3 Data reduction

The data reduction is similar to the one described in Teräsranta et al. (1992), although the upgrading of the antenna lead to changes in some parameters. The flux-calculating procedure is done with Eqs. (1) to (5). The error estimate for the flux is from Eq. (6), where the relative errors of the optical depth, noise tube calibration and flux integreation have been quadratically added.

$$S = K_1 K_2 K_3 \frac{U}{U_{\mathrm{cal}}} {\rm e}^{\frac{\tau}{\sin(el)}}\\ end{displaymath}$$ (1)

$$K_2 = \frac{1}{(1-K_4(P-P_{\rm opt})^{2})}\$$ (2)

$$P_{\rm opt} = P_0 - K_{5} \sin(el) - K_6 T\\ end{displaymath}$$ (3)

$$K_3 = 1 + ( \theta{ / HPBW )}^2$, for Gaussian sources$\\ end{displaymath}$$ (4)

$$K_3 = (\theta{/ 0.6 / HPBW )}^2 / ( 1 - {\rm e}^{-(\theta{/ 0.6/ HPBW)^{2})}}$, $\\ end{displaymath}$$ (5)

for planets

$$\delta{}S = S \sqrt{(\delta{U} / U)^2 + (\delta\tau{ /\sin(el)})^2 + (\delta{Cal} / Ucal)^2)}.$$ (6)

In the formulae,

$$\begin{array} {lp{0.8\linewidth}} S & the flux density in Jy... ...elta{Cal} & the error of the noise tube calibration.\end{array}$$

The optimal position of the antenna focus is a function of the elevation angle and temperature according to Eq. (3). Two fixed positions for the focus were used, one for the summer and one for the winter. This kept the correction factor $K_\mathrm{2}$ still quite small at the used elevation range from 20 to 70 degrees. As the corrections for the focus-offset are larger at higher frequencies, the results at 87 GHz are more severely affected. In Table 2. the values of the parameters $K_\mathrm{4}$ and $K_\mathrm{5}$ are tabulated at each observing frequency with the old (before summer 1994) and new antenna (after summer 1994). The parameter $K_\mathrm{6}$ was the same 0.0025 with both antennas.

 

Table 2: Parameters K₄ and K₅ with the old and new antenna