6 The current efficiencies

The current efficiencies given in Table 2 are primarily based on the measured illumination weighted rms-value $\sigma$$_{\rm T}^{*}$. The aperture efficiency $\epsilon$$_{\rm ap}$ and the beam efficiency $B_{\rm eff}$ are related by $B_{\rm eff}$ = 0.8899[$\theta$$_{\rm b}$/($\lambda /D)]^{2}$$\epsilon$$_{\rm ap}$ $\approx$ 1.20$\epsilon$$_{\rm ap}$ (Downes 1989), when assuming a Gaussian main beam and using relation (1).

The relative power P($\Omega$) received in the on-axis solid angle $\Omega$ of opening $\theta$$_{\rm s}$ is

$$P({\Omega}) = {\sum}_{i=0,3}{\int}_{0}^{{\Omega}}{\cal F}_{ ... ...,3}{\int}_{0}^{4{\pi}}{\cal F}_{ i}({\Omega}') {\rm d}{\Omega}'$$ (24)

In Eq. (24), $\cal F$₀ is the diffracted beam $\cal A$$_{\rm T}$ and $\cal F$ _i (i = 1, 2, 3) are the error beams. When using the diffracted Gaussian main beam $\cal G$$_{\rm T}$ we obtain for P($\Omega$)= P($\theta$$_{\rm s}$/2) the relation

$${ P}({\Omega})\!\! =\!\! {\sum}_{ i=0,3}\! { a}_{ i}{\Theta}... .../ \! {\Theta}_{ i}]^{2})]\,/\,{\sum}{ a}_{ i}{\Theta}_{ i}^{2}.$$ (25)

The function P($\Omega$), based on the parameters of Table 1 and Table 2, is shown in Fig. 9 for $\lambda$ = 3 mm, 2 mm, and 1.3 mm. In particular, the beam efficiency is $B_{\rm eff}$ = P($\Omega$$_{\rm fb}$) with $\Omega$$_{\rm fb}$ the solid angle of the full beam of diameter $\theta$$_{\rm fb}$ as given in Table 2.

  

Table 2: Efficiency parameters of the IRAM 30-m telescope (after July 1997)

Update from the values compiled by Kramer (1997). The entries of the Table are: $\theta$$_{\rm b}$: beam width (FWHP) (measured); $\theta$$_{\rm fb}$: full width (to first minimum), $\theta$$_{\rm fb}$ $\approx$ 2.4$\theta$$_{\rm b}$(calculated); $\epsilon$$_{\rm ap}$: aperture efficiency (measured $\&$ calculated from $\sigma$$_{\rm T}^{*}$); $B_{\rm eff}$: main beam efficiency, $B_{\rm eff}$ $\approx$ 1.20$\epsilon$$_{\rm ap}$;$F_{\rm eff}$: forward efficiency (from sky dips), $\epsilon$$_{\rm M}$:Moon efficiency (measured); $S/T_{\rm A}^{*}$ = (2k/A)$F_{\rm eff}$/$\epsilon$$_{\rm ap}$ = 3.906$F_{\rm eff}$/$\epsilon$$_{\rm ap}$: antenna gain (calculated $\&$measured). P₁ - P₃: relative power of the error beams (calculated). The accuracy of the values is $\sim$$\pm$ 5$\%$. The entries of P₁ illustrate the partially transient nature of this error beam. In brackets are given the widths (FWHP) of the corresponding error beams. * Not frequently used frequency and somewhat poorly known telescope performance. The values valid before July 1997 are published by Kramer (1997) and are found in the 30-m Telescope Manual (Wild).

  

Figure 9: Relative power P($\Omega$) (Eq. (24)) received in the solid angle $\Omega$ of opening $\theta$$_{\rm s}$ given in fractions of the full beam width $\theta$$_{\rm fb}$ (Table 2). P($\Omega$) at $\theta$$_{\rm s}$/$\theta$$_{\rm fb}$ = 1 is the beam efficiency $B_{\rm eff}$; the normalization of the curves is made to these values given in Table 2. The values are shown for $\theta$$_{\rm s}$ 1000 - 1400'', i.e. the extent of the profile measurements where also $F_{\rm eff}$ $\approx$ $\epsilon$$_{\rm M}$ (Table 2). The remaining energy for larger angles $\theta$$_{\rm s}$ is mainly in the backward beam and is of the order $1 - F_{\rm eff}$

For observations of extended sources it is important to know the fraction of the power contained in the diffracted beam and the error beams. The integrated relative power P _i of the beam component [i] is

$$P_{ i} = {\int}_{0}^{4\,{\pi}}{\cal F}_{ i}({\Omega}){\rm d}... ...0,3}{\int}_{0}^{4\,{\pi}}{\cal F}_{ i}({\Omega}){\rm d}{\Omega}$$ (26)

or when using the diffracted Gaussian main beam $\cal G$$_{\rm T}$ we obtain

$${ P}_{ i} = { a}_{ i}{\Theta}_{ i}^{2}\,/\,{\sum}{ a}_{ i} {\Theta}_{ i}^{2}.$$ (27)

Table 2 gives the values P _i (i = 1, 2, 3) calculated from Eq. (27) and the parameters of Table 1. The total power contained in the error beams is $P_{\rm e} = \sum P_{ i}$.

From the calibrated scans taken at New Moon (Fig. 10a) and the temperature of the New Moon published by Fedoseev $\&$ Chernyshev (1998) we derived the Moon efficiency $\epsilon$$_{\rm M}$ of which the values are given in Table 2. The similarity of the values of the measured forward efficiency ($F_{\rm eff}$, Table 2) and of the Moon efficiency says that the forward beam has approximately the size of the Moon's disk. The similarity of the values also says that the calculated beam pattern should not be used beyond the off-axis distance of $\sim$700 - 900'', a fact we respected in Fig. 8 and Fig. 9. It is evident that caution is required when using Eq. (24)-Eq. (27) which imply integrations over the full extent of the beam. The accuracy of the values P($\Omega$) and P_i (Fig. 9, Table 2) is a few percent.