- 2.1 The structure of the beam pattern
- 2.2 Large-scale deformations
- 2.3 Small-scale deformations
- 2.4 The combination of small-scale and large-scale surface deformations

(1) |

We assume in the following that the beam is degraded by phase perturbations
of the wavefront 2(2/) which are primarily due to deformations
of the main reflector surface. For a good quality telescope we may
assume also that the phase perturbations are small compared to the
wavelength so that the resulting beam degradation is the sum of the
individual degradations (see Shifrin 1971; Sect. 2.4). In addition we
assume that the main reflector surface is constructed from a large number of
panels. Large-scale surface deformations, which do not change
significantly over several panel areas or a considerable fraction of the
reflector surface, degrade the diffraction pattern but preserve, in
general, the main beam and sidelobe structure. Small-scale wavefront
deformations, which change significantly over single panel areas or panel
sub-sections, produce the underlying error beams. Surface deformations
which change over distances of wavelengths behave like *rough*
surfaces, and are discussed in optical journals.

Different mathematical formalisms are used to calculate the beam degradation from spatially large-scale and small-scale wavefront deformations.

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

(9) |

(10) |

(11) |

(12) |

The surface of the 30-m reflector consists of 7 rings of panel frames (in total 210) with each frame holding two panels. A panel (average size meter) is attached to its frame by 15 screws, arranged in 5 parallel rows with approximately 1/4 2 m 0.5 m spacing. These support screws were used to adjust the panel contours to an average precision 0.03 mm, as measured in the factory (Baars et al. 1987). From the geometry of the panel support and contour maps of the panel surfaces (Fig. 1) as measured in the factory, we anticipate that the residual deformations of the adjustments have a correlation length of approximately 1/4 length of a panel, so that m and 1/75. The width of the anticipated error beam is 75 (Eqs. (1, 12)).

A panel frame (average size meter) is attached to the backstructure by adjustment screws located at the four frame corners. A panel frame which is misaligned in piston and/or tilt represents a surface area of correlated deformations. The weighted distance between the centers of adjacent panel frames gives the correlation length m so that 1/17. The width of the anticipated error beam is 17 (Eqs. (1, 12)).

For two independent small-scale surface error distributions [_{1}]
and [_{2}], with Gaussian correlation length distributions *L _{1}*
and

(13) |

(14) |

(15) |

(16) |

Following the explanation of Sect. 2.2, additional large-scale deformations cover areas of several panel frames so that their correlation length is, say, 5 . The width of the anticipated error beam is 5 (Eqs. (1, 12)). For large-scale deformations the diffraction pattern of Eq. (16) is replaced by the corresponding low order Zernike polynomial diffraction pattern , for instance a comatic or astigmatic beam.

Copyright The European Southern Observatory (ESO)