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2 The gain-elevation dependence G($\epsilon$,$\epsilon$0)

Following Ruze's (1966) antenna tolerance theory, the normalized elevation-dependent on-axis antenna gain of the reflector optimized at $\epsilon$0 is
{G}({\epsilon},{\epsilon}_0) =
{\rm exp}[-(4{\pi}{R}{\sigma}_{\rm g}({\epsilon})/{\lambda})^{2}]\end{displaymath} (3)
where the factor R ($\approx 0.8 - 0.9$) takes into account the steepness of the reflector and the illumination taper of the receiver so that R$\sigma$$_{\rm g}$ is the radio-effective surface deformation (Greve & Hooghoudt 1981). The function G($\epsilon$,$\epsilon$0) depends exclusively on the construction-specific values $\sigma$$_{\rm g}$($\epsilon$)which do not change with time and surface adjustment. The homology-corrected telescope-independent flux [S] of a source is obtained from its calibrated flux [S'($\epsilon$)] measured at the elevation $\epsilon$ by application of the correction G-1($\epsilon$,$\epsilon$0) so that[*]
{S} = {S}'({\epsilon})\ {G}^{-1}({\epsilon}, {\epsilon}_0).\end{displaymath} (4)
The literature does not provide explicit information how to deal with extended sources. We will show that for the specific case of the IRAM 30-m telescope, the on-axis gain-elevation dependence $G(\epsilon$,$\epsilon$0) holds also for extended sources not exceeding in diameter approximately two half-power beamwidths (i.e. $\theta_{\rm S}$ $\mathrel{\mathchoice {\vcenter{\offinterlineskip\halign{\hfil
$\displaystyle ... 2$\theta$$_{\rm b}$); a weaker gain-elevation dependence applies for more extended sources (i.e. 2$\theta$$_{\rm b}$ < $\theta$$_{\rm S}$). The half-power beamwidth (FWHP) of the 30-m telescope is $\theta$$_{\rm b}$ = 1.16$\lambda/D$ [rad], with $\lambda$ the wavelength of observation and D the diameter of the reflector; the relevant beamwidths are given in Table 1. Note that the diameter of the full beam is $\sim$2.4$\theta$$_{\rm b}$.

Table 1: Beamwidth $\theta$$_{\rm b}$ of the 30-m telescope for receivers of $\sim$-13 dB edge taper, and the largest source diameter $\theta$* [planet] suitable for determination of the gain-elevation dependence at the specific wavelength

Wavelength & Frequency & $\theta$$_{\rm b}$\space...
 ... & 350 GHz & 8.3$''$\space & $\sim$15$''$\space & Mars \\  
\hline \end{tabular}

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