We exclude small-scale periodic deformations which act like gratings (for instance warped panels, regular surface ripples from machining, etc.), although such deformations occasionally do occur. The grating theory of a paneled reflector surface is not available; however, some special investigations have been published (Cortes-Medellin $\&$ Goldsmith 1994; Hills $\&$ Richer 1992; Harris et al. 1997).

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The values $\sigma$ and $C_{\delta}$ can also be calculated for large-scale deformations, however, they do not always contain a physical meaning as for small-scale random deformations (Greve 1980).

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...that

Shifrin (1971) analyzes also the exponential correlation length distribution; however, arguments are given that the Gaussian correlation length distribution represents the more realistic case.

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...length

L = 2c, with c the correlation radius (Ruze 1966; Baars 1973).

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...1970a)

The term $\cal F$ $_{\rm c}$ ( $\theta$ ) of Eq. (10) was first derived by Väisälä (1922) to quantify the precision of optical surfaces. The term was re-discovered by Marechal (1947), Scheffler (1962), Ruze (1966), Robieux (1966), and others, however, with the understanding of being valid only in the case of an uncorrelated error distribution (L = 0). Nevertheless, this term is frequently used in efficiency calculations although, apriori, being correct only in case of uncorrelated errors (see Sect. 3.5).

The derivation of the beam pattern Eq. (8) is valid for a shallow reflector as used in optical telescopes. However, Eq. (10) can also be used for a steep radio reflector in case the appropriate diffraction pattern $\cal A$ $_{\rm T}$ is used (see Sect. 5).

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...reflector

The subreflector of the 30-m Cassegrain telescope and the Nasmyth mirrors may have additional surface errors. However, in general, these mirrors are more precise than the main reflector, and thus may be neglected (see Rush $\&$ Wohlleben 1982).

For other reflectors with several error distributions see, for instance, the Itapetinga 14-m telescope (Kaufmann et al. 1987) and the JCMT 15-m telescope (Hills $\&$ Richer 1992; Prestage 1993).

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...intensity

Except the measurements at 1.3 mm wavelength (Fig. 3) made with a noisier receiver.

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...structure

For instance, differential thermal dilatations of the subreflector support produce a shift of the subreflector and by this a focus offset and a slightly comatic beam. In a rigorous way, these displacements produce a deformation of the wavefront, and are not main reflector errors.

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...improved

The rms-values before July 1997 are (in mm): $\sigma$ ₁ $\approx 0.03 - 0.06$ , $\sigma$ $_{\rm a}$ $\approx$ 0.07, $\sigma$ $_{\rm p}$ $\approx$ 0.055 so that $\sigma$ $_{\rm T}$ = R $\sigma$ = 0.075 - 0.085; after July 1997 they are: $\sigma$ ₁ $\approx$ 0.03 - 0.06, $\sigma$ $_{\rm a}$ $\approx$ $\sigma$ $_{\rm p}$ $\approx$ 0.055 so that $\sigma$ $_{\rm T}$ = R $\sigma$ = 0.065- 0.075 (see Table 1).

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