1 Introduction

The IRAM 30-m telescope (Baars et al. 1987, 1994) is a homologous construction (von Hoerner 1967a,b) so that for all elevation angles ($\epsilon$) the best-fit reflector surface is a paraboloid. The homology does not eliminate the gravity deformations of the reflector [$\delta$$_{\rm g}$(i,$\epsilon$) for the surface elements i = 1, 2, ..., N]; however, the root mean square (rms) value $\sigma$ of the surface deformations of the best-fit parabolic reflector is

$${\sigma}({\epsilon}) = {\sqrt{{\sum}_{i}{\delta}_{\rm g}(i,... ... {\lambda}_{\rm min}/15\ \ {\rm to}\ \ {\lambda}_{\rm min}/20$$ (1)

for all elevation angles (0$\hbox{$^\circ$}$ $\leq$ $\epsilon$ $\leq$ 90$\hbox{$^\circ$}$) and wavelengths $\lambda$$_{\rm min}$ $\leq$ $\lambda$, with $\lambda$$_{\rm min}$the shortest wavelength of observation of the telescope. If at the elevation angle $\epsilon$₀ the special adjustments -$\delta$$_{\rm g}$(i,$\epsilon$₀) are applied on the reflector surface, then (von Hoerner & Wong 1975) the reflector is free of gravity deformations at $\epsilon$₀ (= 43$\hbox{$^\circ$}$ for the 30-m telescope) and the rms-value of the residual surface deformations is

$${\sigma}_{\rm g}({\epsilon}) = {\sqrt{ {\sigma}(0)^{2}[{\rm ... ...ma}(90)^{2}[{\rm sin}{\epsilon} - {\rm sin}{\epsilon}_0]^{2}} }$$ (2)

with $\sigma$$_{\rm g}$($\epsilon$₀) = 0, and $\sigma$(0) and $\sigma$(90) (see below) the gravity induced deformations at horizon ($\epsilon$ = 0$\hbox{$^\circ$}$) and zenith ($\epsilon$ = 90$\hbox{$^\circ$}$). The elevation-dependent surface deformations $\sigma$$_{\rm g}$($\epsilon$) introduce an elevation-dependent loss of gain for which astronomical observations must be corrected. The rms-values $\sigma$$_{\rm g}$($\epsilon$) are derived from finite element (FE) calculations of the reflector backstructure or from radiometric measurements of astronomical sources. We use both methods and explain, in particular, the gain-elevation dependence as function of the source diameter ($\theta_{\rm S}$). We provide information how to correct observations made with the 30-m telescope. (See Baars et al. (1987) for an earlier emphasis that a gain-elevation must be applied, at least at short wavelength.)