5 Results

The reduction of the solar spectra should improve the S/N ratio in the spectra but on the other hand the shape of the spectral lines must be not affected. Therefore we tested both the noise propagation through the data and analysis of corrupting of the shape of the spectral lines. First, the standard deviations of different types of arrays were computed and secondly, the accuracy of the spectral characteristics determined from the simple, extended and precise reductions was examined.

5.1 Standard deviations

Generally noisy data have a higher standard deviation of the signal then the good data. This is not the case for the solar spectra. One must distinguish between the noise coming from defects and noisy flats and between the real physical variations of the intensity across the image. For example the best solar spectra of the solar granulation reach a standard deviation of the intensity variation along the slit between 6%-7% after reduction. Therefore, it is important to analyze if the standard deviation was decreased by the reduction process and not to be afraid of the big standard deviation of the resulting spectra.

The standard deviations of the signal of the original as well as of the reduced spectra are given in Table 2 and the standard deviation of the signal of the "supporting'' arrays (G, F, M) are shown in Table 3. We estimated the standard deviations only from a limited area of any spectral array, to exclude the contribution of the spectral lines to the values. An area was selected in the upper right corner of the arrays, marked by the rectangular box in the array in Fig. 5. Because of the absence of spectral lines in the flat-field matrix M the calculation of the standard deviations in these arrays (the last four column in Table 3) was done in the whole area between the wires WL. We will discuss these results in Sect. 6.

5.2 Spectral characteristics

The stability of the shape of the spectral lines was tested using spectral characteristics of the spectra R_k, k=1, 2, 3 resulting from the simple, extended and precise reduction respectively. Only 946 scans selected between the WL wires were used for the analysis. Several manipulations were applied to every scan of the R_k before the spectral characteristics were calculated:
a) the local continuum of every scan was determined on the left and right side of the spectral line as a maximum of the second order polynomial fit of selected intervals of intensities. Because of the very small spectral region recorded on the CCD chip (no true continuum level available beside the lines), these intervals are not the 100$\%$ continua valid for this spectral region. They could be recalculated to the true continua using the solar spectrum atlas. The intensity of the "quasi-continuum'' interval available beside the lines in the spectrum is compared with the intensity of the same interval available in the solar atlas. The ratio between them serves for correction. But for our purpose, to compare the relative difference of spectral characteristics, this was not necessary;
b) Fast Fourier Transform was used for high frequency signal filtering to smooth data of every scan. Optional Gaussian filtering of high frequency noise (cf. Gray 1992) has effectively filtered all power above 1/10 of the Nyquist frequency;
c) the zero position for determination of shifts of line centres and bisectors was calculated as the position of the centre of the mean profile. The mean profile was constructed as an average of the 946 profiles;
d) a spectral line inclination in R₁ which resulted from the simple flat-fielding was eliminated, i.e. we applied de-stretching after the flat-fielding in this case.

The spectral characteristics, continuum intensity ($I_{\rm c}$), line centre intensity ($I_{\rm o}$), line Doppler shift ( $L_{\rm sh}$), bisectors Bi and full width at half maximum (FWHM) were calculated separately for every scan for all three types of resulting spectra $R_{\rm k}$. In Fig. 9 the line center intensity fluctuations $I_{\rm o}$ along the slit (Y direction) resulting from precise, extended and simple reduction are shown. For comparison of the results we used the differences of the spectral characteristics. We use the results given by the precise flat-fielding as a standard for the estimation of the relative errors of the values resulting from the other two reduction approaches. The relative differences of the line centre intensities RD_3,i, (i=1, 2) expressed as a percentage were calculated as:

$$RD_{3,i} = \frac{{I_{{\rm o}3}}-{I_{{\rm o}i}}}{I_{{\rm o}3}} * 100. ~, ~~~i=1,2 ,$$ (14)

and the mean of the result was normalized to a value of 0.0. The relative differences of $I_{\rm c}$ and of FWHM were calculated in the same way. The results are shown in Fig. 10.

Figure 9: Line centre intensity fluctuations $I_{\rm o}$ along the slit (Y direction) resulting from: a)  precise, b)  extended and  c) simple flat-fielding. The difference of the first and third panel is shown in Fig. 10b and the difference of the first and second panel is shown in Fig. 10e.

The absolute differences of the line centre shifts AD_3,i, (i=1, 2) expressed in m s^-1 were calculated according to the equation:

$$AD_{3,i} = L_{{\rm sh}3}-L_{{\rm sh}i}~, ~~~i=1,2 ~,$$ (15)

where $L_{\rm sh3}$ denotes the line shifts resulting from precise flat-fielding (spectrum $R_{\rm 3}$), and  $L_{\rm sh1}$ and  $L_{\rm sh2}$ denote the line centre shifts resulting from simple flat-fielding (spectrum $R_{\rm 1}$) and from extended flat-fielding (spectrum $R_{\rm 2}$), respectively. The results are shown in Fig. 11.

The absolute differences of bisectors Bi were calculated in the same way as for the line shifts and the results for bisectors at 0.2, 0.4, and 0.6 of the line intensity are shown in Fig. 12.