The instrument parameters are under computer control except for the spectrograph slit which is adjusted manually. They are operated from a VT100-type terminal emulation, and they provide spectrograph settings, object identification, and exposure with a number of submenus.

The FOCES échelle data reduction software (EDRS) consists of a number of modules written in IDL (Version 4). Such modules comprise the basic input/output and data-handling routines, display functions that allow inspection of the original and reduced data, auxiliary routines which support detection of features and image processing, and échelle spectrum extraction. In addition to the basic modules there exist application command files to extract well-calibrated one-dimensional spectra in a fully automatic mode. The single routines contain entry and exit variables (arguments), and optional keyword parameters. Since the language is interpreted, the FOCES software package consists of source code. All procedures or functions include a documentation header that can be read online with an INFO command. All efforts have been undertaken to make the EDRS software package as independent of operating system features as is possible under IDL, however, the principal use is currently under a DIGITAL UNIX system. No attempts have been made to generalize the EDRS software for use with data obtained from other spectrographs.

FOCES spectrum extraction is subdivided into a number of consecutive steps for which a standard set of exposures must be available if the automatic extraction mode is to be used successfully. These exposures must all refer to the same set of parameters such as CCD camera and center wavelength setting etc. If only one of the above exposures is missing the automatic extraction will not give the desired result. The EDRS automatic data reduction is able to co-add or average object, bias, dark, flatfield or calibration exposures. Bias and dark subtraction are done as usual leaving only the true spectrographic images, corrected for much of the instrumental response. Additional parameters determining details of the spectrum extraction process are entered by editing a FITS-like parameter file, USER.PAR. The following subsections describe the reduction steps.

$\begin{figure} \centering \includegraphics [width=8.8cm]{h0572f8.ps}\end{figure}$

Figure 8: Cross-order intensity tracing over the whole wavelength range. Note the logarithmic scale. Order # 145 (left) corresponds to 3950 Å, order # 78 (right) to 7340 Å. Order separation is between 20 pixels in the blue and 10 pixels in the red. The straylight background is everywhere less than 1% of the adjacent order signal

4.1.1 Order detection

The primary detection routine, ORD_PATT, finds the approximate positions of the échelle orders by using cross-order scans starting at the center of order dispersion where the signal is highest. From there it follows the order ridges to both sides, and it approximates the order ridge positions by polynomials of low degree. This procedure is reasonably robust against hot pixels and bad columns since it first applies a median filter to the image which does not affect the search for the true position of the order ridges. Since the object exposures are normally faint, the order positions should be obtained from the corresponding order flatfield exposure instead. The above algorithm works on continuous orders; it fails to detect the order positions of wavelength calibration exposures and of pure emission line objects.

4.1.2 Background correction

Even the best spectrograph cannot completely avoid scattered light. This is found between the spectral orders at an intensity level sometimes significantly above zero. However, for FOCES this light level is very low as is demonstrated in Fig. 8 which also shows that the interorder minimum signal is uniformly proportional to the order maximum signal if the intermediate slit is in place. Due to the narrow cross-order intensity profile ( $\approx 3$ pixels) the crowding of the orders in the red does not lead to a strong increase of the interorder minimum signal. Using the model of Gehren & Ponz (1986) assuming a local straylight origin, the contribution to the extracted order spectrum is between 0.9% in the blue and 1.8% in the red. This is roughly proportional to the inverse order separation. Simple subtraction of the interorder minimum intensity represents a global straylight approximation, and it leads to a contribution that increases with order separation; this would suggest much higher straylight contamination of between 5.2% in the blue and 2.6% in the red. Since in the red (where the signal is high) both methods differ by less than 1% it is not evident from tests which of the two methods yields the more consistent results. At present the interorder minimum subtraction is therefore preferred. We note that removing the intermediate slit increases the background straylight by both a global component and a local component that is increased by a factor > 2.

4.1.3 Order extraction

Once the order positions are known the appropriate order extraction is applied to all remaining échelle images (object, order flatfield, and wavelength comparison). There are basically two ways to sample the échelle orders, one using the order ridge positions y^(m)(x) and a specified sampling width $\Delta y$ , y being the cross-order coordinate. With these data the pixel intensities found at constant x within $y^{(m)}(x) \pm \Delta y/2$ are added to define the spectrum order flux.

$\begin{figure} \centering \includegraphics [angle=90,width=8.8cm]{h0572f9.eps}\end{figure}$

Figure 9: Difference between the results of RAW_ORDER and OPT_EXTR demonstrating essentially the removal of cosmic events. The two spectra are offset by a constant amount

After order extraction has been performed, the order spectra still contain the échelle blaze which is essentially a $(\sin x)^2/x^2$ function. The blaze is mostly removed by dividing the object exposure through the extracted (one-dimensional) order flatfield. Since the order flatfield spectrum is exposed through the same fibre as the object, it should leave the resulting object continuum modulated with the ratio of the continuous spectra of object and flatfield lamp. Figure 9 shows that for sufficiently high signal the difference between the two extraction modes mentioned above is mostly due to the different treatment of cosmic ray events.

$\begin{figure} \centering \includegraphics [width=8.8cm]{h0572f10.ps} \vspace{-3mm}\end{figure}$

Figure 10: Accuracy of wavelength calibration in a single order obtained with the Tektronix 2048² chip with 24 $\mu$ m pixel distance

$\begin{figure} \centering \includegraphics [width=8.8cm]{h0572f11.ps} \vspace{-3mm}\end{figure}$

Figure 11: Rms error in mÅ of wavelength calibration obtained with the Tektronix 1024² chip with 24 $\mu$ m pixel distance varying with order number. Here, order #0 is in the blue (4170 Å), order #71 in the red (8850 Å)

4.1.4 Wavelength calibration

WAVE_CAL provides the wavelength calibration of the extracted order spectra; first it compares the extracted multi-order comparison spectrum with a template spectrum that consists of a multi-order intensity tracing combined with an appropriate wavelength calibration. Centering of the order spectra with respect to the x coordinate as well as the correct identification of the order pattern (with the center wavelength) is achieved using a very simple version of a spatial correlation function. A nearly perfect calibration of the new spectrum is thus already obtained as a first approximation. A calibration spectrum line list containing a sufficient number of emission lines is then compared with lines detected on the calibration exposure. The emission line maximum positions are found with a maximum parabola fit procedure. The solution is iteratively improved excluding all deviations of single line positions $\gt n\sigma$ (the default of n is 3), as long as there are still enough lines left. The minimum number of lines left is restricted by the degree of the polynomial approximation. At the end of the calibration procedure the extracted wavelength calibration lamp fluxes are replaced by the wavelengths at the corresponding pixel positions. The results of this process are displayed in Fig. 10 for a single order. The high accuracy of 0.15 kms^-1 obtained in a single order confirms the expected performance of the spectrograph with the 24 $\mu$ m Tektronix chip. Figure 11 demonstrates that the rms mean calibration error of all orders is just as low although there exists a small degradation towards the red. Experience shows that the Loral 2048² chip with 15 $\mu$ m pixel distance provides a similar accuracy. A single order rms error of 2.5 mÅ in the visible spectrum corresponds to an accuracy of 150 ms^-1; the formal error of the 70 order mean is only 18 ms^-1. The latter value is reproduced for a number of exposures, and it verifies the expectactions of instrumental accuracy. This compares favourably with the results found for the ELODIE spectrograph of Baranne et al. (1996).

4.2 Comparison of predicted and actual performance

The performance of the spectrograph was originally estimated to be around 13%, using as much as possible the specifications given by the corresponding instrument data sheets including mirrors, fibres, prisms, lenses, and the CCD. This is degraded by two telescope mirror reflections to roughly 10%. Thus assuming ideal observing conditions with no atmospheric extinction and a seeing below 1 arcsec, the limiting performance in the V band should yield 40 photons per second and 2-pixel resolution element for a 10th magnitude star.

$\begin{figure*} \centering \includegraphics [width=18cm]{h0572f12.ps} \vspace{-5mm}\end{figure*}$

Figure 12: Selected spectra of cool stars observed during test runs. Stars are ordered roughly according to decreasing metal abundance. The spectral region includes the Mg Ib lines with some strong contributions of C₂ and MgH, particularly strong in cool stars such as HD 6582

On the 1024² Tektronix CCD the image of the échelle spectrum covers approximately 70 orders in the visual with full overlap to the first minimum of the blaze function up to $\approx$ 5200 Å. A typical exposure is displayed in Fig. 3. During the first test observing runs a total of more than 200 exposures for 73 stars have been obtained. A small part of some of the typical spectra around the Mg Ib lines is shown in Fig. 12. As is evident from Fig. 9 the spectral continuum is well defined. Thus it is possible to measure line profiles such as the Mg Ib lines to an accuracy better than 1% (under most circumstances even better than 0.5%).

One of the main drivers of fibre-fed spectrographs installed outside the telescope dome is the absence of any kind of mechanical or thermal irregularities, provided that the spectrograph laboratory environment is under control. This should guarantee very small residuals in wavelength calibration as well as a high internal accuracy of the dispersion scale. This was in fact observed during the test runs. The results are reproduced in Fig. 10. The accuracy of the dispersion calibration (obtained in the fully automatic mode) can be estimated in particular from Fig. 11 which produces a mean error of the complete échelle spectrum of less than 20 ms^-1. Comparison of multiple exposures confirms that not only internal velocity differences are rather small but also the absolute values are highly accurate.

$\begin{figure} \centering \includegraphics [width=8.6cm]{h0572f13.ps} \vspace{2mm}\vspace{-3mm}\end{figure}$

Figure 13: Spectral window of 2 metal-poor stars of similar stellar parameters. HD 45282 (bottom) displays maximum resolution (R = 40 600) with a number of medium to faint Fe I and Ti I lines. G28-43 (top) emerges to be an SB2-type binary, just at the resolution limit

During the first test observations the resolution was still limited by the CCD pixel size (i.e. $24~\mu$ m for the Tektronix chip). The corresponding resolution limit is nicely demonstrated by comparing spectra of a single star and a binary in Fig. 13. Here, the faintest lines are just being resolved, and the binary nature of G28-43 becomes evident. Since the actual resolution product of FOCES is near $R\phi = 60~000$ , the resolution can be improved at the expense of throughput using a 2k chip with $15~\mu$ m pixels and a correspondingly narrower slit without installing a longer camera. A few more recent observations have been taken at the 2.2 m telescope with R = 65 000 using the Loral 2048² CCD. Comparing the different exposures in Fig. 14 the increase in resolution is evident from both line halfwidth and blend separation. We note that with the increased area of the Loral CCD the spectral coverage is extended to 3800 - 9200 Å.

$\begin{figure} \centering \includegraphics [width=8cm,clip=]{h0572f14.eps} \vspace{-3mm}\end{figure}$

Figure 14: Spectra of HD 22879 taken in two exposures with the $24~\mu$ m Tektronix CCD (top), and with the 15 $\mu$ m Loral CCD (bottom), respectively; the entrance slit was adjusted to fit exactly 2 pixel resolution elements such that R = 40 600 (top) and R = 65 000 (bottom). The bottom spectrum is shifted by a constant amount

A final experiment was the installation of the dual-fibre mode intended to be used for background subtraction from faint object signals such as obtained at the 3.5 m telescope. The fibre head consists of two identical diaphragms with 3 mm distance corresponding to 18 $^{\prime\prime}$ . The position angle can be adjusted rotating the telescope guide unit if necessary. Both diaphragms feed identical $100~\mu$ m fibres through microlenses, and both fibres are aligned on the spectrograph slit. Thus the échelle pattern is double; between each pair of object spectral orders the corresponding sky background order is placed.

The cross dispersion required for the dual-fibre mode is approximately twice as high as in the single fibre mode since camera and detector are the same as in the standard single-fibre mode. It is provided by an additional blue or red grism placed in the beam immediately in front of the double prism. Present observational experience has not yet produced enough evidence to precisely describe the performance of the dual-fibre system.

FOCES has been in regular use now at the 2.2 m telescope for a number of observing runs dealing mostly with high-resolution stellar spectroscopy. However, the cross-order flatfield and the optimal fibre configuration will have to be improved.

The FOCES project was generously supported by grants 05 5MU414(8) and 05 2MU114(7) obtained from the German ministry of science and technology (BMFT). We are particularly grateful to G. Avila, H. Dekker, B. Delabre, and S. D'Odorico of the European Southern Observatory, Garching, who supported our spectrograph project from the beginning, and who worked out much of the final optical design; to K. Birkle, H. Elsässer, K.H. Marien, W. Rauh, J. Solf, U. Thiele and K. Wagner of the Max-Planck-Institut für Astronomie in Heidelberg, who helped us find a working compromise between a fully autonomous instrument and one that can be scheduled for the typical astronomer.

4 First observations

4.1 FOCES data reduction software

4.1.1 Order detection

4.1.2 Background correction

4.1.3 Order extraction

4.1.4 Wavelength calibration

4.2 Comparison of predicted and actual performance