moreover, using the measured intensity of the unidentified lines a relationship between ghosted and parent intensities can be determined.

Using these methods it was possible to reconstruct the intensities of no more than a few lines, namely the lines reported in Fig. 4 and the Fe XIV 334.2 Å and Fe XVI 335.4 Å lines observed at the end of the GIS 2 detector, whose counts give rise respectively to the 317.6 Å and 318.8 Å lines. The paucity of the unambiguously identified and corrected ghosts compared to the great number of affected lines observed in the present dataset (more than half the total) is due to the complexity of the spectra themselves.

5.3 Line fitting

In order to measure line positions, widths and intensities it is necessary to use a fitting routine that adapts a known line profile to the observed spectral lines. In the present work use has been made of the ADAS fitting routines (Summers et al. 1996); full details can be found in Lang et al. (1990) and Brooks et al. (1998a). This routine is based on a maximum likelihood program which performs a multiple Gaussian fit together with a linear background.

The fit has been carried on leaving the background and line widths free to vary in order to better reproduce the observed spectrum.

  

Figure 4: Probable ghosting regions for the GIS 1 wavelength range. These show the corresponding spectral regions in the adjacent arms of the spiral detector pattern. Similar examples are available in the CDS software for the other detectors

The observed background emission results from a combination of true continuum emission, scattered light, detector effects, ghosts, contribution from weak emission lines. A proper evaluation of the background emission will be possible only when detector effects (some of which are present at the edges of the detectors) can be removed through flat-fielding. It should be noted that the background may be depleted by ghosting.

  

Figure 5: Line widths for the GIS spectrometer, observed in quiet (dashed line) and active (full line) Sun conditions. The straight lines represent the mean of the pre-flight measured values and its experimental uncertainties. a) GIS 1; b) GIS 2; c) GIS 3; d) GIS 4

The ADAS program provides also the uncertainties of the fitted quantities. These include the uncertainties on the pre-flight sensitivities, as reported in Table 5.

5.4 Line widths

Some comments are needed about line widths, since their values are very important for the measurement of line intensities.

In their calibration report, Bromage et al. (1996) have measured the line Full Width Half Maximum (FWHM) line widths for the four GIS detectors using a narrow-beam source of EUV radiation (Hollandt et al. 1994).

Some modulation of the FWHM along each detector was observed as expected, due to the configuration of the detectors along the Rowland Circle and to the variation of the point spread function and dispersion with wavelength. These values include broadening due to the limited width of the beam used.

The mean of the half-widths measured along each of the four GIS detectors is displayed in Fig. 5 (straight lines), together with their uncertainties.

The authors suggested that some broadening of the lines should occur in-flight (when the instrument aperture is fully illuminated), due to slight deviations of the light passing through the edges of the aperture; this increase was expected to be smaller than 15% of the provided pre-flight line FWHM for most lines. However, the effect may vary along the detector with some indication that the problem might be worse nearer the ends than the middle.

In the present study the FWHM of the lines has been measured, using the adopted fitting program, for some very strong and isolated lines, where no blending effects were present and where no ghosting line was expected. The behaviour of the FWHM for all the four detectors for both active and quiet Sun has been investigated, and the results are displayed in Fig. 5. The uncertainties have been determined as statistical uncertainties of the fitting, and their values represent the estimated 95% confidence limit of the fitted quantity. The slit used in the observation is the $2'' \times 2''$ slit. Different lines were used for the measurements in the two different spectra due to the lack of hot lines (such as Fe XIV, XV and XVI) in the quiet Sun spectrum.

These values have been compared to the FWHM measured in the pre-flight study by Bromage et al. (1996). It is important to note however that in the pre-flight study a narrow beam source has been used which did not fully illuminate the grating of the spectrometer. For this reason line widths were expected to be higher than in the case of full illuminated grating. This effect is greatest for GIS 4 (a 1.6 magnification factor) and smallest for GIS 1 (no magnification), and these factors are included in the pre-flight measured line widths reported by Bromage et al.

It is possible to see that in nearly all cases there are significant deviations from the pre-flight FWHM. In all cases the in-flight measurements of line width are greater than the preflight ones reported in Bromage et al. (1996). The differences between the two measurements range between a factor 1.4 to 2.4, and present some slight variation between the four detectors. It is interesting to note that also Brooks et al. (1998a) find that their NIS in-flight FWHM measurements are greater than the pre-flight values, although the differences are somewhat smaller and range between a factor 1.1 to 2.2. It was also noted that during ground calibration the spectral line positions moved when illuminating different parts of the GIS aperture. This optical effect is a suggested cause for the increase in original line profiles shown in Fig. 2a.

The differencies between the Bromage et al. (1996) laboratory mean FWHM and the values displayed in Fig. 5 are dependent on wavelength inside each channel. This wavelength dependence is consistent with pre-flight results.