OHP Preprint No. 101 : Thin shallow meniscus mirrors

Influence functions of a thin shallow meniscus-shaped mirror

Luc F. A. Arnold

Laboratoire d'Astrophysique Observationnelle, Collège de France and Observatoire de Haute Provence (CNRS) F-04870 Saint-Michel-l'Observatoire, France E-mail: arnold@obs-hp.fr

Applied Optics (in press)

Abstract
Thin shallow spherical shell theory is used to derive the general influence function, due to uniform and/or discrete (actuators) loads, for a thin shallow meniscus-shaped mirror of uniform thickness, with a central hole and supported at discrete points. Small elastic small deformations are considered. No symmetry on the load distribution constrains the model. Explicit analytical expressions of the set of equations are given to calculate the influence functions. Results agree with Finite Element Analysis (FEA) to within 1%. When FEA required megabytes of RAM memory, the analytical method only needed kilobytes and ran typically 30 times faster. This is a crucial advantage for iterative optimization of mirror supports such as large passive or active meniscus-shaped primary mirror supports, or Cassegrain/Gregorian adaptive secondary actuators configurations. References are given that estimate the shear effects (thick mirror), the thickness variation effect and the influence of the size of the support pads.

Keywords : Telescope mirrors, mirror deformations, active optics, influence functions, meniscus-shaped mirrors.

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