4 The current surface accuracy

We have presented in detail the data taken before July 1997 since this complete set of multi-wavelength Moon scans (Fig. 3) and corresponding beam parameters (Fig. 5) illustrate that a consistent theory exists to describe the beam degradation from several surface error distributions. In this theory it is possible to anticipate the structure of the beam pattern and the number of beam components from details of the reflector surface construction. Although it may be possible to approximate the measurements by some other analytic function than Eqs. (10, 16), the decomposition used here is consistent with proven concepts of the antenna tolerance theory and with the surface structure of the 30-m reflector. We believe that the use of a priori knowledge of the beam structure allows the derivation of meaningful parameters of the error beams, in particular of very extended low level error beams which are difficult to measure with high precision. We believe also that the predictability of the beam structure from details of the reflector construction allows a meaningful estimate of the influence of surface improvements, as done in the following.

It is evident from the 30-m reflector construction that the correlation lengths $L_{\rm p}$ (panels, 3rd EB) and $L_{\rm a}$ (panel frames, 2nd EB) are fixed quantities, hence also the widths $\theta$$_{\rm e,p}$ and $\theta$$_{\rm e,a}$ of the corresponding error beams. Since only panel frames can be adjusted, only the associated rms-value $\sigma$$_{\rm a}$ may change, leading to the improved value $\sigma$$_{\rm a}^{*}$. The associated change of the power amplitude $a_{{\rm e},a}$ (Eq. (11), Fig. 5) of the corresponding 2nd error beam is

$$a_{\rm e,a}^{*}/a_{\rm e,a} = [1 - {\rm exp}(-\sigma_{\rm \varphi,a}^{*~2})]\,/\,[1 - {\exp}(-\sigma_{\varphi,\rm a}^{2})].$$ (22)

Approximately 80% of the power removed by the surface adjustment from the error beam appears as an increase in power of the diffracted main beam, the remaining $\sim\!20\%$ appear in the sidelobe pattern (see Born $\&$ Wolf 1980).

A holography measurement (Morris et al. 1997) has shown that the panel frame adjustment of July 1997 has improved the illumination weighted reflector surface accuracy from $\sigma_{\rm T}= 0.075 - 0.085$ mm to $\sigma ^{*}_{\rm T} = 0.065 - 0.075$ mm. This general improvement is due to a reduction of the panel frame rms-value from $\sigma _{\rm a,T}$$\approx$ 0.07 mm to $\sigma$$^{*}_{\rm a,T}$ $\approx$ 0.055 mm. Using Eq. (22), the associated reduction of the power amplitude of the 2nd error beam is $a^{*}_{\rm e,a}$ $\equiv$ $a^{*}_{\rm e,2}$ $\approx$ 0.6$a_{{\rm e},a}$.

  

Figure 7: Composite profiles $f_{\rm M}(u)$ which illustrate the improvement of the reflector surface accuracy; measurements before July 1997 (24 Dec. 1994): open circles, after July 1997 (19 Nov. 1997): solid dots

In addition to the holography measurements, we confirmed the improvement of the reflector surface precision from a measurement of the beam pattern and of the aperture efficiency at 0.86 mm (350 GHz):

- at the lunar age of 21.3 days ($\sim$ Last Quarter, 19 Nov. 1997) we obtained with the improved reflector a scan across the Moon at 2 mm wavelength, and constructed from this the composite profile shown in Fig. 7. From an earlier observation we constructed a composite profile for the lunar age of 19.6 days (24 Dec. 1994), also shown in Fig. 7. The observations are sufficiently close in phase to allow a comparison of both profiles (see the Appendix). The improvement of the reflector surface is evident in Fig. 7 as a reduction of the error beam.

- we derived in 1994 and 1998 the aperture efficiency at 0.86 mm (350 GHz) from measurements of the planets, using the same SIS receiver (see Table  2). The measured increase of the aperture efficiency from $\sim\!12\%$ to $\sim\!16\%$ (Table 2) agrees with the improvement of the reflector surface.

Using these data, we proceeded in the following way to arrive at representative parameters of the telescope performance for the time after the July 1997 surface adjustment:

(1) we use the values $\theta$$_{\rm e}$ and $a_{\rm e}$ derived from the multi-wavelength set of Moon scans (Fig. 5), but update the values $a_{\rm e,2} = a_{\rm e,a}$ (panel frames, 2nd EB) by application of Eq. (22) as explained above. In Eq. (22) we use the values $\sigma$$_{\rm a,T}$ = 0.070 mm and $\sigma$$_{\rm a,T}^{*}$ = 0.055 mm based on the earlier and recent holography measurements (see footnote 9).

(2) we use the holography measurement of the reflector surface precision ($\sigma$$_{\rm T}^{*}$) and of the 350 GHz aperture efficiency to update the earlier efficiency data compiled by Kramer (1997) from a large set of observations, as not yet available for the improved reflector.

The current beam parameters are shown in Fig. 5 and are given in Table 1; the current efficiencies are given in Table 2.