Optimized axial support topologies for thin telescope mirrors

Thin and highly flexible telescope mirrors need to be supported carefully to avoid undesirable elastic deformations and a reduction of their optical quality. In this study, a wide variety of support topologies are examined to provide a basic set of optimized point supports for these telescope mirrors. This is carried out for mirrors without a central hole, with circular and annular entrance pupils. Efficient topologies introducing a small amount of zenith-angle-dependent defocusing are also proposed. The number of supporting points ranges between 3 and 36. Optimal forces and locations of point supports are calculated using thin-plate bending theory. Numerical methods include a linear least-squares method for determining the best forces, and a downhill simplex algorithm to optimize the support locations. The robustness of the proposed solutions is tested by simulated annealing. Scaling laws are briefly reviewed, and support efficiencies are given for each optimized topology. Results show that taking into account the central obscuration ratio (annular pupil) and tolerating a homologous (paraboloidal) deformation of the mirror allows an improvement of efficiency of up to 50% over the case of an unobscured pupil where defocus is not permitted. This work includes a study of support efficiencies versus the Poisson's ratio of the mirror material. Wavefront errors are also estimated in the case of a defective cell, to specify tolerances on forces and support locations.