Error Budget Calculation OFFRE XXXX Design, Manufacture, Transport and Integration on-site in Chile of ALMA Antennas Error Budget Calculation PM#07- 13-14 September 2006

Pointing Error - Approach OFFRE XXXX Error Budget Calculation without metrology correction: Pointing Error Pointing Error - Approach Geometrical ray tracing, by means of CODE-V, is used to calculate pointing error. Diffraction is taken into account to determinate energy centroid. The displacements of the nodes representing the optical elements of the antenna and the rotations of the frames associated to them are determined by thermo-elastic analysis. Displacements and rotations are applied in the CODEV model and results are shown. The optical model treats the main reflector as a rigid body, but its translations/rotations introduced in CODE-V are derived from the parabolic best fit of the deformed surface of the paraboloid computed with FEM analysis (Levy’s procedure).

Pointing Error – Wind component OFFRE XXXX Error Budget Calculation without metrology correction: Pointing Error Pointing Error – Wind component

Pointing Error – Weighted wind component OFFRE XXXX Error Budget Calculation without metrology correction: Pointing Error Pointing Error – Weighted wind component RMS errors are compared with EIE’s output

Error Budget Calculation without metrology correction: Pointing Error OFFRE XXXX Error Budget Calculation without metrology correction: Pointing Error Ray Tracing approach – code V Analytical approach- Ruze equations RMS errors are compared with EIE’s output

The above RMS errors are compare with those obtained by EIE OFFRE XXXX Error Budget Calculation without metrology correction: Pointing Error The above RMS errors are compare with those obtained by EIE Differences between EIE and AAS-I are < 1% (0.17%!) Complete convergence is being checked for all the remaining budgets Some details of the FEM model require fine adjustments