1 Introduction

Knowledge of exact positions of celestial objects on the sky (solar system bodies, stars, galaxies) is important in many fields of astronomy (astrometry, celestial mechanics, astrophysics, stellar astronomy, galactic studies). The most exact data are being obtained from the extraterrestrial platforms which provide much better astrometric accuracy than any ground-based observation. The number of astrometric measurements from space grows very fast, parallel to their accuracy (10 - 1000 microarcsecs) and limiting magnitudes (10 - 20 mag) in the most ambitious HIPPARCOS, DIVA and GAIA projects. However, these projects are expensive, the space missions are rather rare and only last few years. The ground-based observations may be performed practically at any time and retain their significance, especially for fast-moving (asteroids) and/or short-living (comets) objects.

We may expect that in future a dense network of accurate extraterrestrial positions of stars will be created, and ground-based positions will be performed mainly differentially (relative to the positions of the reference stars measured from space). The accuracy of such ground-based relative astrometry can be rather high and may even approach the accuracy of extraterrestrial positions for the reference stars. As an example we mention some ground-based interferometric programs, currently being planned to perform relative astrometry in very small fields to the level of 100 microarcseconds (Gubler & Tytler [1998]). According to Kovalevsky (2000) ground-based astrometric observations should concentrate now on small fields and relative motions. Among present-day astrometric tasks, measurements of double stars and positions of minor components of the solar system (moons, asteroids) are mentioned.

To determine the exact positions of celestial objects it is necessary to include all the displacements and motions involved in the reference system. Among these the refraction should be taken into account. By definition, atmospheric refraction, or simply refraction R, is

R =z-z₀, (1)

where z₀ is the apparent zenith distance on the ground, z is the zenith distance that would have been measured if there were no atmosphere.

A real source has a certain spectral energy distribution and the terrestrial atmosphere acts on it like a prism changing the zenith distance of a source. The effect is diminishing from blue to red, and therefore the point source is being transformed into a rainbow. If the light refraction (as a function of wavelength) is known, the exact position of the source may be calculated as the source's light gravity center by convolution of the refraction with the following relevant functions: intrinsic spectral energy distribution caused by interstellar reddening, atmospheric transmission, transmission of the telescope in combination with the quantum efficiency of the detector. The most comprehensive analysis of the problem has been performed by Stone in his two papers (Stone [1984], [1996]). He has applied an approach in defining the refraction with Danjon's formula and Owens ([1967]) refractivities which produces a very good approximation for zenith distances $z_0 \leq 75^{\circ}$. It only requires knowledge of the meteorological conditions at the observing site (ground-based atmospheric temperature, pressure, relative humidity) and the apparent zenith distance of the object being observed. The appropriate analytical expressions are used to calculate $R(\lambda,z$). The published spectral energy distributions of stars of different spectral types and luminosity classes together with the functions just mentioned in the previous paragraph have been applied. It has been found that the calculated dependencies of stellar positions on spectral types agree extremely well with the observations. The color effect is rather small but significant: for example, the refraction changes by about 0.1 arcsec if one goes from spectral type B to M at a zenith distance of $60^{\circ }$. However, one may suspect that this effect should be much larger in case of using detectors with wider spectral sensitivity range (passband). Schildknecht ([1994]) has used a similar approach in calculating refraction but the passband is 4700 - 8800 Å. Thus the respective variation with spectral type (B - M) reaches 0.5 arcsec at the zenith distance of $60^{\circ }$. Schildknecht has not discussed the variations with luminosity class and interstellar reddening.

The recent paper of Gubler & Tytler ([1998]) deals with the refraction calculations based on a more detailed atmospheric model and using a numerical integration by iterations. Some simplified and faster methods have been tried out with the result that they agree well for any reasonable set of atmospheric parameters. In these calculations, the assumption has been made that the star radiates as a blackbody at a temperature equal to the surface temperature of the star. Another simplifying assumption is that atmospheric transmission, filter transparency and detector efficiency are constant values (=1) in the filter bandpass. Authors have discussed how accurately the relevant quantities (ground-level atmospheric temperature, pressure, relative humidity, as well as temperatures of two stars) must be measured to limit the errors in the differential refraction to 10 microarcsec or less per input parameter. The most stringent of these requirements is that the stellar surface temperature should be known accurately ($\sim 100$ K) if the star is cool. Determining the temperatures of stars from their spectral or photometric data is a task of stellar classification. For classification we need a certain information on stellar spectral energy distributions (low resolution spectra or photometric measurements in filters) in order to apply appropriate classification methods (systems) to these data. In general, any spectral feature depends on three basic stellar physical parameters: effective temperature, gravity and metal abundance. Classification methods use available spectral information to assign these values (or some relevant parameters) to a star. A conventional approach is to assign MK spectral types and luminosity classes (or absolute magnitudes); the latter are closely connected with the basic physical parameters. The available calibrations "spectral type versus effective temperature'' and "luminosity class versus gravity'' may be applied to MK data if necessary. Metal abundances are characterized by [Fe/H] values.

As a typical example we mention here the photometric classification method elaborated by Vilnius astronomers (photoelectric measurements in some filters are required). There, stars brighter $14^{\rm m}$ (with a 1 m telescope) are routinely classified (Straizys [1992]). MK spectral types, absolute magnitudes and [Fe/H] values are defined. As to spectral classification methods, Houck ([1994]) performs the Michigan Survey (being completed in 7 volumes by   2004) based on photographic objective prism spectra 2 Å resolution) and providing MK types and luminosity classes (by visual inspection) for many thousands of stars over the sky. Some recent spectral studies provide quantitatively the MK types and luminosity classes based on 10 - 15  Å resolution spectra, diode-array and CCD detectors are being used (Malyuto & Schmidt-Kaler [1997]; Malyuto et al. [1997]; Weaver & Torres-Dodgen [1997]).

In the present paper we analyze the possibility of performing high accuracy refraction measurements with the 10'' LX200 telescope installed at the Lohrmann Observatory in Dresden. The Stone ([1996]) code has been applied to calculate the refraction with the use of the published representative stellar spectral energy distributions of different spectral types and luminosity classes (Sviderskiene [1988]) at different degrees of interstellar reddening; appropriate meteorological parameters, atmospheric transmission, transmission of the telescope in combination with the quantum efficiency of the CCD detector have been involved. We discuss which stellar parameters are useful and how accurate the stellar input and ground-based atmospheric parameters should be to provide accurate calculations for atmospheric refraction. We describe some stellar spectral classification and photometric systems which may provide the necessary accuracies of stellar parameters. Future improvements of the systems are discussed.