An Analytical Determination of the Flexure of the 3·5 m Primary and 1 m Test Mirror of the ESO's New Technology Telescope for Passive Support and Active Control

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Abstract
The active optics control concept of the ESOs 3·5 m New Technology Telescope (NTT) is based on the correction of aberrations by pre-calibrated changes of the axial forces that provide passive astatic support of the primary. The corrected aberrations are the basic orders of spherical aberration, ordinary astigmatism, triangular and quadratic astigmatism, and furthermore, coma up to the fifth order. This paper is concerned with the analytical determination of the force changes necessary, in either certain groups or the entirety of the supports, to produce any one of these aberration modes. The calibration is derived for two meniscus-shaped mirrors, the NTT primary of aspect ratio 1 : 15 and a thin test mirror of 1 m diameter and aspect ratio 1 : 56, designed to prove the control principle. The theoretical approaches used are adapted to the different stress distributions resulting from the different mirror shapes. Realized as flexural Fourier modes, the generated aberrations are orthogonal to each other and therefore exclude operative interference. The deviations from the desired radial laws amount to very few percent at most. Preparatory to this analysis, the paper treats both the passive axial supports and the radial edge support of the primary. A novel solution for the latter restricts the unavoidable flexural coma to low orders that are readily correctable by active control. Wherever possible, the analytical results are compared with related finite-element results obtained by other authors.