3 Extraction of Echelle orders

The extraction of the Echelle spectra from the Echelle detector images in x-direction (main dispersion direction) is done by summing up 11 pixels (orders 40 to 49) or 9 pixels (orders 50 to 61) in y-direction. The center of the extraction in y-direction follows a straight line along each order, but is located on integer pixel numbers.

Some Echelle images show tilted absorption lines within the strip of the Echelle orders. The reason for this effect is still unclear. In such cases the extraction was done by summing up the pixels tilted by 45 degrees, which results in a significant increase in resolution. However an additional wavelength error was introduced by this procedure since the observed wavelength in this way became dependent on the centering of the Echelle order within the extraction strip. This is a nonlinearity error of the size of one pixel, which corresponds to 1/3 of the optical resolution element and is equal to $\Delta$$\lambda$=$\lambda$/30000.

3.1 Background

Between the Echelle orders a 3 pixel wide area was used to estimate the background. With exception of orders 40, 41 and 42 the background was calculated as average of the strip above and below the corresponding order. For the first three orders only the background values below each order were calculated. The so calculated background was smoothed prior to being used for subtraction.

The intrinsic background of the detector was about 10^-5counts/s/pix. As 9 or 11 detector pixels are added to one spectral pixel, this corresponds to about 10^-4counts/s/pix in the extracted spectra, which is negligible.

By far the strongest contribution to the background is straylight from the Echelle grating. The contribution in counts/detector-pixel is about 5% to 10% for the low Echelle orders and 10% to 20% for the high Echelle orders as these are closer together. The percentage values refer to the maximum counts/detector-pixel values of the Echelle orders. The contribution in counts/spectrum-pixel is about 15% for spectra with a rather flat continuum.

The Echelle straylight is scattered exactly horizontally across the detector, whereas the spectral orders run slightly tilted across the detector corresponding to the dispersion of the cross disperser. Hence emission lines produce additional straylight while broad absorption lines lead to a reduced straylight contribution in a horizontal line at the y-position of this absorption line. These varying straylight contributions are not yet correctly handled by the background subtraction algorithm.

An additional contribution is caused by particle events related to the South Atlantic Anomaly (SAA). These produced count rates of up to 1000 counts/s resulting in up to $2\ 10^{-3}$ counts/s/pix on the detector and $2\ 10^{-2}$ counts/s/pix in the spectra. The maximum duration of the passage through the SAA was about 12min and the count rate curve showed a quasi Gaussian shape during this time. In the case of weak targets where the SAA background reduces the signal to noise ratio of the spectrum significantly, we are able to integrate the spectrum from the single photon records excluding the SAA transit period.

3.2 Correction of the blaze function

The efficiency of blazed Echelle gratings varies as $(\sin(x)/x)^{2}$ (blaze function) (Schroeder & Hiliard 1980), where x depends on the deviation of the output angle from the specular angle of maximum efficiency (blaze angle) and on the wavelength. The optimized diffraction direction was preflight adjusted to the y-centerline of the Echelle detector. In the flight data we found the center of maximum efficiency to differ between the Echelle orders and furthermore both the position and the width of the blaze function differing from observation to observation. Therefore it was necessary to introduce an individual blaze correction for each observation. For spectra that showed a relatively undisturbed continuum the blaze correction could be done with a rather high accuracy. However for many spectra which are dominated by absorption lines only the overlap region between two adjacent orders could be used as a criterion for a good blaze correction, resulting in a less reliable correction.

After completion of the blaze correction for all observations no systematic time dependent effects in the variation of the blaze function were found.

3.3 Wavelength calibration

The wavelength calibration was calculated from the positions of 814 interstellar absorption lines in the Echelle images of 12 different objects. The centers of the lines were determined by fitting Gaussian functions to the profiles using a preliminary wavelength calibration. After identification of the lines a table with laboratory wavelengths and corresponding detector pixel numbers was created. Using the preliminary wavelength calibration, a mean radial velocity component for each object was estimated and corrected for. This approach assumes, that for each individual object all identified interstellar absorption lines, mainly H₂ and neutral elements, originate in the same volume of gas.

  

Figure 2: Residuals of the wavelength calibration fit. 814 positions of interstellar absorption lines from 12 different objects were used to fit 7 wavelength calibration parameters

  

Figure 3: Apparent wavelengths of the geocoronal Ly-$\alpha$ emission line plotted versus time of observation. For each of the 9 observing blocks for the Echelle spectrometer the large crosses mark the average Ly-$\alpha$ position, which was later used for correction of the time dependent wavelength shift. For these measurements no wavelength corrections except for the satellite's orbital velocity were applied

With a least square fit algorithm we then determined a new set of pixel to wavelength conversion parameters.

In Fig. 2 the residuals for all lines demonstrate that the mean accuracy of the wavelength correspondence is better than $\pm$0.005nm, i.e. better than the optical resolution of the instrument.

The above procedure results in a relative wavelength calibration. In order to determine an absolute scale we used the position of the geocoronal Ly-$\alpha$emission line as a reference. We found that for different observing blocks the position of the Ly-$\alpha$ line changed by up to 0.006nm (Fig. 3). The reason for this shift is still unclear, we assume that it emerges from temperature drifts of the telescope and the Echelle spectrometer. A correction for this effect has been applied in each observing block.

Shifting of the Echelle spectrum on the detector surface (e.g. displacement of the target within the aperture) basically results in a relative wavelength shift and thus in a radial velocity shift rather than in a wavelength shift. The reason is, that the wavelength dispersion is proportional to the wavelength.

The wavelength scale of the targets were shifted to correct for radial velocity components due to the Earth's movement (heliocentric correction) and due to the satellite's orbital movement.

A further shift occurs when the target image is not exactly centered within the 20$^{\prime\prime}$ diaphragm. The maximum resulting uncertainty due to the 10$^{\prime\prime}$radius of the diaphragm is $\pm$1.2 10^-4 as a relative wavelength error (corresponding to $\pm \,36\,{\rm km\,s}^{-1}$). This error was not corrected up to now.

3.4 Correction of loss of sensitivity in the detector edges

In the corners of the detector area and at the left edge the efficiency of the repeller grid is reduced, probably due to an inhomogenous field close to the edge of the detector. A step occurs between lower and normal sensitivity. In some images a circularly shaped area is visible due to this effect. We estimated a loss of about 25% and corrected this by applying a "smooth'' step function. The position, width and height of the step was estimated for each order from the sum of all Echelle measurements.

A detailed flat field correction was not applied, due to the fact, that the optical light path of the spectrometer cannot be reproduced in our laboratory. This however would be essential for an exact estimation of the flat field behavior of the detector. Any other correction methods are too uncertain to be useful.

3.5 Absolute flux calibration

We used an HST archive model of G191B2B "http:// www.stsci.edu/ftp/cdbs/calspec/g191b2b_mod_002.tab'' as a reference for the absolute flux calibration. The calibration was crosschecked with a model of BD+28$^\circ$4211 (R.Napiwotzki 1997, priv. comm.). We estimate an accuracy of $\pm$10% for the flux calibration, provided the object was fully centered within the aperture, which was not always the case.