2 Method of calculations and data sources

Dr. R. Stone (U.S. Naval Observatory) has kindly sent us the code developed for computing refraction in his SDSS survey (Stone [1984], [1996]). He considers this approach to be very simple (only analytical expressions are used), fast and also very accurate: for zenith distances under $z_0 \leq 65^{\circ}$ the error in the computed refraction is 0.01 arcsec and smaller.

The refraction, really observed at a telescope, is so called mean refraction; it can be calculated by

$$R_{\rm m}(z)={{\int_{\lambda_{{\rm min}}}^{\lambda_{{\rm max}... ...E}(\lambda)A(\lambda,z)L(\lambda)D(\lambda){\rm d} \lambda}},$$ (2)

where $R_{\rm m}(z)$ is the mean refraction at zenith distance z, $R(\lambda,z)$ is the selective refraction for monochromatic light at wavelength $\lambda$; $S(\lambda)$ is the spectral energy distribution for a star being observed; $E(\lambda)$ is the transmittance of interstellar matter for the color excess E(B-V); $A(\lambda,z)$ is the transmission of the atmosphere; $L(\lambda)$ is the transmission of the telescope optics; $D(\lambda)$ is the quantum efficiency of the detector being used. In the Stone code the mean refraction is computed by integrating numerically the Eq. (2) across the passband with Simpson's Rule. This mean refraction corresponds to the light gravity center of the image of a point source and the approach used is the only correct one, at least for broad passbands (Schildknecht [1994]).

We apply the Stone code to analyse the data which are obtained with the 10'' LX200 telescope installed at the Lohrmann Observatory in Dresden. The transmission curve of the telescope optics and the quantum efficiency of the CCD detector (KAF-1600 device) have been received from manufacturers. No filters are installed. The empirical curve of the transmission of the atmosphere taken by Stone from Palomar has been replaced by the typical transmission function of the Earth's atmosphere at the zenith, given in the Straizys's monograph (Straizys [1992]).

We use the more recent, compared to Stone ([1984], [1996]), stellar spectral energy distributions for selected spectral types from O to M as well as for different luminosity classes from I to V, as given by Sviderskiene ([1988]). These tabulations have been commented by Pickles ([1998]): "its scope, consistency and accuracy of energy distribution make it an ideal check on all other input spectra for flux calibration and accuracy''. To calculate interstellar absorption as a function of a wavelength $\lambda$, we use the same approach as in the Stone code (based on the extinction law, tabulated by Allen [1966]).