4 Reductions

 

4.1 Geometric rectification

  

Table 2: The coordinates of the tangential points, the parameters of distortion and offset, and the resulting errors are given for each image

Due to the precise manufacturing of the GAUSS camera, its distortion can be assumed as radially symmetric with respect to the optical axis of the system. Hence, the coordinates to describe this distortion have been chosen as spherical ones: the radial distance $r_{\rm P}$ of an image point from the center of a plane plate and the rotation angle $\phi_{\rm P}$. The catalogued galactic coordinates of about 120 stars on each image have been converted into celestial spherical coordinates: the radial distance $r_{\rm S}$ of the stars from the assumed tangential point in the sky and the rotation angle $\phi_{\rm S}$ starting from the meridian of the tangential point. An iteration around the center point of the plate and the estimated corresponding tangential point in the sky has been performed. For each step the spherical celestial coordinates have been compared with the spherical plate coordinates, a polynomial has been fitted to the data, and the deviation has been computed. This deviation has been minimized by the iteration resulting in the correct coordinates ($x_{\rm C}$, $y_{\rm C}$, $l_{\rm C}$, $b_{\rm C}$) of the tangential point, and in the polynomials

$$\begin{eqnarray} r_{\rm P} &=& A\,r_{\rm S}^3 + B\,r_{\rm S}^2 + C\,r_{\rm S} \\ \phi_{\rm P} &=& \phi_{\rm S} + \Delta\phi\end{eqnarray}$$ (1) (2)

describing the distortion and the angular offset of the camera. The parameters for the selected images are given in Table 2. The mean error of this rectification is about $\rm\pm 4\,\mu m$ or $0\hbox{$.\!\!^\circ$}02$ in the sky.

4.2 Photometric calibration

  

Table 3: The calibration parameters are given for each image

The former Bochum surface photometries (Paper VII; Paper VIII) have been calibrated by the mean of gradation curves that have been exposed using ESO's wedge spectrograph ETA. Additionally, during the photographic exposures absolute calibration data and information on airglow, scattered light and extinction have been measured photoelectrically.

Since none of these measurements has been done during the spacebound observation, the gradation curves had to be reconstructed from the images themselves. This requires measuring the star densities to compare them with their catalogued fluxes. As reference, the catalogues of Jamar et al. (1976) and of Thompson et al. (1978) have been taken, both resulting from the measurements of the satellite TD1. The stars have been identified on the images, the maximum of their density has been determined, and for all recovered stars (about 1500 on each image) these maxima have been set in relation to the catalogued flux. The transformation from the measured densities to relative intensities were done by using the characteristic curve after Moffat (1969)  

$$D = \frac{\gamma}{n}\lg(1+(\frac{I}{I_0})^n) + D_0$$ (3)

where D is the measured density, and D₀ the density of the chemical fog of the photograph. $\gamma$, n and I₀ are free parameters that have been derived by fitting the curve to the data. The typical mean error of this calibration is about 2%.

Absolute calibration was obtained by integrating the relative photographic intensities of each identified star, subtracting its individual sky background, and comparing the resulting aperture star photometries $F_{\rm AP}$with the catalogued fluxes F_*. This yields a linear relation with a typical mean error of about 3%.

To obtain the surface photometries, the calibrated images have been divided by $\rm (5.37 \pm 0.1)\ 10^{-7}\, sr$which is the mean area of one pixel. The parameters D₀, $\gamma$, n and I₀ of the relative calibration, the ratio $F_{\rm AP} / F_*$ describing the absolute calibration, and the resulting mean error are given in Table 3 for each image.

4.3 Elimination of foreground stars

The elimination of disturbing, individual foreground stars has been done in two steps. First, all stars brighter than $\rm 3\ 10^{-14}\ W/m^2\,nm$ have been removed from the images. These stars have a characteristic intensity profile that has been used for their identification. Beginning in the center of each star, the average radial differences have been computed and compared to the inner error. As soon as the difference became smaller than the mean error, the hereto belonging circle was defined as the "edge'' of the star and the intensity inside this circle was replaced by the average of the individual background.

The fainter stars which do not have this characteristic profile do only cover an area of maximally four pixel and could be removed by a filter similar to the one described in Paper VII. Herewith, all stars brighter than $\rm 2.5\ 10^{-15}W/m^2\,nm$ have finally been eliminated from the images.

4.4 Zodiacal light and Shuttle Glow

To correct for zodiacal light, we used the values published by Tennyson et al. (1988). Since the zodiacal light at 217nm and 280nm is distributed quite homogeneously (Murthy et al. 1990), and since its intensity is also very small, it is sufficient to substract an average value from each image. This value has been determined to $(0.9\pm 0.3) \ 10^{-11}\frac{W}{\rm m^2\ sr\ nm}$ at 217nm and to $(5.7\pm 2) \ 10^{-11}\frac{W}{\rm m^2\,sr\,nm}$at 280nm.

Much stronger is the additional light emission that is produced by the shuttle while interacting with the upper atmosphere. Many of the images are influenced by these shuttle glow effects (see Jütte 1996 for a thorough investigation of these phenomena). The classical Shuttle Glow is generally considered to be relatively strong in the red and near-infrared passbands but negligible in the UV. However, we have detected quite intense light phenomena at shorter wavelengths that seem to be related to the shuttle: large, bright clouds surrounding the shuttle and even the camera itself. They seem to be of variable origin and change on timescales of seconds to hours. To eliminate these clouds from the images, they have been fitted with twodimensional polynomials of fourth order. These fits reproduced the shape of the clouds in a reasonable way, however, the zero point of the sky background could not be derived by this method. Therefore it has been estimated from the darkest parts of the images, which have been regarded as unaffected by the glow. The error of this estimation is very high with about 20% of the mean Milky Way brightness. However, there is no other possibility to derive the correct sky background. We consider these glow phenomena to be a major obstacle to all photometries obtained at Low Earth Orbits.

4.5 Transformation and averaging

The derivation of the geometric parameters (Table 2) allows the transformation of the images into maps of the Milky Way in cartesian coordinates l, b. The stepsize has been chosen as $0\hbox{$.\!\!^\circ$}25\times 0\hbox{$.\!\!^\circ$}25$ for comparison with the $U,\ B,\ V,\ R$ photometries (Paper VII; Paper VIII). The individual maps have been added up to give a picture of the Milky Way by averaging the overlapping regions. Due to the small number of usable images, there are only a few regions where the sky coverage is equal or better than three images (see Fig. 3).

 

Figure 3:   The number of images that have been averaged for each point of the final maps (above: 280nm; below: 217nm)