5 The current beam pattern

Figure 8 shows the current beam pattern at 3.4 mm, 2.0 mm, and 1.3 mm wavelength calculated from Eq. (16) and the values of Table 1. The values of Table 1, the curves of Fig. 5, and Eqs. (11, 12) can be used to derive the parameters of the beam pattern for other wavelengths than the reported measurements.

  

Figure 8: IRAM 30-m telescope current beam pattern calculated from Eq. (16) and the parameters of Table 1. The heavy lines show the case of a Gaussian approximation of the main beam (Eq. (23)). The accuracy of the profiles is $\sim$$\pm$ 1 dB beyond the main beam area. The beam patterns are shown on logarithmic scale (dB). For each wavelength the profile is normalized to 1/2 width of the full beam $\theta$$_{\rm fb}$(see Table 2)

The calculation of the beam pattern requires a knowledge of the diffraction pattern $\cal A$$_{\rm T}$. Without entering into lengthy calculations (see Minnett $\&$ Thomas 1968; Goldsmith 1987), the diffraction pattern of the 30-m telescope is obtained with sufficient accuracy, when compared to measurements, from the approximation $\cal A$$_{\rm T}(u)$ = $\alpha (u){\cal A}(u)$, with ${\cal A}(u) = [J_{1}(u)/u]^{2}$ calculated from the expressions given by Abramowitz $\&$ Stegun (1972) and the reduction factor $\alpha (u) = 0.12$, 0.22, 0.27 for the 1st, 2nd, and 3rd sidelobe. In this calculation the beam width (FWHP) of the Airy pattern ${\cal A}(u)$ is $\theta$$_{\rm b}$ (Table 1) at u = 1.62. As evident from Fig. 8, at the level of the 3rd sidelobe the diffraction pattern and the error pattern have similar intensities. The sidelobe structure and the error beam seen in Fig. 8 are not observed in regular pointing scans made with the 30-m telescope because the sensitivity of the procedure is only -10 dB to -15 dB. The sidelobe structure is also not seen in the composite Moon scans (Figs. 3, 4) since this detail is lost in the convolution (Eq. (18)).

In many applications the diffracted beam $\cal A$$_{\rm T}$ is approximated by a Gaussian main beam without sidelobes

$${\cal A}_{\rm T}\ {\approx}\ {\cal G}_{\rm T} = {\rm exp}[-({\theta}\,/\, {\Theta})^{2}]$$ (23)

with $\Theta$ = $\theta$$_{\rm b}$/(2$\sqrt{ln\,2}$) = 0.60$\theta$$_{\rm b}$. Figure 8 shows also the approximated Gaussian main beams.