| Abstract
| - Context. Adaptive secondary mirrors (ASM) are, or will be, key components on all modern telescopes, providing improved seeing conditions or diffraction limited images, thanks to the high-order atmospheric turbulence correction obtained by controlling the shape of a thin mirror. Their development is a key milestone towards future extremely large telescopes (ELT) where this technology is mandatory for successful observations. Aims. The key point of actual adaptive secondaries technology is the thin glass mirror that acts as a deformable membrane, often aspheric. On 6 m − 8 m class telescopes, these are typically 1 m-class with a 2 mm thickness. The optical quality of this shell must be sufficiently good not to degrade the correction, meaning that high spatial frequency errors must be avoided. The innovative method presented here aims at generating aspherical shapes by elastic bending to reach high optical qualities. Methods. This method is called stress polishing and allows generating aspherical optics of a large amplitude with a simple spherical polishing with a full sized lap applied on a warped blank. The main advantage of this technique is the smooth optical quality obtained, free of high spatial frequency ripples as they are classically caused by subaperture toolmarks. After describing the manufacturing process we developed, our analytical calculations lead to a preliminary definition of the geometry of the blank, which allows a precise bending of the substrate. The finite element analysis (FEA) can be performed to refine this geometry by using an iterative method with a criterion based on the power spectral density of the displacement map of the optical surface. Results. Considering the specific case of the Very Large Telescope (VLT) deformable secondary mirror (DSM), extensive FEA were performed for the optimisation of the geometry. Results are showing that the warping will not introduce surface errors higher than 0.3 nm rms on the minimal spatial scale considered on the mirror. Simulations of the flattening operation of the shell also demonstrate that the actuators system is able to correct manufacturing surface errors coming from the warping of the blank with a residual error lower than 8 nm rms.
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